Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Dynamic social structuring in cellular self-organizing systems
(USC Thesis Other)
Dynamic social structuring in cellular self-organizing systems
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
University of Southern California Department of Aerospace And Mechanical Engineering Dynamic Social Structuring in Cellular Self-Organizing Systems by Newsha Khani A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL In Partial Fulfillment of the Requirement for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) May 2015 Copyright 2015 Newsha Khani ii Acknowledgment I would like to express my deep and sincere gratitude and appreciation to my advisor, Prof Yan Jin, for this opportunity and all the time he has given me throughout my Ph.D. program. His perpetual enthusiasm, excellent insight in science and engineering, management skills, patience and guidance provided me with a learning environment to grow personally as well as professionally. I wish to extend my warmest thanks to the professors who served on my committees, Prof. Henryk Flashner, Prof. Geoff Shiflett and Prof. Najmedin Meshkati for their help and valuable feedback. Also, I would like to thank USC Department of Mechanical engineering advisers, Samantha Graves and Silvana Martinez-Vargas, who were very supportive and extremely helpful. I would also like to acknowledge the contributions of my great research colleagues in the IMPACT Lab for their support, in particular, James Humann and Jonathan Sauder for their friendship and various helpful suggestions throughout my PhD life; I would especially like to thank James Humann for his kindness and generosity with his effort and time to help proofread my entire dissertation and Yue Zhou for her great help in generating simulation results. Finally my sincerest gratitude to my parents, Minoo Abolhassani and Bahman Khani for their endless supporter and courage every step of the way; and to my aunt, my best friend and great source of inspiration, Mojgan Abolhassani, for her incredible influence giving me a better perspective towards life. iii Table of Content Acknowledgment ii List of Figures vi List of Tables x List of Equations xi Abstract xii 1 Introduction 1 1.1 Background 1 1.1.1 Limitations of Current Design Approaches 1 1.1.2 A Naturalistic Approach 3 1.1.3 CSO Systems 4 1.2 Research Questions 8 1.3 Research Objective and Approach 10 1.4 Thesis Organization 11 2 Related Work 13 2.1 Introduction 13 2.2 Engineering Design and Methodology 14 2.2.1 Systematic Design 15 2.2.2 Axiomatic Design 16 2.2.3 General Design Theory 17 2.2.4 Conclusion: classical design methodology versus complex systems 18 2.3 Transition from Conventional design to adaptive design 18 2.3.1 Multi-agent System 19 2.3.2 Coordination in Multi-agent System 21 2.3.3 Complexity Theory, Self Organizing Systems and Self Organizing Criticality 24 2.4 Organization Science 28 2.4.1 Contingency Theory 28 2.4.2 Task environment and adaption of organization structure 31 2.4.3 Task Interdependency and Coordination Policy 32 3 The Need for a New Approach 35 iv 3.1 Introduction 35 3.2 Limitations in previous CSO Systems 36 3.2.1 Modeling Limitations 40 3.2.2 Performance Limitations 41 3.3 Basic Approach 43 3.4 Structure necessity 46 3.4.1 Organizational Research 46 3.4.2 Hierarchy in Complex Systems 48 3.4.3 Structure in a Real Complex Network 49 3.4.4 Structure in Natural Evolution 50 4 Dynamic Social Structuring in a Cellular Self-‐Organizing System 51 4.1 Key Terms and Definitions 53 4.1.1 Task Definition 53 4.1.2 Task Field 54 4.1.3 Task Complexity 57 4.2 mCell Description 63 4.2.1 Individual Cell Model 64 4.2.2 Satisfaction 69 4.2.3 Social Rule 71 4.2.4 Social Rule Based Regulator 73 4.2.5 Adoption Rate 77 4.2.6 Dynamic Process Information 78 4.2.7 Emergent Structures 79 5 Case Study 81 5.1 Problem Statement 82 5.2 Problem Approach and Dynamic Social Structuring 83 5.2.1 Task 83 5.2.2 Task Field 88 5.2.3 Individual Satisfaction 90 5.2.4 Social Rules and Social Field 91 5.2.5 Social Rule Based regulator 92 5.3 Simulation 94 5.3.1 Simulation Environment 95 v 5.3.2 Simulation Assumptions 96 5.4 Simulation Results 97 5.4.1 Strong Social Rule Results 98 5.4.2 Weak Social Rule Result 114 5.5 Comparison of Strong Social and Weak Social 123 5.5.1 Level-1 Task 123 5.5.2 Level-2 Task 124 5.5.3 Level-3 Task 126 5.6 Discussion and Conclusions 128 5.7 Hypothesis Revisit 131 6 Contributions and Future Directions 132 6.1 Contributions 132 6.2 Future Work 136 7 References 138 vi List of Figures Figure 1: Form-based approach (Zouein, Chen, and Jin 2010): forming spider and snake forms by mCells. ....................................................................................................... 5 Figure 2: A Behavior regulation based approach to CSO (Chen, 2012). ........................... 7 Figure 3: A Meta ‐Interaction Model Approach to CSO (Chiang and Jin 2011) .............. 7 Figure 4: Points of Departure ............................................................................................ 14 Figure 5: Hypothetical system complexity over order-disorder spectrum Order ............. 44 Figure 6: Hierarchic in structure ....................................................................................... 48 Figure 7: Structure in chemical systems ........................................................................... 50 Figure 10: Activity Diagram for case study ...................................................................... 84 Figure 11: Activity Diagram in right: Chen’s (Jin and Chen 2013); left: Chiang’s (Chiang and Jin 2011). ...................................................................................... 87 Figure 12: Illustration of Task Field ................................................................................. 89 Figure 13: Field generated to reach the box ...................................................................... 90 Figure 15: Social Field representation with agent j in a lower field sending information to the possible existing agents in comparable conflict zones ........................ 94 Figure 16: Six regions around the box; agents send information about the region they belong to .................................................................................................................... 97 Figure 17: Screenshots of a simulation of 25 runs for level-1 task, strong social and 12 agents setting. ............................................................................................................. 100 Figure 18: Effort and time duration comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents .............. 101 Figure 19: Social complexity during the process of moving box towards goal with strong social strategy and 12 agents ................................................................................ 102 Figure 20: Effort comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents ............................................... 103 Figure 21: Duration time comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents ......................... 103 Figure 22: Screenshots of a simulation of 25 runs for level-2 task, strong social and 9 agents setting. ............................................................................................................... 104 vii Figure 23: Success rate comparison for social (SRBR) and non-social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents 105 Figure 24: Effort and duration time comparison for social (SRBR) and non-social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents .......................................................................................................................... 107 Figure 25: Success rate comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents ................................................................................................ 107 Figure 26: Effort comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + one obs” situation with a varying number of agents ............................................................................................................. 108 Figure 27: Duration time comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents ............................................................................................................. 109 Figure 28: Screenshots of a simulation of 25 runs for level-3 task, strong social and 9 agents setting. ............................................................................................................... 110 Figure 29: Success rate comparison for social (SRBR) and non-social (FBR) strategies for the “with wall+ two obs” situation with varying number of agents .......... 110 Figure 30: Effort and time duration comparison for social (SRBR) and non-social (FBR) strategies for the “with wall+ two obs” situation with varying number of agents .............................................................................................................................. 111 Figure 31: Effort per agent comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ............................................................................................................. 112 Figure 32: Duration time comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ............................................................................................................. 113 Figure 33: Success rate comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ............................................................................................................. 113 Figure 34: Duration time and effort comparison for weak social (SRBR) and viii non-social (FBR) strategies for the “with wall” situation with varying number of agents .............................................................................................................................. 115 Figure 35: Effort per agent comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall” situation with varying number of agents .......................................................................................................................... 115 Figure 36: Duration time comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall” situation with varying number of agents .......................................................................................................................... 116 Figure 37: Success rate comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents ............................................................................................................. 116 Figure 38: Duration time and effort comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall” situation with varying number of agents ................................................................................................ 118 Figure 39: Success rate comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents ................................................................................................ 118 Figure 40: Effort per agent comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents ................................................................................................ 119 Figure 41: Duration time comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents ................................................................................................ 119 Figure 42: Success rate comparison for weak social (SRBR) and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents .............................................................................................................................. 120 Figure 43: Duration time and effort per agent for weak social (SRBR) and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ............................................................................................................. 121 Figure 44: Success rate comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + two obs” situation with ix varying number of agents ................................................................................................ 121 Figure 45: Effort per agent comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ................................................................................................ 122 Figure 46: Duration time comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents ................................................................................................ 122 Figure 47: Percentage improvements of performance of strong social with respect to weak social for level-1 task ........................................................................................ 124 Figure 48: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-1 task. ................................................................... 124 Figure 49: Percentage improvements of performance of strong social with respect to weak social for level-3 task ........................................................................................ 125 Figure 50: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-3 task. ................................................................... 126 Figure 51: Percentage improvements of performance of strong social with respect to weak social for level-3 task. ....................................................................................... 127 Figure 52: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-3 task. ................................................................... 127 x List of Tables Table 1: Characterization of task and organization structure (Scott 1992) ...................... 32 Table 2: Coordination policy for each task interdependency ........................................... 33 Table 3: Limitation in Previous CSO system ................................................................... 40 Table 4: Task Complexity defined by Hackman 1969 ..................................................... 58 Table 5: Task Complexity by (Wood 1986) ..................................................................... 58 Table 6: Task Complexity by (Campbell 1988) ............................................................... 59 Table 7: Complexity measures of various box-moving situations .................................... 86 xi List of Equations Equation 4-1 ...................................................................................................................... 56 Equation 4-2 ...................................................................................................................... 60 Equation 4-3 ...................................................................................................................... 61 Equation 4-4 ...................................................................................................................... 62 Equation 4-5 ...................................................................................................................... 63 Equation 4-6 ...................................................................................................................... 63 Equation 4-7 ...................................................................................................................... 67 Equation 4-8 ...................................................................................................................... 67 Equation 4-9 ...................................................................................................................... 68 Equation 4-10 .................................................................................................................... 68 Equation 4-11 .................................................................................................................... 69 Equation 4-12 .................................................................................................................... 69 Equation 4-13 .................................................................................................................... 72 Equation 4-14 .................................................................................................................... 73 Equation 4-15 .................................................................................................................... 75 Equation 4-16 .................................................................................................................... 75 Equation 4-17 .................................................................................................................... 76 Equation 4-18 .................................................................................................................... 76 Equation 4-19 .................................................................................................................... 76 Equation 4-20 .................................................................................................................... 79 Equation 5-1 ...................................................................................................................... 85 Equation 5-2 ...................................................................................................................... 88 Equation 5-3 ...................................................................................................................... 90 Equation 5-4 ...................................................................................................................... 91 xii Abstract Conventional mechanical systems composed of various modules and parts are often inherently inadequate for dealing with unpredictable changing situations. Taking advantage of the flexibility of multi-agent systems, a cellular self-organizing (CSO) systems approach has been proposed, in which mechanical cells or agents self-organize as the environment and tasks change based on a set of predefined rules. To enable CSO systems to deal with more realistic tasks, a two-field mechanism is introduced to describe task and agent complexities and to investigate how social rules among agents can influence CSO system performance with increasing task complexity. A “by emergence” approach is presented to guide self-organization in the system. Besides allowing agents to follow the attractors of their perceived task fields, the concept of “social structure” is introduced to capture explicit and direct interactions among agents and apply “social rules” to facilitate dynamical social structuring among agents. To further increase the level of order, a decision mechanism is proposed for agents to correlate their actions for better overall system performance. Proper interactions of mCells lead to the emergence of social structures that are closely interrelated with the task specifications. The simulation results of case studies based on the proposed mechanism provide insights into task-driven dynamic structures and their effect on the behavior, and consequently the function, of CSO systems. In order to gain detail understanding and explore interplay between task and social structuring components, I investigated different aspect of social structuring including the impact of the population size, specificity of rules and rule adoption rate on the system performance. 1 1 Introduction 1.1 Background As human endeavor expands into space, deep oceans, and other hazardous environments, the complexity of the engineered systems must increase in order to cope with the complex tasks and changing environments. As the system complexity grows, the risk for catastrophic system failure increases because of the increasing potential of unintended interaction among the sheer number of system components. There is a need for new design that can allow engineered systems to change or adapt themselves in response to the changing tasks and operation environments. 1.1.1 Limitations of Current Design Approaches Engineering design is the process of fulfilling customer needs and requirements. To reach a reasonably good design, the problem should be well defined. In order to find a perfect solution, the designer is required to know complete information about the problem objectives, the performance specification, and all necessary resources to match the defined problem. The design process is conventionally a prolonged and iterative process. Initially a conceptual design must be produced. After that, the design concept should be embodied, analyzed, and evaluated based on some computational or experimental studies. Finally, the optimization process takes place to fine tune the design parameters. This process of design, evaluation and optimization is repeated until the design is acceptable and matches the requirements. 2 This conventional approach to designing complex systems is fundamentally “divide-and-conquer,” in which engineers divide the overall complex functions into smaller ones, often through multiple levels, and then devise solutions for these sub- functions based on the prediction of all possible future situations. During the system design and development process, engineers strive for full understanding and full control of all system components and parts based on their predictions of the future possible task environments. In most, if not all, engineered systems, the physical components are designed for a limited purpose and restricted operation range, beyond which the behaviors are not predictable. While this design approach has been highly successful for systems with limited scope of functionality and in situations where future is predictable, when the tasks become too challenging and systems too complex, it will be very difficult for engineers to fully grasp all details and to have full knowledge of the engineered system. In addition, when the future situations become not fully predictable, the engineered system will not be able to function properly and may encounter catastrophic failure in those situations. A major issue with the current approach to developing complex engineered systems is the unintended interdependencies among the system components which imply uncertainty and unknowns to the engineers, making it difficult for them to guarantee a valid operation range for the system to survive its expected lifecycle. Unintended interactions can cause catastrophic system impacts as changing one component can result in cascading changes in other components. 3 1.1.2 A Naturalistic Approach The “divide-and-conquer” design approach described above has the intention of simplifying the original problem by breaking down functional requirements and investigating every piece and its relations. However, according to the law of the requisite variety (Ashby 1956), if a system is supposed to work properly in an unpredictable complex environment, then the system itself must possess an equal level of complexity. Therefore, instead of trying to reduce complexity and simplify the system, the complexity must be embraced in the system. It is intriguing to consider that the nature "faces" all the uncertainties and unknowns and yet the natural systems are "designed" to live with these uncertainties and unknowns as an inherent part of their capabilities. Studying the processes in nature gives intuition about how these systems function and drawing inspiration from these processes can help humans to solve their objectives (Benyus, 1997). Human design and natural "design" are very distinct from each other: human design is more purpose or function driven and takes a top-down approach to avoid possible complexity problems, while the nature "design" is arguably less purposeful and follows a bottom-up approach by making complexity as a "solution" to deal with the arising uncertainties and unknowns (Ashby, 1956). Biological systems are dynamic system composed of interdependent components that co-evolve and have the potential to take multiple roles (Miller, Job, and Vassilev 2000). The major feature of the biological systems is the involvement of self-organizing and complexity. Use of these two concepts helps engineers to develop more adaptive and more resilient systems. Self-organization within a system brings about adaptability and robustness properties by keeping their functionality despite any perturbations. 4 In this research, a Cellular and Self-Organizing (CSO) approach (Zouein, Chen, and Jin 2010) is applied to building adaptive systems. In this approach, a mechanical system is composed of multiple mechanical cells, which can be either identical (for homogeneous systems) or distinct (for heterogeneous systems). Further, the formation of such systems is based on a set of bottom-up, dynamical and self-organized mechanisms that produce emergent system behavior and function. Unlike rigid design techniques, emergence is not fully deterministic. As emergence is a result of interactions among multiple systems, determining local behaviors to achieve a desired global effect needs exploration. Embracing uncertainty results in an increasing level of complexity of the system that gives it the possibility to function in uncertain complex situations. The research on CSO design approach investigates mechanisms that can make the cellular system self-organize at the local level for specific global functionality. Therefore, a CSO system intends to provide guidance for agents to self-organize for desirable global emergent effects. 1.1.3 CSO Systems The main challenge in the CSO approach is to design a self-organizing system with specific desired system level functions. Allowing agents to choose any action at any time during the execution cannot guarantee the system to emerge to the desired global behaviors and consequently the required functions. Therefore, there is a certain need to guide agents’ actions so that the output of the overall system matches the task requirements. 5 In summary, two key approaches to design CSO systems have been explored (Jin and Chen 2013; Zouein, Chen, and Jin 2010; Zouein, Chen, and Jin 2010; Chiang and Jin 2011), i.e., form-based approach (Zouein, Chen, and Jin 2010) and behavior-based approach (Jin and Chen 2013; Chiang and Jin 2011). Form-based Approach: The form based approach provides changeable but relatively deterministic operation and functionality. The designer constructs a somewhat flexible target configuration and a transformation algorithm provides the process steps to the system in order to obtain the target configuration. Sufficient information, as well as the procedure from beginning to the end, is provided for agents in order to create specified structures. Since the pre-specified but flexible shape is given to the agents, it relies on predetermined structures. As a consequence, self-organizing utilization depends on the predefined variety in shape construction. Figure 1: Form-based approach (Zouein, Chen, and Jin 2010): forming spider and snake forms by mCells. 6 Behavior-based Approach: Contrary to form-based design, where a specific target configuration is the main motivation for agents, in behavior-based design the system behavior is most important. The focus in the behavior-based approach is on the end system behavior, not the specific structure. The final functionality of the system is the result of overall collective behavior of all agents. Relying on predefined structures is not helpful at all times, unless all the possible configurations are known by agents, which could not always be the case. Due to the aforementioned issue, the behavior based approach has shown more adaptability in the long run and is a better example of a self- organizing systems. The main concern in behavior based design is to find the bridge between an individual cell’s behavior and system behavior. Behaviors in CSO systems can be decomposed into two different types of behaviors: Independent: Chen explored cellular systems where the system functionality is a result of the sum of the agents’ pooled independent behaviors (Chen, 2012). Independent behaviors are behaviors where the cell only considers itself and its gathered information from the environment to generate its next action, not other agents’ behaviors. Such a method highlights the 'cellular' in Cellular Self-Organizing systems. 7 Figure 2: A Behavior regulation based approach to CSO (Chen, 2012). Interactive: Chiang focused on the interactive behaviors between the cells. In Interactive Behavioral Based Design (IBD) the local behaviors of each cell are influenced both by the perceived environment and the interaction with other cells within the system. This emphasizes the 'self-organization' of CSO systems. To fulfill the collective functionality, a weighted sum of different behaviors with respect to neighbors defines the behavior of each cell. Figure 3: A Meta‐Interaction Model Approach to CSO (Chiang and Jin 2011) The self-organizing behavior of the current CSO systems is regulated by each mCell transforming the task environment into a task-field in which it finds its “most comfortable place” and moves into it. The task is completed by the collective effort of the mCells making themselves “more comfortable.” Each mCell makes their movement 8 decisions completely based on its own sensed information of the environment, its own transformation algorithm, and its own decisions for action. mCells collectively perform the task by first “discovering” what the task is (where is the “comfortable place”) and then “carrying out” the task (move into the “comfortable place”). This distributed and self-interested approach allows for flexibility to cope with changing tasks, robustness to deal with a changing environment, and resilience to still function with system dismemberment. 1.2 Research Questions The previous CSO systems developed to date can only deal with relative simple tasks, such as pushing a square box around obstacles and flocking in congested places. A task-field based regulation (FBR) approach to self-organization was introduced in these systems. Based on FBR, agents independently sense the task situation, transform the sensed information into task-field, find their “most comfortable place” in the field, and then move to the place. This approach, however, has two basic limitations. First, when the task becomes more complex, both the description and transformation of the task-field become highly complicated, potentially becoming a design hurdle. Second, the current approach does not directly address the interaction between mCells with respect to the task context, leaving the power of mCells’ self-organized structures unutilized. These problems become evident when the box-moving task contains not only “push the box” but also include “rotate the box.” The increased complexity of the task can make the simple FBR based CSO system incapable of completing the task in most cases, even when the field description is fully supplied. 9 This research attempts to advance the current CSO framework by introducing dynamic social structures among agents in order to allow agents to deal with more realistic tasks. The basic ideas are: 1) more realistic tasks are more complex, 2) to deal with the tasks that are more complex, the system must possess sufficient level of complexity (Ashby 1956), 3) introducing social structuring among agents can increase the system complexity, and 4) dynamic social structuring combined with the previous work on task-field can be a promising approach to make CSO systems more practically useful. To explore and validate these ideas, the following questions need to be addressed: • Question1: How can one measure the complexity of tasks and the complexity of CSO systems? Since exploring the mapping between the task complexity and proper system complexity is a major task for this research, the first question is naturally about how to measure them. • Question 2: What are the possible and desirable properties of social structures among agents? Social structuring is considered as a major component of self- organization in this research. One needs to elicit requirements for, and develop models of, social structures and explore their properties. • Question 3: Is it beneficial to impose a social field in addition to task-field and, if so, how the integration of the two should be carried out? The previous CSO research has demonstrated the effectiveness of applying the field concept o task domain and forming “task-field”. It is tempting to introduce the “social-field” and combine the two for guiding self-organizing behavior of the agents. • Question 4: How does dynamical social structuring influence agents’ self- organizing behavior and consequently the overall system performance with respect 10 to tasks of different level of complexities? Exploring the interplay between task complexity and social structuring is a major task for this research and hence this question is a major question. It is of particular interest to explore how different properties or aspects of social structuring impact on overall system behavior in different task settings. 1.3 Research Objective and Approach The primary objective of this research is to build understanding of how dynamical social structuring among agents may impact the effectiveness and efficiency of self-organizing systems in different task situations. A computer simulation based approach is taken to pursue this objective and address the research questions described above. More specifically, the following task objectives were identified for this research. 1. Develop measures for complexity of mechanical tasks. 2. Design task scenarios with variable complexity levels for modeling and simulation studies. 3. Define the concept of social structure and identify possible properties of social structuring among agents. 4. Develop measures of system complexity, social complexity, and dynamic process information. 5. Develop models of individual satisfaction, system satisfaction and social rule to facilitate social structuring. 6. Develop a simulation platform for CSO case studies based on the models and concepts mentioned above. 11 7. Explore relations of interplay among task complexity and various social structure properties. 1.4 Thesis Organization In the rest of the thesis, after the review of related work in Chapter 2, a discussion of the need for a new approach is provided in Chapter 3. In Chapter 4, a dynamic social structuring framework is presented and the case studies based this framework is presented and discussed in Chapter 5. Finally Chapter 6 describes the contributions of this work and points out the future research directions. Following is a brief description of each chapter. Chapter 2: Related Work. The literature review of the related work covers design methodology, multi-agent systems and coordination in multi-agent system, complexity theory, self-organizing systems and organization science. Chapter 3: The Need for a New Approach. This chapter starts with addressing the limitations in previous work in CSO system and categorizes the limitation into two types: modeling and performance drawbacks. After that, the motivation of a new framework for CSO systems as well as a new approach for design of CSO systems is presented. A two-field based model is proposed to regular agents’ behavior to further increase the level of order and overcome the limitations of previous work in creating needed system sophistication when tasks become more complex. Then advantages of having structure and organization in various sciences are addressed. Chapter 4: Dynamic Social Structuring in CSO systems. This chapter first introduces the measure of task complexity based on four components: action complexity, 12 object complexity, action relation complexity, and object relation complexity as well as dynamic complexity. The concept of “social structure” is introduced. Then the models of agents, social structures, and social rules, followed by definition of their corresponding complexity measurements are described. Finally a discussion on the key concepts in the design framework, behaviors and social rule based regulation (SRBR) is developed, leading to new design concepts. Chapter 5: Case Study. Case study designs and simulation setups are presented. Simulation results are discussed that demonstrate how higher level task complexity dynamic social structuring and how social rule-based regulation can be applied to increase the order, and consequently the capability, of the overall system. As independent variables, three kinds of strategies were explored, with social structuring (SRBR), without social structuring (FBR) and applying policy in social structuring (compliance). Three tasks were tested. For all settings, the dependent variables are success rate, time duration (number of steps), and total effort per agent. Chapter 6: Contributions and Future Work. This chapter discusses the major contributions of this research work along with several proposed future research directions. 13 2 Related Work 2.1 Introduction This research is built upon the following research areas: Complexity and Self- organizing Systems, Organizational Theory, Engineering Design Theory and Methodology, and Social Science. The concepts in organizational theory and design theory are utilized to gain insight for designing self-organizing mechanisms in complex system. As a designer in mechanical engineering, this research is mainly related to design theories and methodologies. Within the design field, there are several standard classical engineering approaches that describe different processes of design. Additionally, complexity science has gained attention in human engineered systems as the need for more adaptive and robust systems as well as the degree of complexity of the system increases. The focus is on the critical aspect of design, which is complex adaptive system design. Self-organization and emergence are key themes in complexity science and are not yet well-understood. Concepts in organizational theory have been employed which give rise to new insight for developing adaptive systems. A graphical representation of the intersection of these three areas is illustrated as follow: 14 Figure 4: Points of Departure 2.2 Engineering Design and Methodology For the purpose of system development, engineering design theory and methodology is a key element for all engineering disciplines. (Suh 1990) argued that design methodology has a different perspective than general science theory. Methodologies in design theory focus on the process under which a product is generated. The process can contain strategies, principles, and an evaluation discipline while making decisions at every step through the procedure. In order to meet the entire functional requirements in an efficient way, it is critical to have a suitable process for design. Basically, the process has an important role in determining the quality of the product. There are many proposed approaches in design theory, but the most referred to classical paradigm in design theories include: Systematic Design (Pahl and Beitz), Axiomatic Engineering Design & Methodology Complexity & Self Organizing Systems Organizational Theory 15 Design(Suh 2001), and General Design Theory (Yoshikawa 1981; Tomiyama and Yoshikawa 1986). 2.2.1 Systematic Design Having a systematic point of view for a design problem led the development of Systematic Design by Pahl and Beitz (1996). Systematic design originated from observing and studying the engineering design practice over the course of years where all the design details, from very early stage to the final stage, have been clearly defined. It considers both the defined problem and the environmental situation. The design process is divided into four major steps: the planning and clarifying the task phase, the conceptual design phase, the embodiment design phase, and the detail design phase. The steps are as following: Step 1: Planning and Clarifying the Task The Product Planning phase deals with finding market needs while fulfilling the goals of the company. Clarification of the task involves defining all of the functional requirements and the constraints inherent to the problem environment. Step 2: Conceptual Design The solution to the problem is generated in this phase. It starts with problem abstraction that identifies the essential problem, and then functional structures are generated. Once the functional structures are established, exploring suitable working principles is the next step. And finally a combination of all creates the working structure. 16 Step 3: Embodiment Design After conceptualizing the product, it is time to make the design real, which takes place in embodiment design. All the required engineering analysis will take place in this phase to validate the working principles developed in the conceptual phase. The result of this step is the preliminary solution. Step 4: Detail Design The last step as implied in its name, Detail Design, is to investigate the preliminary solution in more detail, allowing for testing and adjusting the result. All the elements of design will be examined in this step, and all the parts are finalized. A detailed product specification is the outcome of this phase. 2.2.2 Axiomatic Design Axiomatic design is a system design methodology developed by Nam P. Suh (1990, 2001) that systematically maps the consumer needs to the product. The process consists of four domains including: customer domain, functional domain, physical domain and the process domain. The final design is the result of interactions of these four domains. The process involves a zigzag mapping between all four of the components. Customer needs determine functional requirements. From functional requirements, compatible design parameters can be generated. And the last step is defining process variables that are mainly related to manufacturing process. He introduced two axioms as a tool to evaluate alternative solutions to the design problem that result in a more proper result. The first axiom, called independence axiom, 17 insists on the fact that functional requirements should be maintained independently. The second one, called Information Axiom, asserts that the information content of a design should be minimized. Maintaining the mentioned axioms results in a more optimal design and creates an easier path to analyze the system. The main attempt in this design is to reduce the complexity and create simpler designs so that, later in the design, if the solution for one functional requirement changes for any reason, there will be no effect on the other ones. 2.2.3 General Design Theory General Design Theory (Yoshikawa 1981; Tomiyama and Yoshikawa 1986; Tomiyama 1995; Reich 1995) is a design theory that argues that design solutions can be generated by mapping design specifications. The process consists of three key elements: entities, attribute values, and functions. An entity is a real object that either already exists or will be part of the system in future. The set of these objects is the entity set. An attribute is a property that can be observed or measured. A value is associated with the attributes defined for an entity. A function, which is a special behavior, is produced under specific situations. All the mappings between function and entity set are parts of the known assumption for the designer without any uncertainty involved. Attribute association relates functions and entities. Although the mentioned property of this theoretical method is very useful in developing CAD systems, applying general design theory is not very straightforward since enough information for mapping these three major elements is not always available. 18 2.2.4 Conclusion: classical design methodology versus complex systems 2.2.4.1 Systematic Design Acting and surviving in uncertain situations and unknown environments are vital requirements for complex systems. From the very early stage in Systematic Design within the Planning and Clarifying Task, this design methodology does not capture characteristics of complex systems, as it does not consider the emergence inherent to self- organizing complex systems. 2.2.4.2 Axiomatic Design The Independence Axiom and Information Axiom counter the main character of complex systems where interaction and reactions are the unavoidable property of any complex system. Moreover, one of the major contributions of axiomatic design is to reduce complexity and increase simplicity, and this is also in conflict with inherent properties of complex systems, which embed complexity rather than avoid complexity. 2.2.4.3 General Design As the mapping between entities, attributes, and functions in General Design are assumed to be known, the methodology is impractical to use for complex systems, which violate the assumption about complex systems. 2.3 Transition from Conventional design to adaptive design Although traditional design works great for many engineering domains, it encounters some deficiencies in other applications, specifically in the applications that 19 involve uncertainty and unpredictable situations. In conventional design, the environment must be well known and the functional requirements must be completely identified. Therefore if the task environment is unpredictable or the functional requirements cannot be fully determined, it may be impossible to design a practical system. Also, the one solution outcome of these methods is not very desirable as it is not an adaptive design: if anything changes, there is a need to go through the whole process again, which can be very costly. To gain a more robust and adaptive systems, there is need for a shift to develop design methodologies for complex systems (Mina, Braha, and Bar-Yam 2006). Doursat argues (Doursat 2011) that engineers should focus more on design on mechanism that allow self-regulation and self-assembly. (Yaneer Bar-Yam 2006) advised that for design in engineering, there should be less emphasis on the components and instead on the interactions among them. 2.3.1 Multi-agent System A Complex, distributed, interconnected and rapidly changing system has ideal characteristics for designing in order to gain high adaptability and robustness. These properties provide a high potential for using multi-agent systems because of their suitability for modeling autonomous, intelligent and interacting agents (V. Lesser, Ortiz, and Tambe 2003; Tynan, O’Hare, and Ruzzelli 2006). Design of complex multi-agent systems has been a challenging research topic. Extensive work has been done to provide application as well as insight for designing this type of system. Multi-agent systems have been applied in a variety of domains such as traffic control, manufacturing, autonomous mobile robots etc. Modular reconfigurable robots, as a subclass of multi-agent systems, are essentially more adaptive than the conventional systems. Their ability to change 20 configuration based on the situation and changing of task and the potential of replacing the modular parts add another advantage to modular robotic systems. Also, the cost associated with building a modular system is less than conventional design as making large batches of identical modules saves money. Previous to multiple mobile configurations, some research focused on robot reconfigurations. One of the approaches, called I-Cubes, consists of active links and passive cubes (Ünsal et al. 2000). The active links have the ability of attaching to and detaching from the passive cubes (Prevas et al. 2002). (Rus and Vona 1999; Rus and Vona 2000) at MIT introduced numerous different modular robotic systems. Reconfiguration occurs through the cubic structures that are capable of internal contraction and expansion of their size. Different self-reconfigurable algorithms have been introduced by (Vassilvitskii, Yim, and Suh 2002; Yim, Zhang, and Duff 2002), where a desired shape is formed through the movement of a cubic in three dimensions. Multiple mobile configurations were first investigated by Yim (Yim 1993; Yim 1994) through PolyBot, which is characterized by modules moving in groups or chains. The required manual reconfiguration of PolyBot is the downside of this approach. Next (Shen et al. 2006) from University of Southern California, introduce SuperBot, which contains modules with three degrees of freedom and three identical dock connectors. SuperBot is a real-time controlled system with digital hormone inspired control (Shen et al. 2006) and wireless communication capabilities, which enables the autonomous modules to reconfigure. 21 The existing work demonstrates the possibility of multiple reconfigurable modular robots. Although many of these approaches had built in central controllers and heuristic planning, which has proven not to be efficient in the case of large systems, the move towards a decentralized system control and cooperation seems to be a more reasonable approach when adaptability and autonomy are the key elements in design. In the next section research on distributed approaches and coordination is reviewed. 2.3.2 Coordination in Multi-agent System Having coordination among autonomous agents to balance their actions in multi- agent systems is a crucial problem. Agents do not have enough information to guide their behavior and find a solution for the whole complex system (Goto, Hasegawa, and Tanaka 2007; Wooldridge 2002). Either there should be a control system to monitor agents’ actions or agents themselves should influence each other’s behavior to act in a positive way. Protocol and behavior mechanisms play an important role for agents to effectively operate and divide the task in a well-organized manner where agents seek to achieve coordination states to achieve system-wide goals. Such challenge is in the heart of multi- agent systems (Weiss 2000; Wooldridge 2002), swarm systems and collective robotics (Bonabeau, Dorigo, and Theraulaz 1999; Kube and Zhang 1992). In multi-agent systems, cooperative control can be categorized as either formation control problems or non-formation cooperative control problems. Applications for formation control include mobile robots, unmanned air vehicles (UAVs), satellites, aircraft, etc. non-formation cooperative control can be applied in air traffic control, task assignment, etc. Issues associated with successful cooperative strategies involve the 22 definition and ways to utilize shared information between agents. Information may be shared in various ways including relative position information, wireless networks or common control algorithms (Russell Carpenter 2002; Fax and Murray 2004; Balch and Parker 2002). A distributed approach (Stoy and Nagpal 2007) has been developed where modules receive information through a directed chemical gradient. Basically, modules move towards other modules in a scaffold and configure a desired shape, which is given to the system. This is a shape forming mechanism where the ultimate structure is provided. The underlying process, rather than illuminating general design principles, is mainly problem dependent. Another approach where agents (cell) can communicate through hormones (chemical), called bio-inspired Digital Hormone Model was developed by (Shen et al. 2004; Shen, Chuong, and Will 2002). Cells react to the hormones where they cause changes in their decision making process. The hormone dissipation mimics the real hormone equation by propagating through the system. Another approach to autonomous robot design is the reactive approach, which originated from (Arkin 1995; Arkin 1998) where animal models have been studied. Individuals in many animal species show great capabilities and are strongly motivated to form groups and perform cooperative tasks. In the robotics literature, extensive work has been conducted on cooperation among robots (Arkin and Balch 1998; R. Brooks 1986; Mataric 1997; Parker 1998), compared to altruistic behaviors. Altruism starts with the following research of (Lucidarme, Simonin, and Liégeois 2002) and (Simonin and Ferber 2000) where robot 23 behaviors are described with a term called “satisfaction” and existing signals from other robots and agents broadcast their intention or a reaction to other agent behaviors. (Simonin and Ferber 2000) proposes a method for integrating cooperative behaviors among distributed autonomous agents based on local communication. Agent satisfaction is defined as a signal to handle action selection and cooperative interaction. Satisfaction is a combination of the agent self-satisfaction that is a measure of progress of the agent task, and empathy satisfaction, which takes into account the satisfaction of other agents. Each robot must satisfy its individual goals while minimizing negative interactions (conflicts) and maximizing positive interactions (cooperation) with other agents and the environment. The model shows the feasibility of using agent intentions in a reactive architecture. Within the multi-robot communication context, reciprocal altruism relations among robots have been used to maximize an individual fitness function. Market-based task auction methods have been exercised to create this type of relation between robots (Goldberg et al. 2003), where (Morton, Bekey, and Clark 2009) furthers this idea by considering imbalanced altruistic relationships: when one robot can perform another robot’s task, but the other robot cannot reciprocate since it is physically unable. The controller permits a robot to build altruistic relationships with the community as a whole (one-to-many), instead of just with single robots (one-to-one) to lose protecting against selfish robots. Although these works provide insight for how agents should interact to signals from other agents to reach the required level of cooperation, the main task is defined and already known by the agents. Thus, the fact that agents might not be aware of what exactly they have to do with respect to the rest of the system has not been covered. As research progresses towards a distributed direction where agents are more responsible 24 for their action with regards to available information, complex theories become very relevant. 2.3.3 Complexity Theory, Self Organizing Systems and Self Organizing Criticality A complex system is a non-linear coupling of interacting agents. System behavior is a combination of individual actions, reactions and interaction where these interactions can have negative, positive, or neutral consequences on the system (Heylighen and Campbell 1995). Self-organization is one of the major topics in complexity theory. Nobel Prize winner, Ilya Prigogine and Glansdorff (Glansdorff and Prigogine 1971) established the term self-organization through thermodynamic studies as the main property of a self- organizing system is to increase order of the system (Prokopenko 2008; Heylighen 2001). Self-organization is a process through which arrangement of a non-equilibrium system’s components causes development of structures and patterns typically without explicit pressure (Prigogine 1997). In self-organizing systems coordination patterns typically emerge at the global level from coordination laws based on local conditions (Viroli, Casadei, and Omicini 2009). The dynamics of interacting components force the system to pass a threshold, causing it to reach a new phase of macroscopic configuration (Haken 1983). Emergence of new pattern causes manifestation of governing parameters. Eventually these parameters become the main dimensions of the system dominating others. (Haken 1983), described this phenomena by introducing the concept of ordered parameters and a more generalized theory, the “enslaving principle”. In principal, dynamics of the system are 25 determined by only a few slow modes causing reduction of the whole system’s initial dynamics to a lower dimension as the faster and short-lasting modes fade away. Another view to self-organizing has been described by (S. Kauffman 2000), who proposed that self-organization is achieved by constraining and conducting the release of energy. Introducing various constraints and control strategies gives rise to a variety of configurations and therefore behaviors that are the key for adaptability (Prokopenko, Boschetti, and Ryan 2007). In engineering, elements in self-organizing systems are designed so that their behavior and interactions will lead to a system level functionality. Although elements are separately performing their behavior, they have to be organized in order to solve the problem. Extensive research has utilized a self-organizing approach to reach a solution for complex problems (Ashby 1956; Beer 1966; Beer 1984; Bonabeau, Dorigo, and Theraulaz 1999; Di Marzo Serugendo et al. 2004; MOTIVATIONS 2005). One of the most referred to works for a discrete model of a self-organizing complex system is the Cellular Automaton which is a dynamical system where the decision of each cell in the grid depends on information received from its neighbors. One of the popular examples of cellular automaton is Conway’s Game of Life (Gardner 1970) where clearly identifiable patterns emerge from simple rules between agents. (Wolfram 2002) developed more cellular automaton based fractals. However, these explorations are the result of fixed local rules. Furthermore, the overall system should be observed after defining rules, thus the system is not desirably adaptive to sudden changes and is not manageable. 26 Radhika Nagpal (Nagpal 1922; Nagpal 2002) generated a descriptive language and introduced the programmable sheet that consists of thousands of randomly and densely distributed agents that assemble themselves into a predetermined global shape. (Viroli, Casadei, and Omicini 2009) addresses the required features of coordination models for self-organizing systems as topology & locality, on-line character, time- dependency and probabilistic behavior. Other applications of self-organizing systems have been investigated in a number of other domains including traffic (Cools, Gershenson, and D’Hooghe 2008) and sensing systems for structural health monitoring (Hoschke et al. 2008). Until recently, while there have been some attempts, no general framework for building self-organizing systems exists and its practical applications have not been thoroughly addressed. Another interesting concept, which attempts to describe complexity in nature, has gained interest and is called self-organized criticality. SOC is originated by (Bak, Tang, and Wiesenfeld 1987) based on the simulation model of the cellular automata sandpile which has been frequently used to demonstrate this concept. SOC combines self- organization and criticality to yield insight about the nature of complexity. Self- Organized Criticality can be described as the critical state of a system at the edge of stability and chaos resulting from internal self-organization of elements over a wide range of length scales. (Bak 1996) idealistically argues that SOC is the only demonstrated uniform mechanism for generation of complexity in a system as evolution of the system is spatial/temporal scale independent just like fractal structures. Various research areas have investigated the concept of SOC including physics, ecology and evolutionary biology (e.g., S. A. Kauffman and Johnsen 1991; Halley 1996; Milne 1998; Li, Wu, and 27 Zou 2000). Research in the context of brain and neurobehavioral studies are trying to characterize these modes to understand universal dynamical model of brain functionality. (Buice and Cowan 2009) shows how phase transitions at a critical point affect brain activities and uncover some underling facts regarding states of the brain close to phase transitions (Kitzbichler et al. 2009; Friston and Dolan 2010). SOC is still in the exploratory phase as there is no development of a universal mathematical formalism or suitable metrics to evaluate the SOC characteristics of a system if it displays any. 2.3.3.1 Natural Self-organizing Systems Animals demonstrate robust behavior through the distributed actions of many independent agents. Well-known examples of natural self-organizing systems include: ants, termites, honeybees, flocks of birds and schools of fish. In such systems, each agent acts autonomously and interacts locally, while the global system exhibits adaptation and executes coordinated behavior. A foraging ant’s role is to explore an environment, find food and deposit a chemical substance in the environment, called a pheromone, whenever it finds any food source (Deneubourg et al. 1991). Artificial systems such as mobile robots have grown with inspiration from ant behaviors such as stigmergy (Werfel 2006; Deneubourg et al. 1991). Computer simulation similar to flocking motion (Boids) was developed early by Reynolds (Reynolds 1987) to simulate the motion of flocks. Simple rules between agents have been utilized to illustrate the emergent collective behavior in swarms. Despite being a significant improvement in the self-organizing field, due to the simplicity of rules, simple collective behaviors emerge while real functional capability is missing. 28 All the methods and models help to move forward both in understanding and applying these concepts in real world applications. However, most approaches do not embrace complexity, and agents have the privilege of having system level awareness, especially in complex system design. Many researchers still use central controllers and top-down approaches. For a distributed system with the purpose of solving a problem or reaching objective functionality, an organized way of sharing information among agents can be very helpful. As mentioned in (Horling and Lesser 2004), organizational oriented design has shown to be effective and is typically used to achieve better communication strategies. In the next section, some concepts in organizational theory is introduced. 2.4 Organization Science In this section the primary organizational theory related to this context in described. Fundamental works of Thompson (Thompson 1967), Galbraith (Galbraith 1977; Galbraith 1973) and (Scott 1992) in contingency theory is reviewed. Later, will describe the task environment and the relationship between the environment and organization structure. 2.4.1 Contingency Theory According to Thompson’s point of view, contingency theory is to explain how organizations attempt to be rational although they are natural and open systems. Knowing that an organization is an open system and subject to a changing environment, how can the organization continue to function as a rational system? Thompson (Thompson 1967) describes ways to adjust different models of the organization to fit different levels of organizational structures, discussed in the work done by (Parsons 1991), which are 29 differentiated as the technical, managerial and institutional levels. The managerial level acts as a mediator between institutional and technical levels. The most affected level by environmental changes is institutional as the system performs as an open system. Thompson (Thompson 1967) tries to tie together the concept of complexity and open systems with the rationality involved in designing an organization. He stated, “We will conceive complex organizations as open systems, hence indeterminate and faced with uncertainty, but at the same time as subject to criteria of rationality and hence needing determinateness and certainty.” Therefore he presented some propositions regarding the actions organizations need to take as a rational system: Proposition 6.1: Complexity leads to differentiation When organizations are encountering heterogeneous tasks, they plan to establish homogenous parts and form structural units to deal with each part. Proposition 6.2: Simplicity allows standardizing, and creating new units based only on capacity constraints According to the capacity of the supervisor, organizational components facing homogenous parts of the task environment are further subdivided. • Proposition 6.2a: A stable task environment leads to further formalization • Proposition 6.2b: Certainty leads to formalization When the degree of certainty is high enough in task environment, adaptation is achieved by standardizing sets of rules. 30 • Proposition 6.2c: Unpredictability leads to decentralization When the task environment is not stable and undergoes a wide range of changes, the organization component responds by observing its environment and performing reactions. • Proposition 6.3: Sequential interdependency is dealt with by hierarchical planning and supervision If the technical and boundary spanning behaviors can be isolated, centralization becomes the solution. Therefore, various managerial levels of hierarchy can be developed. Jay Galbraith (Galbraith 1973) states that that “there is no best way of organizing an organization and any way of organizing is not equally effective.” Galbraith's view can be considered to be similar to systems as he argued that as uncertainty in the task environment increases, the amount of information necessary to deal with the situation and to make the right decision increases. Furthermore, (Scott 1992) argued "Various structural arrangements, such as rules, hierarchy, and decentralization are mechanisms determining the information-processing capacity of the system". Scott also rephrased and added to the contingency theory the fact that the nature of the environment that the organization belongs to has a huge impact on the way of organizing the system. The success rate for an organization depends on the environmental situations. Design of the organization and its subsystems can vary based on the type of their environment. Principally he describes contingency theory as follows: "Contingency theory is guided by 31 the general orienting hypothesis that organizations whose internal features best match the demands of their environments will achieve the best adaptation." 2.4.2 Task environment and adaption of organization structure In this section based on contingency theory, the ways organizations adapt to the given task environment is described. First it starts with describing the basic characteristics of the task environment. Various works focused on this area of research have developed different dimensions for the task environment. Among those, (Scott 1992; Thompson 1967) provided a well-recognized categorization of the task environment. They both have a similar approach to identify the possible dimensions involved with the task environment. The fundamental basic dimensions include complexity, unpredictability and interdependence, where Thompson used the term uncertainty instead of unpredictability. • Complexity: the number of elements and sub-elements in the task environment that the organization should handle. • Unpredictability: the degree to which the changes of task elements and sub- elements are predictable. • Interdependence: demonstrate the level of dependency between tasks to determine to what extent change in one can cause modification in the other one. According to the defined dimensions for task environment, Scott developed various dimensions for organization structure to match the previously defined task dimensions. He proposed the three following dimensions: differentiation, decentralization, and formalization. 32 • Differentiation: to what extent the organizational tasks are divided into different sub-units. • Decentralization: to what extent supervisory power is distributed and is given to lower managerial levels in the organizational hierarchy. • Formalization: what is the level of rules, standards and procedures involved in the system. (Scott 1992) relates task environment and organization by developing sets of propositions. The result is shown in the following table where he also compares the response of rational systems with natural system given task characteristics Table 1: Characterization of task and organization structure (Scott 1992) Task Characteristics Rational System Response Natural System Response Complexity Differentiation Professionalization Unpredictability Decentralization Deformalization Interdependence Formal Coordination Increased Autonomy 2.4.3 Task Interdependency and Coordination Policy In organizations, as the number of different types of task environments increases, the need to further differentiate its structure increases where each subunit faces one external need. Scott argued "To cope with these various environments, organizations create specialized subunits with differing structural features" (Scott 1992). Furthermore, as differentiation levels go higher, coordination of activities within and among the subunits becomes more difficult, and more resources need to be implemented for 33 coordination. In an organization, tasks are related to each other. Thompson, as the most cited work studying organizational science, categorizes the interdependence of tasks into “pooled interdependence”, “sequential interdependence” and “reciprocal interdependence”. In pooled interdependency, the branches are not in iteration with each other, but their existence is necessary for the survival of the whole system. In sequential interdependency, there is an extra relation besides pooled interdependency where the starting point of one activity depends on completion of another partner. Finally, in the third interdependency, both partners are mutually affecting each other where the outcome of one becomes the input of the other one. These different types of interdependence require different types of coordination policies. Thompson proposed three types of coordination, “standardization”, “by plan”, and “mutual adjustment”. He assigns a suitable coordination policy for each task interdependency shown in the following table: Table 2: Coordination policy for each task interdependency Interdependency Coordination Policy Pooled Standardization Sequential Plan Reciprocal interdependence Mutual adjustment 34 Furthermore, organizational analysis tools such as the Virtual Design Team (VDT) have been developed. The VDT model, initiated in the late 1980s, is developed based on organizational contingency theory, and real world observations about collaborative and multidisciplinary work in project organizations engaged in complex, but relatively routine task (Jin and Levitt 1996). VDT explicitly models lateral interdependencies between activities. They analyze how coordination needs arise from activity interdependencies and how organization structure variables can affect the performance of an organization (Jin and Levitt 1996). 35 3 The Need for a New Approach 3.1 Introduction The major challenge in CSO systems is to design the individual’s behaviors to best match system functionality. One of the major techniques to better understand the connectivity between local and global is to increase the complexity of the system. Increasing complexity can consist of enlarging available system states, or adding higher levels of communication between agents. With more possible states, agents have a larger action space to choose from to reach their selected state. Therefore, when a system covers additional global states, it denotes an increase in system complexity. Communication and coordination among agents, or in other words, exchange of information, requires an additional capability for agents, data sharing. Extra capability indicates higher complexity in modeling agents. Current CSO systems do not satisfy the consequential or time dependent requirements. This aspect reflects the complexity in the desired task. Some requirements arise during the execution including the need for additional behaviors to be implemented. Also, some sort of communication or coordination becomes necessary during the operation to increase the possibility of performing tasks either faster, or even to complete it at all. In summary, designing a CSO system’s local behaviors is a critical challenge and needs a more complex model to satisfy the aim of reaching the balance between design and self-organization. The designed self-organizing mechanism can be defined as the navigator of the dynamics of the whole system to the ideal output. Back to the major concern, in order to comprehend the connection between local and global, a new representation of the behaviors must be established and further clarified. 36 3.2 Limitations in previous CSO Systems This section goes over previous work on CSO systems. Three approaches have been developed in order to design CSO systems. George Zouein (Zouein, Chen, and Jin 2010) developed and discussed a self- organizing System Design Framework or SOS Framework for the development of adaptive systems and draws insights for it from principles and concepts extracted from biology. He expanded one facet of SOS by developing an artificial DNA-based Cellular Formation Representation framework (cFORE) for representing and constructing artificial systems in a manner which mimics biological systems. One of the key issues in achieving high adaptability in artificial systems is how to dynamically capture, represent and apply design information pertaining to the designed functions and changing environmental situations. Biological DNA in natural systems plays the key role in keeping, maintaining and transferring such “design information” within and between individuals. Resembling biological DNA, he developed an “artificial DNA” called dDNA (Design DNA) which maintains design information and provides an avenue for generating new designs adaptively. The simulation verifies that a mechanical system’s growth can be realized through a dual control strategy utilizing DNA guided cellular self- organization controlled by a morphogenesis-based algorithm through communication utilizing growth factor proteins. Limitation: There are limitations associated with this work. Given that the information is stored in the dDNA, there is a need to have all sorts of information saved for utilizing and achieving the global system goal. Therefore, there is limited adaptability 37 for the whole system. Since the saved data in dDNA specifies a specific shape, agents are capable of constructing a formation. Basically the global image is given to all the mCells, and their task is to represent that structure. The task definition for mCells is simple, and no variety of tasks has been addressed. Moreover, once all agents reach the desired destination, and the overall system looks like the given shape, they know which direction to move forward. The direction of movement is pre-specified for the whole system. Chang Cheng (Jin and Chen 2013) based on the previous work on mechanical cell (mCell) based system formation, he proposed a novel biology inspired system representation called Behavior-based design DNA (B-dDNA) for the development and operation of Cellular Self-organizing Systems (CSO). Based on the B-dDNA representation, a mechanism called Field driven Behavioral Regulation (FBR) is proposed that implements and synthesizes system Designing, Formation, Operation, and Adaptation processes. FBR of a CSO is a mathematical and selection model that is shared by all and specifies cellular behaviors corresponding to functional, system level, operational and adaptation requirements. The research results have demonstrated the feasibility and advantages of the B-dDNA representation and FBR based mechanisms. Two case studies along with more detailed computer simulations are provided to demonstrate the power of B-dDNA and FBR for designing and developing complex engineered adaptive systems that possess inherent capabilities to cope with the increasing level of system complexities and to exhibit high level flexibility/adaptability in response to both task and environmental changes that occur in mission situations. 38 Limitations: Instead of focusing on shape formation, he focused on choosing the correct action where he introduced behavior-based design. For agents to determine their behavior and to fulfill the system prerequisite, he introduced the field concept by which situations are stored in dDNA. The behavior with the highest expectation is designed to be chosen by agents. That is what he called regulated field based approach. The ultimate global form emerges from agents’ behavior. Compared to George Zouein’s research, his proposal achieved a higher level of self-organizing and total performance through identifying individual agent behaviors. However, the exploration is based on a simple task definition. Moreover, there is close to zero interaction among agents. The only considered interaction among mCells is an implicit communication with other mCells regarding their location with respect to the system. With the purpose of not violating shared space criteria, agents do not occupy the same spot. In view of the fact that mCells have very limited interaction, they fail to deal with complex design with a more complicated task, especially with the existence of task interrelationships. Winston Chiang (Chiang and Jin 2011) his thesis details a new CSO approach inspired by natural phenomena in order to extend the design envelope towards an artificial nature. While natural systems had the luxury of evolution over millions of years, achieving bottom-up adaptability by design represents a major challenge to the systems engineering and design research community. Two fundamental issues must be addressed: one is the analysis problem of predicting the global emergence from local interactions; and the second is the design problem of compiling local rules based on a desired global function. Also, a parametric approach centered upon interactive behaviors is used to develop a Meta-Interaction Model (MIM) of the behavioral model of agent interactions. 39 Instead of designing single specific capabilities, the MIM method designs for emergent functional capacities. This is a fundamental change in design theory. By doing so, designers are trading deterministic functionality for self-organizing and emergent adaptability. The MIM technique can be used to manage adaptability by specifying interaction patterns of agents in a multi-agent system, thus guiding the emergence of functional capacities. A simulation-based study of the Cohesion-Avoidance-Alignment- Random-Momentum (COARM) Behavioral Model is completed in order to analyze the COARM meta-model. Ultimately, The MIM approach provides a design framework for developing CSO systems. It gives top-down control over functional bottom-up organization. Limitations: In contrary to previous works on CSO, the COARM approach to CSO systems focuses on pure interaction among agents. These interactions are implicit interaction with the assumptions that each agent is only aware of its neighbors’ locations, speed and direction within some range. Essentially, he designed a space based on interactive behaviors. Also, he introduced a method to manage and manipulate multi functionality through tunable dynamical design variables. Based on what have been discussed, agents can reach the desired system level functionality; however, there are limited physical implementations. Additionally, it is not always straightforward to determine parameters in order to carry out task requisites, especially when there is a need to accomplish more complex tasks requiring sophisticated interaction and interrelations between mCells. Since global behavior emerges purely from mCells’ adjusting their behavior based on their neighbors, there is no control defined for the system. Therefore, it 40 is critical to correctly specify the design variables that denote the behavior of each agent. The summary of the discussion is shown in the following table (Table1): Table 3: Limitation in Previous CSO system Performance Limitations Modeling Limitations • Efficiency: Energy & time • Functionality: How well the system accomplishes tasks • Practicality: Physical application & complex design • Lack of richness in task description & rules • Very simple task domain: Focus on one aspect of self-organization Overall, the limitation in previous work can be categorized into two types: Modeling and performance drawbacks. 3.2.1 Modeling Limitations Lack of richness in task description & rules: Previous works have been very successful in providing a deep insight into newly developed CSO systems. They principally focus on introducing new concepts and understanding the starting point of CSO systems and their characteristics. Although very successful in that aspect, they lack adequate task descriptions, mainly because simple tasks provide a better opportunity to investigate other aspects of CSO systems. In addition, they fail to act properly when task complexity increases and they are deficient in concepts and rules necessary to properly describe the requirements. 41 Focus on one aspect of self-organization: In order to better understand the characteristics of CSO system, each approach has investigated a unique way to view an adaptive design method. In Zouein’s case, he is trying to construct a shape by multiple mCells where each mCell is holding information about the whole system configuration. Therefore, his approach is form-based dDNA, merely considering forms. Whereas in Chiang’s research, his primary focus is on behaviors where agents sense the environment through sensing the density of attraction and repulsion forces that he conceptualized as a task field, and react to the received information. His approach is purely behavior-based with no definite types of communication or interaction with other mCells. On the other hand, Chiang investigated simply the interactions among mCells. 3.2.2 Performance Limitations Efficiency: The main concern in all the previous work is to accomplish the given task and reach the goal state. The efficiency of performance both in terms of energy and time has not been taken into account. For example, energy consumption could be a major concern in a problem definition, or else the speed and time frame of the total execution time could be a critical requirement in a design. For example, in the case of fire extinction, the speed of firemen plays an important role in evaluation and performance of the team. Therefore, time and energy as two factors of performance can be consider as parameters to better design a system. Functionality: Due to the simple task definition, the functionality of the previous CSO systems in the presence of more complex tasks is not guaranteed, particularly when coordination of agents is required to reach system level functionality. Since their 42 methodology does not support communication and coordination among agents, the functionality of the system is limited, although well designed. Practicality: As mentioned above, due to the limited scope of functionality considering agent capabilities and the provided mechanism, applicability of the system itself is restricted. As a matter of fact, real engineering design manages complex functional requirements. Consequently, to be more comparable to the scale of real design competence, a more complex approach is needed to cover more variety of real world applications. In this research, by defining a more complex design methodology, there is an attempt to expand the limits of practicality of CSO systems. In conclusion, as an alternative approach to adaptive and complex engineered systems, the previous work on cellular self-organizing systems (CSO) has provided useful insights into understanding necessary characteristics of adaptive systems and introducing nature inspired concepts. Each individual work has focused on one side of self-organization. Therefore the major focus of this research is to extend the idea of cellular self-organizing systems to accomplish more complicated tasks while better achieving functionality by adding social aspects to the existing FBR approach. The current FBR approach is fully distributed since every mCell works on its own without concerning other mCells. From a multi-agent systems perspective, the full distribution represents a level of disorder that has two important implications. First, the disorder means limited functional capabilities. While field-based regulation allows individual’s actions to collectively contribute to the overall task for simple task domains, it lacks ways to create corresponding system sophistication when tasks become more complex. Second, 43 the disorder provides an opportunity for us to infuse order into the system and therefore increase the level of overall system capability. The question is how can one devise such order so that “control” of the level of order for best balance of system adaptability and functionality can be achieved? 3.3 Basic Approach As mentioned above, a system needs to possess a certain level of complexity in order to deal with tasks with a corresponding level of complexity (Ashby 1958). Furthermore, it has been demonstrated that a system with higher physical complexity is more adaptable because the higher-level diversity permits satisfaction of changes of constraints around the system (Huberman and Hogg 1986). Although the algorithmic information content-based complexity measure equates randomness with complexity, from a system design perspective, it is more appropriate to count the complexity of a system based on its physical, structural, and effective features. In this case, pure randomness is discounted and the attention is placed on agent interactions and evolving structures. Following Huberman and Hogg (1986), the complexity spectrum of engineered systems over order and disorder is considered bell shaped, as illustrated in Figure 5. A single solid object, such as a hammer, has complete order, as indicated in point (a) in Figure 5; it has close to zero complexity and can deal with very simple tasks, such as punching a nail. By increasing the number of dedicated components and introducing interactions between them, the order decreases in the sense that the system can be in various ranges of possible states. Such systems can be a gearbox (simpler) or an internal 44 combustion engine (more complex). Although this “complexity by design” approach (from (a) to (c) in Figure 5) has been the mainstream approach to complex engineered systems and has been highly effective, the unintended and unknown interactions among the sophisticated components may potentially cause a system crash when the systems demand extreme complexity for highly demanding tasks. Space mission failures and accidents in nuclear power plants are examples. Figure 5: Hypothetical system complexity over order-disorder spectrum Order An alternative approach to complex engineered systems is to start from completely disorganized simple agents (or mechanical cells in CSO term), as indicated by point (b) in Figure 5. While the completely disordered agents cannot perform any task, not even punching nails, introducing order into the system (i.e., among the agents) can potentially lead to a functional system (from (b) to (c) in Figure 5). Physical materials, biological systems, and ant colonies are examples. The distinct feature of this approach to complex engineered system is “complexity by emergence.” It is fully understood that this approach is not currently competitive with the traditional approach, but the approach promises an alternative future for developing complex engineered systems. Since “by 45 emergence” does not require explicit knowledge of specific interactions among agents, the sudden system failure mentioned above can be avoided. Furthermore, this approach may fundamentally expand the conceptualization of engineered systems by bringing biological developmental concepts into mechanical system development. This research on self-organizing systems takes the “by emergence” approach. Besides introducing the concepts of design-DNA (dDNA) and mechanical cells (mCell, i.e., agent), a task field based behavior regulation (FBR) mechanism has been developed to allow agents to self-organize (i.e., introducing order) implicitly/indirectly through each agent following the attractors of its perceived task fields. Although this limited orderliness was effective for completing “pushing box” tasks, it was not enough for “pushing and rotating box.” Defining interactions is the key for developing realistic multi-agent systems (Davis and Smith 1983; Kraus 1997; Y. C. Jiang and Jiang 2005; Y. Jiang and Jiang 2009). Despite the implicit and informal nature of some multi-agent relations, all multi-agent systems possess some form of organization, even as simple as avoiding occupying the same grid in the environment. Determined relations and rules provide a spectrum between the centralized and fully decentralized approaches for agent coordination. To further increase the level of order, in this research the concept of “social structure” is introduced to capture explicit/direct interactions among agents and apply “social rules” to facilitate dynamical social structuring among agents. Social relations should be implemented to constrain the actions of agents according to their task; as a consequence, the desired goal and harmony of the system can be reached. Introducing 46 rules and relations that lead to emergence of structure, confining the possible actions for each agent. The structure, if managed properly, can result in having simple agents exhibit complex behaviors and help sophisticated agents reduce the complexity of their reasoning. 3.4 Structure necessity Advantages of having structure and organization have been addressed in various sciences: 3.4.1 Organizational Research In organizational research, it has been repeatedly shown that a proper way of organizing a system can have substantial impact on its short and long-term performance. The structure of an organization depends on the internal and external variables. It has been proved that the behavior of the system depends on the shape, size and characteristics of the organizational structure (Galbraith 1977; Durfee, Lesser, and Corkill 1987; Horling, Mailler, and Lesser 2004; Matson and DeLoach 2003; Barber, Goel, and Martin 2000; So and Durfee 1998; C. H. Brooks and Durfee 2003). Research on this aspect has suggested that there is no single type of organization that is a best match for all circumstances (Corkill and Lander 1998; V. R. Lesser 1998). In some scenarios, there are some cases where various operating organizational structures are needed instead of a single organization (Gasser 1991). With what being said, although there is a good attempt to establish a suitable organization for a specific condition, (Romelaer 2002) has shown that no perfect organization exists for any situation, due to uncertainties and multivariable optimization decisions that must be made in any realistic instance. 47 Different approaches have both beneficial and unfavorable sides based on the governing situation. What determines a preferred approach is the environment and goal for that organization. Each approach should match the characteristic of the solution to the problem. In organization research, one extreme of having some sort of organization is to have one layer of management, which is called a flat organization. A flat organization can be pictured as having a central controller in multi-agent systems. However, in organization research, flat structure is considered more flexible and adaptable than taller structures, due to having only one commander that takes control of everything. Whereas in taller organizations, there are multiple commanders in different levels, in flat organizations, a manager has the responsibility to command all the workers at the lower level; therefore the organization can take advantage of direct communication with one boss. Although the advantage of having only direct and faster communication eliminates miscommunications and disagreements, there is an overhead communication only for one agent. Above all, what an organization really does is to essentially reduce the uncertainty. Reduction in uncertainty occurs when the number of available actions and interactions decreases. By shrinking the available scope, the probability of picking a certain action will increase, which means more information about the system results. Furthermore, teams are important components of organizational work (Hackman 1987; Sproull and Kiesler 1992). When tasks become too large and complex, it becomes almost impossible for one individual to undertake the whole project within a certain 48 deadline. Additionally, as complexity, multiplicity of tasks and dependencies between tasks grow, the need for a larger team size, and thus team coordination increases. 3.4.2 Hierarchy in Complex Systems Many complex systems are hierarchical in structure, including social systems, biological systems and physical systems. More important to the study of complex systems are hierarchies that can be characterized by functional relationships. Hierarchies can be expected to grow out of simpler systems through stable intermediate forms. A hierarchical system is usually composed of only a small number of kinds of subsystems (Figure 6). Hierarchies that exhibit near-decomposability have behavior that is easier to describe, and many arrangements are possible (Simon 1962). Therefore the redundancy in the hierarchies can cause a form that is easier to describe with a small alphabet. Figure 6: Hierarchic in structure In a nearly decomposable system, the short-run behavior of the subsystems is approximately independent of the short-run behavior of the other subsystems. The long- run behavior of any one subsystem is dependent only in an aggregate way on the 49 behavior of the other components. Markets, formal organizations, and water are nearly decomposable systems. Since many hierarchical systems are nearly decomposable, insignificant links can be ignored in the description. As a result, by recoding, some unobvious structure may be revealed which can lead to replacing a state description with a process description. 3.4.3 Structure in a Real Complex Network It has been shown that a scaling law is the characteristic of many real networks including the World Wide Web, and the semantic web. This scaling law represents the hierarchical nature of the complex network systems. As a matter of fact, grouping the nodes in the network that are well connected can create modules of the system where each module has some similarities based on the network itself. For example, in society, each group can be a group of friends or collaborators. Clustered modules are not completely disconnected, while having limited connectivity; they are related in some aspects. Accordingly, it can be said that many real networks are scale-free, and their clustering nature is an obvious fact. Also it has been investigated that the main reason for complex networks to embrace these features is their hierarchical organization. Different groups join each other in a hierarchical manner and generate larger groups. The hierarchical architecture and scale free property embedded in real complex networks prove the existence of order in complex systems. Based on gathered data, the scaling law has been indicated that determines the size and the number of the different groups (Ravasz and Barabási 2003).Therefore, even clustering is not randomly initialized; rather the law of scaling governs their creation. 50 3.4.4 Structure in Natural Evolution Natural systems have participated in the evolution process for billions of years. Over eons of time, systems have attempted to organize themselves into a more complex and favorable arrangement. Natural systems and living organisms pose a genetic program, which directs their formation (Lewin 1982). Developing a more organized and more efficient system requires energy (Williams 1981); therefore energy is needed in different forms for various systems. As one know from thermodynamics, systems tend to evolve to equilibrium with less order and higher entropy. On the other hand, evolution, even though happening naturally, tends to move towards a more profitable and better-organized arrangement. Consequently, it would be a valid conclusion that nature uses energy to place useful constraints on the existing system (Figure 7). One way to mimic natural systems is to design a system that uses minimum energy and is capable of performing complex behaviors while organized in an ordered manner (Fox 1971). Figure 7: Structure in chemical systems 51 4 Dynamic Social Structuring in a Cellular Self-Organizing System Therefore, in order to deal with more complex and interrelated tasks, there is a need to make some adjustments to the previous CSO system to empower its capability to properly handle these situations. As mentioned above, limiting the available capacity of action for mCells and managing them and their relations in an organized manner can be beneficial to the overall system. Coordinating multiple mCells to achieve a complex task requires solving two distinct control problems: the low-level control problem of ensuring that each mCell actually performs the correct actions to accomplish its task, and the high- level control problem of ensuring that each mCell plans to execute a useful task. This thesis establishes a framework to focus on developing structure for CSO systems based on arising relations among mCells that are environmental and task oriented. But what is Structure? What governs the building of the structure? Basically the main question is what does it take to evolve a structure: How can agents form and achieve structure? What kind of cellular relationships should be considered to form that structure? Before the structure can be constructed, the space of organizational structure of agents should be mapped to their ultimate goal. In this research, the main goal of agents is to accomplish a task in a CSO system. The first question would be what different types of tasks are and how to model tasks? Once the task definition for the overall system becomes clear, the next step would be to generate a mechanism for agents to receive useful information regarding what needs to be done. Even if the information is valid there might be a need for sequential actions or 52 precisely coordinated actions to achieve a reasonable performance. Hence, a more complicated mechanism to implant a better solution to the current concerns and deficiencies in CSO systems is needed when a more complex task should be executed. The new mechanism should embrace a proper task representation while providing a useful tool for agents to coordinate their action. For example, there could be a scenario where one agent is not capable of finishing a task and another agent’s help is required. Agents should be able to ask for help, or other agents should be somehow aware of going towards other agents and offering assistance. The complexity of the mechanism is highly dependent on the complexity of the task itself. Note that the new self-organizing mechanism is not considered as an optimal solution for a defined problem; rather it’s a procedure through which agents create an organized order which has been originated from functional requirements and the ultimate goal of the system. The following sections, first introduces the measure of task complexity and then describes the models of agents, social structures, and social rules, followed by the social rule based regulation mechanism. The subsequent case study sections and simulation results will demonstrate how higher level task complexity demands dynamic social structuring and how social rule-based regulation can be applied to increase the order, and consequently the capability, of the overall system, followed by conclusions and future work. 53 4.1 Key Terms and Definitions 4.1.1 Task Definition When the functional requirement becomes more complex, having a more complex mechanism becomes a necessity. According to Ashby’s law of requisite variety, the system needs to have similar complexity as the working environment in order to adapt. (Ashby 1956) and (Y. Bar-Yam 2003) argued that in order for any system to survive in a complex environment, the complexity of this system should at least be equal to the complexity of the environment. Moreover, if the system is exposed to changes both in terms of environment and functional requirements, the system needs to have sufficient complexity to keep up with all the changes. In order to have a good estimation of the amount of complexity required for the CSO system design, a good measurement of tasks is required. A prerequisite for studying task complexity is a proper task representation. What is a proper way to characterize task requirements for CSO systems? How does one define task requirements systematically for a decentralized multi-agent system? Two levels of sophistication are involved with the definition: first how the task is defined in the general and big picture, and second, how the task is defined for subsets of the system (agents). Since physical and mechanical tasks are the point of attention, the description of task should involve the object depiction. The present definition of task from the mechanical design point of view is practical. It is critical to have a solid description of task to understand the nature of task complexity. Thus object participation in a task is considered as one of the main elements in analyzing the task. Making characteristics of 54 objects an important aspect in CSO systems is one of the key differences in this approach. In contrast to the previous approaches, the starting point is from the very beginning with appropriate task definition and then measures the complexity of the task to capture a better understanding of the system design. To solve the design problem from a general functional requirement to local agents’ behavior, the designer should decompose the main task/design specification to a set of functional requirements. All the functional requirements are assumed to be able to be decomposed to the local level. All the functional requirements can be translated into the combination of the perception of objects and the verb (action). Basically, tasks can be defined as set of functional requirements in a CSO design by the assumption that the E- M-S (Energy-Material-Signal) flow is maintained. A fundamental portrayal of functional requirements in engineering design can be described as “Adverb” + “Verb” + “Noun”. 4.1.2 Task Field It is very important that enough information of the current situation is fully represented by the local agents. The limitation for such a modeling process includes: only local agents observe, and their understanding of the overall system is bounded; the decision making process is only limited to local cells, which means there may not exist a “super” brain agent which tells other agents what needs to be performed. The problem is how the system can perform and survive by pure localized agent-based parallel decision- making processes. Before giving the decisions that the local agents need to make, the first problem is how to present information such as localized functional requirements and the 55 environmental status so that a better representation may result in a better design and better understanding of the overall process. In classical AI and multi-agent systems, a goal for a particular task is shown as a desired state of the world. Meanwhile, there has been wide research on finding an optimal path to the goal state. Accordingly, an agent may have a memory to map between any world states. Preferences over various states are established based on an agent’s specialty. For example, a soccer agent will mostly prefer to score, will prefer less to stand with the ball in front of an empty goal, and so on. Accordingly, the preferences for the desired states can be given by the system designer. For example, if emergence of systems is contingent upon guiding agents in a certain way, then there is a need to provide system preferences for agents. A method to formalize the concept of state preferences or guidance is to assign each state a real number. In this research, the concept of field is being utilized to assign a value to states. The concept of field is needed to bring tasks and environmental constraints into the mechanical cells’ self-organizing framework. This is also the case in dynamical systems, where gravity fields are fundamental. To act accordingly, some fields are needed in which mechanical cells can self-organize. The main challenge here is how to properly incorporate field ideas into the world states so that it encapsulates the task requirements. Intuitively, the field of a state expresses the forces or gradients that are either applied on the system from external circumstances or is guidance towards a goal state (attractors) and against harmful states (repels) for the agent. mCells in the CSO framework have a wide range of state space, although as discussed above, there should be some mechanism to limit agent choices to guide their 56 emergence. For the mentioned reason, the concept of task field has already been presented in previous work (Chen and Jin 2011) where it is dependent on the environment, functional requirements, and sensory information of agents. As discussed in earlier work on CSO systems, although mCells have limited sensory information and possible actions, any functional requirement and any operation environment can be represented and sensed by local mCells. One parameter has been added to this previously defined term, which is the communication signal from other mCells. In most of the cases this signal is mainly some sort of help message from an mCell. This message could be regarding the survival of the cell or if an mCell finds a valuable entity in the environment that has not been sensed from the beginning by all agents. Definition 1 (Task Field and Field Formation): 𝑡𝐹𝑖𝑒𝑙𝑑 ∶=𝐹𝐿𝐷 ! (𝐹𝑅,𝐸𝑁𝑉) Equation 4-1 where, FLD t : field formation operator, FR is set of functional requirements of task, and ENV is set of environment constraints. In CSO systems, unviable states are represented as repelling fields. Particularly, if energy consumption or time is an issue for the system, field degree will be scaled based on the given constraints. Therefore, field can play an important role in the process, where having a very precisely articulated field can narrow down to show the optimal paths to get to the goal states while considering all the constraints. The information flow for agents should be consistent with the ultimate global effect. It is critical to understand the 57 task and design requirement very well from the beginning. Design requirements, if not properly formalized, may hinder agents’ attempts to reach a practical performance level. The next step is for agents to have sensor information, where they sense the task field and react to it. Since the main purpose of this research is to gain insight into designing a self-organizing mechanism for complex systems, and not the hardware capability of agents, there is an assumption of perfect sensing capability for agents without any noise. 4.1.3 Task Complexity The concept of task is essential to the CSO systems. The role of task is especially significant for agents in charge of accomplishing the task. In this framework, task complexity appears as an important concept. When designing a mechanical system, it is crucial that the complexity of a task be measured (Lysaght et al. 1989; Sheridan and Simpson 1979) due to the fact that complexity is a key factor in determining the workload. While investigating appropriate characteristics of task and a proper reliable definition of task complexity is a challenging process, many definitions of task complexity have been proposed. Within the literature review, definitions of task complexity developed by (Wood 1986) and (Campbell 1988) are most widely cited. In the first approach, (Wood 1986) studied the four distinct theoretical frameworks for task definition suggested by (Hackman 1969) in stimulus-response terms ("Task qua task"), 2) as a set of behavior requirements, 3) as a set of behavior description, and 4) as a set of abilities requirements. 58 Table 4: Task Complexity defined by Hackman 1969 Task Complexity Task qua task Set of Behavior Requirements Set of Behavior Description Set of Abilities Requirements His definition of task rests upon the idea that task complexity definitions should be only a function of the task itself, not performer dependent. Therefore the “behavior description” and “ability requirements” are both rejected and a combination of the “behavior as requirements” and “task qua task” frameworks seems to be more reasonable for the general theoretical foundation to develop and analyze the task complexity. He describes the building block of every task as three fundamental components: products, (required) acts, and information cues. He derived task complexity from three sources: 1) the number of different components associated with the task (component complexity), 2) the level of interaction between the components (coordinative complexity) and 3) the degree to which the relationships between task-related input and output cues change over time (dynamic complexity). And the ultimate complexity is the weighted sum of the mentioned complexity elements. Table 5: Task Complexity by (Wood 1986) Task Complexity Number of different Components Level of Interaction between Components Change of Relations over time 59 The second approach (Campbell 1988) likewise defines task complexity based mainly on task characteristics. The characteristics proposed are: 1) multiple paths, 2) multiple end states, 3) conflicting interdependence, and 4) uncertainty or probabilistic linkages. Table 6: Task Complexity by (Campbell 1988) Although both definitions appear to be different, the two approaches are merely related to characteristics of the task and not the nature of the performer. As in the present work, complexity should be defined for mechanical tasks; the first approach (wood) appears to be more suitable for the objectives of this research. Their concept is used to establish a new task complexity for CSO framework. 4.1.3.1 Action and Action Relation Complexity Task in CSO is a combination of verbs and objects. Task can be viewed as a number of functions and different objects involved in the process. Verbs in task definition normally represent the actions that need to be taken with agents. The number of distinct actions could be a measure for complexity. As the number of verbs (actions) associated with a task increases, the skills and information for a task also increase, simply because agents need to be more knowledgeable to be able to perform the task. Note that the actions need to be distinct; so there is one basic way to reduce the complexity: remove Task Complexity Multiple Paths Multiple End States Conflicting Interdependence Probabilistic Linkages 60 redundant verbs. In other words, the overlap of skill requirements for different actions should be eliminated. If agents know how to accomplish an action, the complexity of this action will not increase if agents do it over and over. Hence, it is important to consider different verbs in calculating the complexity. A general way to include action complexity is to sum distinct verbs used to describe a task. For a given task, in addition to the number of actions, there can be various relationships between these actions that must be maintained for the completion of the task. Examples include timing between actions (e.g., parallel, sequential, or specific delay) and number of relative occurrences. Action and action relation complexity is close to the definition described in (Wood 1986). This change in phase of agent action can add a fair amount of complexity to the system. The existence of these relationships requires coordination of actions within an agent and between multiple agents. This change in phase of agent action can add a fair amount of action relation complexity to the system. Definition 2 (Action and Action Relation Complexity): 𝐴𝐶= 𝑉 + 𝑟𝐴𝑐𝑡 !" !"# !"# Equation 4-2 where, V={v 1 , …, v n } is the set of all distinguished actions and 𝑟𝐴𝑐𝑡 !" is action relations between action (verb) i and j, which can be sequential or reciprocal. 4.1.3.2 Object Complexity As one of the main elements of task definition, objects can play an important role in changing the complexity of the task. In addition to the number of objects, the characteristics of the objects involved in a task, such as shape, dimension, and mass, also 61 contribute to the task complexity. Therefore the number of parameters used to describe the distinctive objects can be used to define the object complexity of the task. The more the parameters there are, the higher the complexity level is. SRBR mechanism supplies various evolutionary paths for the system, starting from any initial state. Since several path directions as a solution may be implemented by the system and these evolved emergent paths might have different situations in terms of number of functions to be fulfilled during the execution time, we use average number of object instances to encounter in all possible paths. We define object complexity of a task as: Definition 3 (Object and Object Relation Complexity): 𝑂𝑏𝑅𝐶= 𝑂𝑏𝐶 ! ! ! ! + 𝑂𝑅𝐶 !" ! ! ! ! ! ! = 𝑃 ! ! ! ! + 𝑂𝑅𝐶 !" ! ! ! ! ! ! Equation 4-3 where, |O| is number of unique objects involved in the task, ORC ij is the added relation complexity between objects i and j. |Pi| is the number of parameters for describing object i and therefore a set of attributes and values set of attributes and values: P ! = a !" ,v !" , a !" ,v !" ,… , a !" ,v !" . SRBR mechanism supplies various evolutionary paths for the system, starting from any initial state. Since several path directions as a solution may be implemented by the system and these evolved emergent paths might have different situations in terms of number of functions to be fulfilled during the execution time, the added difficulty brought 62 by relations between object instances to encounter by agents of all possible paths is used to calculate object relation complexity. Definition 4 (Object Relation Complexity): 𝑂𝑅𝐶 !" = A𝑑𝑑𝑒𝑑𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡𝑦 𝑟𝑂𝑏 !" Equation 4-4 rOb ij is the relation between objects i and j which is subjected to interpolation and definition of the task. rOb ij relation mainly defines the condition on objects’ locations with respect to each other and the difficulty that brings to the task which can include the distance from each other (for example two extremes are when they have to be connected to each other or keep some specific distance), positioning location (for example if one should always be on left of the other one, etc ...). 4.1.3.3 Dynamical Complexity Another level of complexity deals with environmental changes. When the environment changes, the task field for the agents will change. Depending on the degree of variation, an agent’s behavior for action and coordination should be adjusted. This dynamically generated shift for the agents contains both modifications of their action plus their coordinated behavior. Therefore, such dynamic complexity is captured by calculating the sum of differences across a certain time period for the above mentioned three complexity components, as described in (Wood 1986): 63 Definition 5 (Dynamic Complexity): The overall complexity is the weighted sum of the previously mentioned complexity: Definition 6 (Task Complexity): 𝑇𝐶= 𝑊 !" 𝐴𝐶+𝑊 !"#$ 𝑂𝑏𝑅𝐶+ 𝑊 !" 𝐷𝐶 Equation 4-6 Examples of how these complexity measures are applied and computed are given in the case study section. After defining task complexity in the CSO framework, the appropriate questions then become: what does the complexity of the task to be accomplished tell us about the design of a CSO system. What will complexity affect the most in CSO framework? What should be the compatible complexity of the CSO system to be able to accomplish the task? What other capabilities should be embedded in the system or agents to not only finish the task properly but also execute it in an efficient manner in terms of both time and energy consumption? 4.2 mCell Description To better design CSO system in terms of both efficiency and accomplishing more complex tasks, a new framework for CSO systems is proposed, and to further the discussion on this new design approach, a few examples will be illustrated. This section 𝐷𝐶= 𝐴𝐶 !!! −𝐴𝐶 ! + ! ! 𝑂𝑏𝑅𝐶 !!! −𝑂𝑏𝑅𝐶 ! Equation 4-5 64 will outline the system model and provide detailed descriptions for each part of the model. The main purpose of this research is to find an insight of agents’ decision-making processes and develop a self-organizing mechanism through which functional requirements can map to agent behaviors and provide agent’s behavior selection from a local cell point of view. 4.2.1 Individual Cell Model Agents in CSO systems must typically coordinate their actions to achieve complex system-wide goals. Agents own passive sensors that are limited to processing information and communicating. The information that reaches the sensors of each agent in a CSO system is typically distributed: located in different sections of the environment, the agents may observe spatially different information. They might receive the data within a different time span (temporally). Therefore agents are seeing the world state partially and from different aspects, which can highly affect agents’ decision-making processes. There are further features required for a mCell that make the application of CSO methodology quite challenging: Physically homogeneous: All the agents in this model have some physical attributes: sensing, communication, and actuator. Agents have a limited sensing range, and since they are physically distributed, the internal decision-making protocol may not be equal between agents. Initially, all the agents start with no communication or any control power. During system operation, some type of relationship among agents might be needed which may result in developing hierarchy among some portion of agents. For example, a more informed agent might want to lead others to a better direction. 65 Physically homogeneous: All the agents in this model have some physical attributes: sensing, communication, and actuator. Agents have a limited sensing range, and since they are physically distributed, the internal decision-making protocol may not be equal between agents. Initially, all the agents start with no communication or any control power. During system operation, some type of relationship among agents might be needed which may result in developing a hierarchy among some portion of agents. For example, a more informed agent might want to lead others to a better direction. Physically distributed: Since agents are typically allowed to pick a location in the environment, they are physically distributed. Resource Constraints: There are constraints regarding energy and time. It is not possible to let the system run forever to reach the desired functionality, hence requiring that they exhibit behaviors that cope with defined constraints. Other agent recognition: Agents are assumed to be able to recognize like-cells and sense certain information carried by those agents. Agents are able to distinguish other agents from possible entities in the environment such as obstacles or any other objects. No explicit modeling: Agents do not produce or maintain models of each other. Analyzing other agents’ behavior and generating a good estimation of other agents’ behavior is outside the scope of this research, as the main focus is on self-organizing rules and simple interaction among agents. Therefore, agents only react to the signals and informational field they receive from their environment. 66 Implicit and explicit Communication and Coordination: Agents are not receiving a big picture of the system, as they only have limited sensor capability. Cells do not carry the global state of the system, although as an exception, the constraints are embedded in them, which is originated from functional requirements and environment. More like awareness of cells from dangerous states within an environment act as a red flag to warn them about the possible danger. For example a human knows if he continues moving forward towards a cliff, there is a high probability for him to die. Each cell is assumed to be able to communicate wirelessly over a finite spatial range. Agents can receive information from and perform direct communication with other agents within their communication radius. Moreover they are capable of non-directed communication where they send out social gradients to the environment. These types of gradient messages are not limited to a specific set of receivers. There might be situations where agents are within communication range, but there might be obstacles or any object between them to interrupt the communication signals. Since the main purpose is to develop an insight into adaptive CSO systems, the amount of information that can be carried between agents in this situation is inspected and there will be more elaboration on this subject in later chapters. Cell models have been used in various researches as a model for agents and sensor nodes, and to mimic cells in biological tissue. In this work, a cell model is used to describe mechanical design components. The modeling starts with a mechanical cell definition in CSO systems as the basic elements of the system. In the CSO framework, mechanical components are treated as mechanical cells (mCell, i.e., agents). Although for a CSO system design, the appearance or the structure of its mCells may be different, a 67 mCell should be able to sense the environment and process material, energy and/or information as their actions. Following the previous work in CSO systems (Chen and Jin 2011), mechanical cell definition is as follow: Definition 7 (Mechanical Cell): mCell = {Cu, S, A, B} Equation 4-7 where Cu: control unit; S = {s 1 , s 2 , ...}: sensors/sensory information; A = {a 1 , a 2 , ...}: actuators/actions; B: designed behavior, or design information (see definition 4 below). From the sensory information, the self-organized mCells calculate all the sensor information, and based on their perceived information, choose a proper behavior out of sorted possible actions in the list. The process of mCells choosing an appropriate action is discussed in this section. Before describing the process in more details, some other concepts should be clarified. Definition 8 (State): State = {S C , A C } Equation 4-8 where 𝑆 ! ⊂ 𝑆 𝑎𝑛𝑑 𝐴 ! ⊂ 𝐴 are current sensory information and actions, respectively. State is used to represent the situation. It is the combination of the current sensor information Sc and current actions Ac. 68 The behavior set of each agent is defined as all the available actions when the agent is in a particular state. A behavior b is the designed action for given situations or states. The Cu of the mCell should be able to judge the situation and make decisions on next actions. The design information of a CSO system is the fully developed behavior for each mCell. Definition 9 (Behavior): b = {S E , A E } à A N Equation 4-9 where 𝑆 ! ⊂ 𝑆 𝑎𝑛𝑑 𝐴 ! ⊂ A are existing sensor information and actions, respectively; and A ! ⊂ A are next step actions. An mCell’s architecture copes with its internal properties. Capabilities of mCells, as the fundamental units of the CSO system, play a significant role in anticipation of system level competence. Along the similar line of thinking about task complexities mentioned above, and by focusing on the physical and effective features (Gell-mann 1995, Huberman and Togg 1986), the complexity of an mCell is considered in terms of the mCell’s number of actions, number of behaviors, and communication capacity (e.g., range and number of channels). Individual agent complexity is defined as follows: Definition 10 (Individual Agent Complexity): C !"#$% ! =N ! +N ! +C !"# Equation 4-10 where, N a is the number of actions, N b is the number of behaviors, C com is the communication capacity. 69 Summing all agent’s complexity give us system’s agent complexity: Definition 11 (System’s Agents Complexity): 𝐶 !"#$%& = 𝐶 !"#$% ! ! !!! Equation 4-11 where, N is the number of agents. 4.2.2 Satisfaction One important feature of a CSO system is that each agent is self-interested in the sense that they always seek attractions (i.e., attractors) that make them “happier.” It is this self-organizing behavior that makes the overall system robust and adaptive to change. However, such self-organizing behavior (i.e., decision-making mechanism) must be effectively guided so that structures, and therefore complexity, can emerge (see Figure 5 from (b) to (c)) and the overall system can be functional. In this research, the notion of satisfaction is used to capture the happiness of an agent in choosing its actions. Fundamentally, this notion acts as the connection between the field representation of task and agents’ actions. For a single agent, without considering the existence of other agents, its satisfaction can be defined as below: Definition 12 (Agent Satisfaction): 𝑆𝑎𝑡 ! (𝐵𝑒ℎ ! )= 𝐸𝑓𝑓𝑜𝑟𝑡 𝐵𝑒ℎ ! × 𝑓(𝑡𝐹𝑖𝑒𝑙𝑑 ! − 𝑡𝐹𝑖𝑒𝑙𝑑 ! ) Equation 4-12 where, Beh i ={beh 1 ,…,beh n } is the set of behaviors available to agent i, Effort is the estimation of effort of agent and f is a function of effectiveness with respect to the current tField. 70 An individual agent’s satisfaction is a function that maps all available behaviors of the agent to a value representing the agent’s satisfaction and the effectiveness of that behavior by taking into account agents’ effort to execute that behavior, and the perceived task field distribution. The higher-level notation for overall system contentment, the system satisfaction, Satsys, is a function of the satisfaction of the n elements forming it (𝑆𝑎𝑡 !"# = 𝑆𝑎𝑡 !"! ! ! ∈! ). Formally, system satisfaction is the global emergence at each time step and is measured based on how the dynamics of the system correspond to the functional requirement. The larger the satisfaction of an agent within a state, the better the state is for that agent. Formally, for two states s and s’: Sat(s) > Sat(s’) if and only if the agent prefers state s to state s’, and Sati(s) = Sati(s’) if and only if the agent is indifferent between s and s’. The values of an agent’s satisfaction for each possible behavior in the current task field constitute a profile of probabilities of executing all possible behaviors. This is identical with FBR described in (Chen and Jin 2011). The organization and coordination problem in CSO systems can be roughly expressed as forcing the system to be in the appropriate state space starting from any initial conditions inside the set, by proper assignment of the feedback in the form of rules and relations. A system consists of state variables and regulation rules. State variables are subject to changes under the impulse of agents, and regulation rules act like a feedback controller for the system. It is required to introduce certain controls or regulations for the agents to choose proper actions in different situations. While an agent takes actions in the 71 system, it should select a plan that can match the system. If an agent’s behavior cannot match its organizational norm, it may collide with other agents’ actions during the process. Therefore, as the set of restrictions on agent actions, the social rules should be established to satisfy the organizational needs in CSO workflow systems. Therefore, how to devise regulation rules for the systems is investigated to satisfy those constraints of organization, thus minimizing conflicts among agents and actions, and maximizing cooperation and unity. Based on the problem definition, rules and suggestions need to be transmitted to the agents. Note that in a multi-agent system, there is a possibility that a state may be pleasing to a specific agent while undesirable to another agent. This is beyond the scope of this research due to the homogeneity assumption for agents. 4.2.3 Social Rule Due to the limited information scope of agents with respect to their environment, agents need some means to compensate for their limited knowledge. Increasing the emergent complexity and level of sophistication of a multi-agent system requires embedding order into the system, as indicated in Figure 5. In this research, order is created by introducing social rules among agents. To adjust the behavior of agents in order to reach a higher level of harmony with system-wide goals, in addition to task field, social constraints in terms of rules and relations are employed. Structuring in CSO is an abstraction used to describe the overall architecture of a CSO system and to demonstrate the constraints enforced on the agents. More specifically, graph theory principles is 72 applied to capture the interactions among agents. Assume G is a set of all possible graphs that can be formed by N agents Ag = {a 1 , a 2 ,…, a N }. Definition 13 (Social Structure): G(t) = (N, E(t)) Equation 4-13 where, N is the number of agents, N b is the number of behaviors, E(t) is the links of interactions/relations between agents at time t. As shown above, social structure G(t) is a function of time and is directly dependent on the evolution of agents’ interactions. For simplicity, agents are assumed to be constant nodes in the graph while edges between the nodes change over time resulting in a dynamic structure. The ideal situation is to keep the topology of agents frozen throughout the process and adapt swiftly when the task and/or environment changes. In CSO systems, the social structure represented as a connectivity graph is realized by defining social rules that specify how agents interact with each other. These social rules can be general (e.g., “move in a similar direction as neighbors) or task specific (e.g., “move closer to neighbors on the edge of a box”). A social complexity measure of agents is defined based on their connectivity graph that originates from social rules. This type of graph complexity is notably similar to the complexity measures defined in molecular chemistry. As mentioned in the literature (Randi and Plav 2002; D. G. Bonchev and Rouvray 2003; Danail Bonchev et al. 1983), structural complexity is inherently different from descriptive complexity. 73 (Randi and Plav 2002) introduced the notion of extended connectivity to attain a scheme for labeling of atoms in a structure. The complexity of a graph has been suggested as an augmented valence sum (AVS) which is the sum of augmented valences of all vertices of a graph. Although AVS seems to be a proper measurement as it corresponds to the increase in size and density of a graph, an alternative approach is considered to graph complexity shown in earlier studies (D. Bonchev 2003a; D. Bonchev 2003b; Danail Bonchev 2004) that is more suitable for our purpose. The vertex degree magnitude-based information content I vd , as shown in the analysis, satisfies the standards for measuring a graph complexity. It is directly related to the connectivity and other complexity factors, such as the number of branches, cycles, cliques, etc (Danail Bonchev and Rouvray 2005). Definition 14 (Social Complexity): SC= d ! log (d ! ) ! !!! / N Equation 4-14 where, d i is the degree of each node i (how many other agents are communicating with agent i). 4.2.4 Social Rule Based Regulator The main objective of this research is to explore ways to facilitate emergence of order and therefore complexity (i.e., to move from (b) to (c) in Figure 1) so that a CSO system can deal with more complex tasks. More specifically, dynamic social structuring methods can be devised to help guide self-organization of agents. A social rule based 74 behavior regulation approach can be taken and various local and bottom up social relations to achieve dynamic social structuring can be explored. Generally speaking, the deficiency of disorder or disorganization can be divided into two categories. One is “conflict deficiency” and the other “opportunity-loss deficiency.” For simple tasks (e.g., pushing a box to a destination in an open space) where an individual agent’s “goal” is mostly consistent with the system goal, the agents’ effort can additively contribute to the system overall function. When tasks become more complex, conflicts between agents’ actions (e.g., pushing box in opposite directions due to space constraints) may occur and cooperation opportunities (e.g., pushing box in opposite directions at different locations in order to rotate a box) may be lost. In order to minimize the conflict and promote cooperation opportunities, social rules and social relations can play an important role to specify which actions should be avoided and which actions are recommended together with corresponding conditions. A social rule is a description of a behavioral relationship between two encountering agents that can be used by the agents to modify their otherwise individually - rather than socially - determined actions. Two agents acting on a given social rule are said to be engaged in a social relationship. Based on definition 13 mentioned above, when agents are engaged in social relations by following social rules, social structures emerge, leading to more order and higher complexity of the system. The conditions are often task domain dependent, although they can also be general. The following mathematical representations formulate this relation: 75 Definition 15 (Social Rule): sRule = <C, ForA, RecA> Equation 4-15 where C is a condition specifying a set of states; ForA: forbidden actions for states specified by; RecA: suggested action. Social rules defined above introduce relations among encountering agents. It is conceivable that when an agent encounter neighbors and neighbors encounter their neighbors the cascading effect may lead to a large scale network structure with varying densities. The distribution of such densities can be defined as a social field in which every agent has its own position, and the awareness of the social field allows agents to reach (i.e., be aware of) beyond the encountering neighbor agents. Exchanging information among agents should be systematic, as providing too much information for agents can be confusing and eventually hurt the overall functionality. Social field acts as a communication protocol for agents to transfer necessary information. Definition 16 (Social Field): sField = FLDs (sRule) Equation 4-16 where FLDs is the field formation operator; sRule is a social rule. Social field adds another layer to the design of CSO systems as a helpful mechanism to ensure synergy in the system. To measure the complexity of integrated rules in the system, the number of conditions where any rule can be invoked is considered: 76 Definition 17 (Rule Complexity): CRule = # of conditions specified in rule definition Equation 4-17 In this research the effect of social field is explored and the focus is on allowing agents to adjust their otherwise individual satisfaction behavior, based on applying social rules to the encountering neighbor agents. If the behavior of an agent is aligned with system satisfaction, which means it matches governing rules and relations, there is no need for agents to change their selected behavior. On the other hand, if information received through social field or relations matches the condition specified in social rules, agents should obey the rules to justify their action up to the point where no more rules can be applied to their behavior. This social rule based behavior regulation (SRBR) can be defined as follows: Definition 18 (Social Rule Based Behavior Regulation): SocSat !"# ! =SRBR(Sat !"# ! ; SR ! ,NA ! ) Equation 4-18 where, SRBR is social field based regulation operator for behavior correction; Sat !"# ! is tField based behavior satisfaction (see definition 10); SR i is the set of social rules; NA ! is the set of encountering neighbor agents; SocSat !"# ! is socially regulated behavior satisfaction. Definition 19 (Total System Complexity): SysC=𝑊 !"#$%& 𝐶 !"#$%& +𝑊 !" 𝐶 !" +𝑊 !" 𝐶 !" Equation 4-19 77 System complexity is composed of agents’ complexity and structure complexity that consists of relations between agents (social complexity) and complexity of relations (rule complexity). Based on the nature of the problem weights associated with each complexity can fluctuate. In this thesis, we examine the effect of each complexity on the system performance by varying different combination of strength of each system complexity components. The above is a general definition. To apply SRBR, an agent needs to 1) generate its independent satisfaction profile through FBR (see definition 10), 2) identify and communicate with its neighbors, 3) possess social rules, 4) know which rule to apply for a given situation, and 5) know how to generate new social satisfaction behavior. All these steps will transfer to a valid behavior profile for agents. Each of the 5 steps can be task domain dependent. 4.2.5 Adoption Rate The purpose of determining adoption rate is to control use of topology and the level of agents’ interactions. Policy (which is used interchangeably with adoption in this thesis) on top of topology controls the degree of relationships among nodes to constrain the flow of information. Policy was developed as an attempt to incorporate social related constraints on agents’ interactions and communication. In this thesis, I explore how policy implementation mechanisms can impact the performance associated with a given number of agents and system characteristics. Analysis of system performance shows that system complexity should correspond to task complexity allowed by tuning adoption rate and topology that is caused by agent interrelations. It is shown that the topology of the 78 system strongly affects the evolution of cooperation. This dissertation examines the role of introducing inter-relation topology and implementation of adoption rate in design of CSO systems and their impact on the process. This organization process can be roughly expressed as forcing the system to be in the appropriate state space starting from any initial conditions inside the set, by proper assignment of regulation rules. Imposing rules on the system ensures that the selected behavior should not violate other agents’ actions and be consistent with specified social rules for a problem domain. This a representation of a self-organizing mechanism, through which agents’ individual actions lead to a desired system functionality. Not only system functionality but also structuring emerges from individual behavior and relations. 4.2.6 Dynamic Process Information Finally, an information measure of system progress is developed through the process. This measurement is based on the Shannon entropy and defines information as the reduced entropy of progress rate of the overall system relative to the maximum entropy that can exist in a system with the same number of agents and uniform progress rate in the process. The underlining principle of this measurement comes from the fact that if a central controller with full knowledge of the system governs the agents in selecting their behavior, no matter how complicated the situation is, agents would be able to maintain a close to steady progress rate throughout their execution. By means of this measurement, the aim is to identify circumstances where more information is needed for agents to increase their adaptability and compatibility with the situation. The environment 79 of operation is divided into n states and the dynamic information process can be calculated after accomplishing each state. Definition 20 (Dynamic Process Information): DPI ! ! = t ! ! × [ ! log 1 i − t ! ! T log ( t ! ! T )] ! ! Equation 4-20 where, S= (s ! , s ! ,… ,s ! ) is set of n states; i is the ith state where system has passed on its path to desired functionality; T is the total time the system has been operating; t ! ! is the time spent in the state i; 4.2.7 Emergent Structures Structuring in CSO is an abstraction used to describe the overall architecture of a CSO system and to demonstrate the constraints enforced on the agents. Structuring may arise mainly from the following: • Relations and interactions • Defined relations and interactions among agents where their involved relations affect agent’s behavior. • Rules among agents • For a certain situation, to minimize the conflict between agent behaviors • Regulation rules provide selected behaviors for agents to pick based on the alignment of the behavior with other agents and with overall system requirements. • Resources 80 • When agents are sharing a resource, it puts a constraint on their action selection based on their consumption of that particular resource Defining rules that govern agents’ behaviors and authorize interactions between the individuals is problem dependent and will lead to forming a structure. 4.2.7.1 Formation and Transformation Structuring consists of two phases: formation and transformation. Formation is the process of constructing the structure, and transformation is when the need for a conversion or an evolution arises. When perturbations happen either in the environment or functional requirements, the current single structure and configuration of agents might no longer be an appropriate solution for the system. These disturbances are typically challenging. When instability of the system passes some threshold, individuals should change their state trajectory in order to adjust their relations and general structure. The following section discusses how these steps can be implemented and how the above-mentioned concepts can be applied. 81 5 Case Study The objective in this case study is to explore and demonstrate how social rule based behavior regulation can increase the order, and therefore the complexity, of the overall system and how this increased order is essential for dealing with more complex tasks. The case study demonstrates how to deal with more realistic tasks. A two-field mechanism is utilized in a CSO system, and the emergence of structure based on defined relations and rules is simulated. To pursue this objective, a multi-agent simulation system is developed with the intention of addressing the following hypothesis: • H1: Importance Hypothesis: Task Driven Social Structure is the key aspect to be effective and efficient, and should be the central focus of design • H2: Design Hypothesis: A Task Driven Structural model can be developed and applied to CSO systems for adaptability and efficiency Figure 8: Experiment Design Figure 8 illustrates the design of a simulation-based experiment. As independent variables, three kinds of strategies were explored, with social structuring (SRBR), without social structuring (FBR) and applying policy in social structuring (compliance). Time duration (# of time unit) Simulation Independent variable Dependent variables Behavior regulation Strategy (SRBR, FBR) Success rate (%) Task (level-1, 2, 3) Number of agents Total effort (agent-distance) Dynamic Information Entropy 82 Control variables are used to test different task and agent situations. Three tasks were tested, pushing a box without an obstacle (level-1), pushing a box with an obstacle (leve- 2) and pushing a box with two obstacles (level-3). For all settings, success rate, time duration (number of steps), and total effort per agent (total distance traveled by the agents divided by the number of agents) as dependent variables are measured. The goal of this research is to provide a better insight towards design of any complex adaptive system. In this section the new proposed mechanism for CSO systems is examined, and in the next chapter three case studies are presented and the results are explained. The first set of case studies is designed to investigate the concept of two-field approach and the second set is to demonstrate the effect of complexity of social field on overall system performance based on the NetLogo platform (Wilensky 1999), a popular tool used by researchers of various disciplines. 5.1 Problem Statement The system is composed of n agents: 𝐴= 𝑎 ! 𝑖= 1,… ,𝑛 . Initially no constraint is imposed on the agents. Agents start from random initial points with the purpose of moving a box toward a destination. Guided by the task-field of attraction and repulsion, each agent is supposed to contribute to the correct movement of the box in a way that the emergent movement of the box is toward the goal. In addition to the main mission, there could be time and energy constraints on the system for agents to consider. In order to gain better coordination from the individual contributions, regulation rules have been devised for this problem to make sure there is no conflict for agent behavior. Although this strategy (i.e., “non-social”) works well for “open-space with a few 83 obstacles” (Chen and Jin 2011), when more constraints, such as “wall” and more “obstacle”, are added, new strategies (e.g., “social structuring”) are demanded due to higher task complexity. 5.2 Problem Approach and Dynamic Social Structuring Agents need to figure out a way to spin and move the box within the defined environment. Therefore, the functional requirement can be expressed as below: FR1 = “Move the box to the destination point (G)” FR2 = “avoid obstacle while moving” FR3= “Spin the box if required” 5.2.1 Task The box-moving task used for the case study is illustrated in Figure 9. Multiple agents intend to move the box to the destination or goal “G”. Given that the channel becomes narrower, the agents must rotate the box to horizontal as it gets close to the entrance of the narrowing part. Further, there can be an obstacle “obstacle” in the way. Box obs agent Attraction field wall wall Figure 9: Box-moving Task used in Case Studies G 84 The specific tasks can be expressed as follows. T1= <Aim><Goal> T2 = <Push><Box>to<Goal> T3 = <Move Around><Box> T4 = <Avoid><Wall> T5 = <Avoid><Obstacle> Before describing the new approach that is implemented in this problem, the complexity of the task must be evaluated. In this case, since all the descriptive complexity of objects involved in the system is considered, the verbs associated with objects that are executed by agents are also considered. There are four distinctive verbs and one reciprocal (i.e., move and rotate) and two sequential activities (i.e., aimàmove, and aimàpush) that are interacting with each other. Agents attempt to be away from the wall where avoiding can be rephrased as moving away, which cause this action to fall into the same category as sequential activity of aimàmove. Therefore, the action and action relation complexity consists of three interconnected actions resulting in having the complexity of seven in total for this portion. The diagram of activities shows the following: Figure 10: Activity Diagram for case study Push Aim Move 85 The object complexity is calculated for all the objects involved in this task. Descriptive complexity has been used that captures the amount of information (bits) required to characterize each object. Three parameters: (x, y, r) has been used to describe target and obstacles, which are x and y coordinates of their center and the radius associated with their spread length. The characteristics of the box include its location (x, y), dimensions width and length and its orientation angle. For simplicity, the angle is considered to be 90 degrees. Thus the objective complexity sums up to four for this item. Wall can be described by three points and a line passing each node, resulting in complexity of six suppose each node can be seen as a two dimensional data (x, y). Therefore, Total descriptive complexity of objects adds up to 13 for no-obstacle case and 16 for one-obstacle and two-obstacle cases dues to the added obstacles. Object relation complexity is calculated based on the representation of problem and distribution of instances of all the objects in the environment. The difficulty of agents moving the box through environments is based on the distance between two objects constraining and effecting the attempt of agents and direction of their movements. In this case, object relation complexity is proportional to the distance between objects and walls to be avoided with respect to the minimum characteristic of the box to be carried (its width) in an emergent path towards goal. Average of object relation complexity in all possible paths is the final object relation complexity measure. ORC for each emergent path= 1 Dist(Obj ! ,Obj ! ) w !"# !"# ! ! Equation 5-1 86 In no obstacle case, there is only wall-wall relation and one path towards goal, which leads to objective complexity of 0.45 (1/ (5.794w/w) + 1/ (3.35w/w)). In the one obstacle case study, there exist two identical paths; each path has 4 areas between objects to path that includes both obstacle-obstacle, wall-wall and wall-obstacle relations. There are two obstacle-wall distances (3w, 2.67w) and two wall-wall distances (5.8w and 3.35w) to pass, which make it, adds up to 1.154 for object relation complexity. Adding another obstacle provides two different possible paths to get to the goal. In the first scenario there are two obstacle-wall distances (3w, 2.26w), two wall-wall distances (6w and 3.353w) and one obstacle-obstacle distance (3w) to pass, resulting in 1.575 and another path of two obstacle-wall distances (3w, 2.5w) and two wall-wall distances (6w and 3.353w) which gives 1.184 for object relation complexity. The maximum object relation complexity becomes 1.575. Total complexity is the weighted sum of mentioned complexity measurements. Weight of one for object and action complexity and 10 for object relation complexity has bee used leading to the total complexity of 24.5 for the “with wall” situation, as indicated in Table 7. Based on a similar calculation, the “wall + obs”, “wall + two obs” situations have complexity values of 34.53 and 38.75, respectively, shown in Table 7. Table 7: Complexity measures of various box-moving situations Situation 1: With Wall 2: With Wall + Obs 3: With Wall + 2 Obs Complexity 24.5 34.53 38.75 87 To better enhance the argument, the complexity of two recent previous works done in CSO is calculated. First in Chen’s work (Jin and Chen 2013), a task consists of the following combination of verbs and objects: T1 = <Aim><Goal> T2 = <Move><Box>to<Goal> T3 = <Avoid> <Obstacle> Aggregating number of verbs (3) and action relations as illustrated below is one sequence of action, gives us 4 for action complexity. Objects involved are goal, obstacle (x, y, r) and box. As the box in this case has the same width and height with 90-degree angle, the object complexity is calculated as 3 (x, y, l) that add up to 9 for object complexity. In this case if an example of two obstacles is considered with the same distance calculated for complexity of new approach, object relation complexity would be 0.9. Thus total complexity would end up with of 18 for this problem definition. Figure 11: Activity Diagram in right: Chen’s (Jin and Chen 2013); left: Chiang’s (Chiang and Jin 2011). Following the same procedure in Chiang’s case, here are the combinations for task: T1 = <Sense><Neighbors> T2 = <Move>with<Neighbors> Aim Move Sense Move 88 There is no object and object relation complexity, as there is no real object to deal with. Action relation complexity is one sequential activity among agents. Therefore, two verbs, and one activity lead to a total of three for action complexity. 5.2.2 Task Field By the assumption that entities in the environment are within an agent’s sensor range and can be sensed perfectly by the agents, the task field can be produced. A task field is generated to transform the functional requirement and environment to useful information for agents’ decision-making. The task fields include the attraction field from the “goal” and the repulsion fields from the walls as well as the obstacle if present, as indicated in Figure 12. For the “goal” field, a gravity-like field is applied, and for the “walls” and the “obstacle”, a gradient-based repulsion distribution is introduced to provide “warnings” of collision as agents get closer to them. The gradient distribution of the constraints (i.e., walls and obs) together with the sensory range of agents determine how much “ahead” agents can predict the collision and find ways to avoid it, although this feature is not examined in this research. In this simulation study, higher positions (i.e., higher value) in the field are more desirable to agents. For moving the box, an agent always tries to find a “low field position” around the box and from there to move the box toward a “high field position” which is often, but not always, the “goal” position. a potential field is used for the goal, the same description applied to gravity, electrical and magnetic fields. The description is provided as follows (assuming the source is “point”): Attraction Filed=αe !! Equation 5-2 89 Where r is the radial distance from the goal position. For the walls and obstacle, starting from the first layer of their boundaries, the negative field begins and gradually decreases with respect to the perpendicular deviation from the tangent of the connection. Figure 12: Illustration of Task Field Note that at the very beginning agents are assigned random initial position to start with. Before agents start to move the box towards the goal. As their first step is to go around the box and support it. The generated task field operates as a mediator to guide them in the direction towards the box following the same equation described for the target. In a sense that agents examine the surrounding states around them and move to the one with higher field until finally they reach the perimeter of the box. Once they reach the box their task changes to moving the box towards the defined goal. 90 Figure 13: Field generated to reach the box As the dynamics of the box depend on agents’ behaviors, unpredictable behavior of agents creates an indeterminate dynamic of the box. The box dynamic is illustrated as follows: (x !" ,y !" ,θ) !!! =φ (x !" ,y !" ,θ) ! ,b ! ∀i∈ A Equation 5-3 where φ is a function of the location of the box at a previous time and x !" ,y !" and θ are x and y coordinates of box and its orientation respectively. 5.2.3 Individual Satisfaction Agents’ responsibility is to move the box towards the goal given the provided information through the task field and additional knowledge by the social field. Hence, for agents to push the box to the higher field, occupying lower field areas around the box is more demanding. Every time step, agents can calculate locations close to the box with minimum task field. Meanwhile agents consider their effort to move to the new location. Given that, agents evaluate their effort in reaching new locations. For example, if the 91 difference between the field of their current position to the field of the new position is not larger than a threshold, they simply pick the closest available lower field. An agent’s satisfaction of its chosen behavior depends on the field value of the new location as well as its distance. Sat ! (beh ! )= 0, ∆TF !"# ! →!"# ! > 0 1 Dist !"# ! →!"# ! , ∆TF !"# ! →!"# ! < 2 −∆TF !"# ! →!"# ! , Otherwise Equation 5-4 After agents prioritize their behavior purely based on their desire and task information, it is time to check other agents’ actions in the system to avoid any inconsistency. 5.2.4 Social Rules and Social Field As mentioned above, social rules usually are designed to allow agents to avoid conflicts and/or to promote cooperation. In this case study, the social rules are set to provide guidance for agents to become aware of, and subsequently avoid, potential conflicts. Figure 15 (a) and (b) illustrate possible force & torque conflicts between agents i and j, respectively. 92 Due to the fact that agents’ awareness of the system is very limited, to better coordinate their actions, social rules become very handy. Agents send information about their location and their standpoint on the field through the Social field that is propagated vertically and horizontally via agents along their force direction to ensure that other agents know about the existing forces, and perpendicular to their force direction to inform others about torque in the system. If an agent is facing this information and it evokes a specific condition within the rules embedded in it, it is an order to modify its selected behavior to be in alignment with the rest of the system. Otherwise, agents can ignore the signals and keep their location. 5.2.5 Social Rule Based regulator To facilitate description of rules, the “box neighborhood” is introduced by defining 6 zones, as indicated in Figure 16. Agents are aware of their location in terms of which zone they are in. Furthermore, they can broadcast their location information and field density value to neighbor agents. The following communication rule is considered: Social rule 1 (communication rule): <condition: enter box neighborhood> <recommended action: broadcast [location] and [field strength]> When an agent receives broadcast information from an agent in the neighborhood, it will attempt to determine if a force conflict or a torque conflict exists and then decide if i j i j i j (a) Moving force conflict (b) Rotation torque conflict Figure 14: Possible conflicts of agents i & j; and box neighborhood 93 it will take the recommended actions provided by the following conflicting avoidance rules: Social rule 2 (force conflict rule): <condition: force conflict> <forbidden action: push in opposite-direction in opposite zone> <recommended action: find a new location> Social rule 3 (torque conflict rule): <condition: torque conflict > <forbidden action: push in opposite-direction in opposite zone> <recommended action: move to next neighbor zone> A message received by an agent, if it contains any information regarding a lower filed, implies the obligation for the agent to move towards the source of that field, proportionally to the strength of the pressure created by social field. The number of agents involved in sending social field, as well as the difference between an agent’s field and the collected lower field can both affect this strength. 94 Figure 15: Social Field representation with agent j in a lower field sending information to the possible existing agents in comparable conflict zones Agents have the option to ignore any or all of the above three rules. When the probability for agents to follow the rules decreases, the system is called less socially active, and otherwise more socially active. 5.3 Simulation In this chapter, how social rules among agents can influence CSO system performance with increasing task complexity is investigated. The effect of the dynamic social structuring approach against two different contexts is explored; first the effect of complexity of task in addition to number of agents involved on the self-organizing functionality of CSO systems is examined. For functionality, three different performance measures are explored: total time to finish a given task, effort per agent during the process within the successful runs, and success rate. Effort per agent reflects the average i j Field +Location 95 energy consumed by agents and is measured by dividing the total distance travelled by all agents while finishing the job by the number of agents involved in the system. Two types of social effects are investigated, complexity of the rules (e.g. complex, simple) as well as strength of applied policy (e.g. less, more social). As mentioned before, task complexity increases by a value of two when an obstacle is added to the environment. In this thesis, I refer to task complexity of the “with wall” situation as level-1 task, “with wall and one obstacle” as level-2 task and “with wall and two obstacles” as level-3 task. The benefits of implementing social structuring for CSO systems when task complexity increases is presented, not only performance-wise but also in some cases as a necessity for the system to successfully accomplish the task. All results indicated in the graphs are averages of 25 simulation runs for that specific setting. All the assumptions through the simulation and the results are described in detail. 5.3.1 Simulation Environment It is difficult to analyze highly complex systems with mathematical theory due to the numerous unpredictable interactions among agents within the system. Computational methods are more relevant to be used in this context. While equation-based models create useful predictions about the system behavior, agent-based models are a natural way to describe systems characterized by many levels of interactions. As mentioned before, one critical difference is that agent-based models can capture emergent phenomena that mathematical models are not capable of (Tang, Parsons, and Sklar 2007). Therefore in this research agent-based software called NetLogo is used. NetLogo (Wilensky 1999; Wilensky 2001) is an open source multi-agent programming language created at the Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern 96 University. It has been used across a wide range of disciplines and research levels. The simulation study is done with 2-dimensional space, but can be extended to a 3-D space. Each agent in the simulation is considered as an individual thread. Therefore agents are not on parallel threads. The simulation runs in discrete time where at each time step, agents sense the environment, communicate, obey social rules if necessary and finally take an action. In the following section, the impact of dynamical structuring on performance in the context of number of agents and the level of task complexity is explored. 5.3.2 Simulation Assumptions As mentioned before, there are some assumptions for agents to better communicate their location and field. The area around the box is divided into six regions; each region contains some agents. When agents send information regarding their situation, instead of sending the exact location, they send the region to which they belong. However, in some cases, the box acts as an obstacle that can block information from passing through. The field is generated regardless of the existence of the box and can completely pass any object including the box. Agents can fully communicate with other agents within their range of vision, which means they can know any information from another agent as long as they are in the same region. 97 Figure 16: Six regions around the box; agents send information about the region they belong to Change in the position of the box, which consist of moving in the x and y directions followed by a rotation, is the result of agents’ locations and actions around the box. The total movements of the box do not exceed 1 step each time. Also, the maximum possible rotation for the box is 45 degrees. The amount of rotation is calculated based on the proportion of the agents causing the rotation. Even when the box is angled, agents’ force is parallel to the main axes. The agents only apply normal forces to the box. 5.4 Simulation Results In order to illustrate the advantages of the new approach in CSO system, the performance of new approaches with the field based regulation (Jin and Chen 2013) approach is compared. For agents to behave comparably with previous method requirements, agents tend to occupy areas around the box with lower field, which leads to moving the box toward the higher field and ultimately towards goal. Therefore, no social rules or 0% social policy is implemented in the simulation. 98 Applying two distinctive rules in terms of their complexity to govern and modify agents’ behavior is examined. Within each degree of rule complexity, the value of having various adoption rates of rules that is the respect level of agents toward given rules is examined. It has been demonstrated that even though this new approach is beneficial, identifying proper rules can make a difference in the outcome of the system. First applying strong social rules are investigated and the simulation results of full social (100% policy) and no social (FBR; 0% policy of social rule) based on various numbers of agents are compared. 5.4.1 Strong Social Rule Results As mentioned, complexity of rules is measured based on the number of conditions described as part of the rules. The complex rule algorithm is illustrated in pseudo code in the following. InCross = Agents located across the box from current push InParal = Agents located in parallel with current push on the other side of the box The rules based on the defined terms are described as follows: If number of agents InCross > 0 [ Ifelse field of current agent >= field of InCross [ If field of InCross <= field of InParal [ If field of exact opposite location < 0 [ask InCross agents to be fixed] Move to InCross location proportional to the number of agents in InCross ] If field of InCross > field of InParal [ Ifelse (difference between field of current agent and field of InParal | <= 2) 99 [ [ Move to middle of the current side of box ] [ Move to InParalel location proportional to the number of agents in InParalel] ] ] ] [ If ( field of InParal <= field of current agent) [ Ifelse (difference between field of current agent and field of InParal | <= 2 and number of agents in InParal != 0 ) [ [ If ( field of InParal < 0 ) [ Move to middle of the current side of box ] ] [ Move to InParalel location proportional to the number of agents in InParalel ] ] ] ] Once agents pick their desired location based on the field of the new location as well as distance to that location, the presented rule determines their next action with respect to the field they receive from other agents. Even though agents receive information from two regions around the box, the other regions remain unknown. Thus agents adjust their selected location based on reachable information. As an example, two consequence graphs are shown below: First, the performance on level-1 task is examined. Here are the screenshots of a simulation of 25 runs for level-1 task, strong social and 12 agents setting: Time Step: 000 Time Step: 000 Time Step: 040 100 Time Step: 070 Time Step: 080 Time Step: 090 Time Step: 110 Time Step: 140 Time Step: 150 Time Step: 160 Time Step: 170 Time Step: 200 Figure 17: Screenshots of a simulation of 25 runs for level-1 task, strong social and 12 agents setting. Figure 18 illustrates the comparison of effort per agent throughout the process and time duration for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with a varying number of agents. As the task complexity is manageable with different strategies, the success rate for non-social strategy (i.e., no social rule & no structuring) and social is 100%. 101 Figure 18: Effort and time duration comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents The change of social complexity over simulation time in a typical simulation run with social structuring strategy and 12 agents are shown in Figure 19. As shown in the figure, social complexity increases when agents start to communicate with each other by following social rule 1 and “help” each other by following social rules 2 & 3 when rotating the box in the middle of the process. Social complexity through social structuring varies over time; it increases when needed by the task situation (rotating the box) and decreases when the situation is resolved. This task driven variability is the key difference from the agent complexity obtained through adding more agent-power. While adding more agents somehow relies on “randomness” to increase the success rate and consequently loses efficiency, social rule based self-organization builds competence through local, bottom-up but explicit structuring efforts. 0 100 200 300 400 500 7 9 11 13 15 Effort/Agent Social NoSocial 0 1000 2000 3000 4000 5000 7 9 11 13 15 Time Social NoSocial 102 Figure 19: Social complexity during the process of moving box towards goal with strong social strategy and 12 agents Adding more agents increases the overall system complexity, resulting in less distance traveled and time spent in both social and no social scenarios. Applying policy to the structure has not shown much improvement of the performance (Figure 20, 21). Increasing the number of agents helps more with no social, and as the number of agents increases, the difference between social and no-social and the various percentages of applying social rules among agents (various ranges of strength) fade away and become less noticeable. 0 2 4 6 8 10 12 14 0 200 400 600 800 1000 1200 Social Complexity Social Complexity 103 Figure 20: Effort comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents Figure 21: Duration time comparison for social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents The dynamic process information of when strong social rules are imposed as well as when there are no explicit rules defined between agents are calculated. The measurement result of 162.1816838 and 1886.363026 are achieved respectively. The difference between analyzed values is an obvious indicator of the information requirements of the system in order to achieve desired goals in a more efficient manner. 0 50 100 150 200 250 300 350 400 450 7 9 11 13 15 Effort/ Agent Social NoSocial 70%social 50%social 30% Social 10% Social 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 7 9 11 13 15 Time Social NoSocial 70%social 50%social 30% Social 10% Social 104 To further explore how more complex tasks demand social structuring, simulations for the “with wall + obs” situation is carried out. The task complexity measure for this situation is 34.53 (see Table 7). Here are the screenshots of a simulation of 25 runs for level-1 task, strong social and 9 agents setting: Time Step: 000 Time Step: 035 Time Step: 040 Time Step: 045 Time Step: 060 Time Step: 065 Time Step: 070 Time Step: 075 Time Step: 080 Time Step: 082 Time Step: 085 Time Step: 087 Time Step: 093 Time Step: 097 Time Step: 100 Figure 22: Screenshots of a simulation of 25 runs for level-2 task, strong social and 9 agents setting. 105 The social structuring approach proves to be more reliable and the success rate remains 100% for all agent number settings. The increase of system complexity from adding social rules, and consequently social structures, has made the system more effective to deal with complex tasks. It can be seen in Figure 23 that when agents are fewer (7, 9) and more (15) no social reaches maximum success rate. Figure 23: Success rate comparison for social (SRBR) and non-social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents Figure 24 shows the comparison of total effort and time duration for completed (i.e., The difference between social and no-social performance in terms of both time and effort per agent) is clear as the added rule complexity increases system complexity and makes it more compatible with the given task complexity. However, it is interesting to see that for the 9-agent case, the absence of social rules and structuring has made the system almost as efficient as a system with structuring. In this specific setting of number of agents and level-2 task complexity, social drive seems to be consistent with no-social drive. Agents with no social relations only following lower field can be perceived as 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate No social 100%social 106 agents receiving social field and acting upon that signal. However, the efficiency of no social drops again once the number of agents deviates from this tipping point (9 agents). For cases where the agent number is much larger than 9, the social structuring strategy appears to be more efficient in terms of both effort and time duration (Figure 24). It is interesting to see that adding more agents is helping with increasing complexity when social rules are applied. The implication of these results is important: while increasing complexity from (b) to (c) in Figure 5 can be realized by either social structuring and/or adding more agents, the “impact” of them is different. Adding not-enough agent power may run the risk of failures in no social and adding too much agent power may lead to a waste of time and effort in social. Basically, adding more agents after some critical setting, here 9 agents, causes the system to move back towards point (b), resulting in less complexity of the overall system and therefore higher failure percentage for no social. However, in any number of agents, adding proper social structuring removes the failure risk and maintains an adequate level of efficiency. Observations of human organizations seem to reflect this insight. The difference can be explained by system complexity measures shown in Table 7. 107 Figure 24: Effort and duration time comparison for social (SRBR) and non-social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents According to Figure 25, adding policy to the structure has shown improvement in the success rate of the system after the critical point (9). Figure 25: Success rate comparison for social (SRBR) with various topology and non- social (FBR) strategies for the “with wall + One Obstacle” situation with varying number of agents 0 1000 2000 3000 4000 5000 7 9 11 13 15 Effort / Agent No social 100%social 0 10000 20000 30000 40000 50000 7 9 11 13 15 Time No social 100%social 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate No social 10%social 30%social 50%social 70%social 100%social 108 Performance of the systems seems to increase with adding policy to the system, especially in high numbers of agents where it even beats the overall performance of social (Figure 26, 27). Consequently using policy not only performs better, but it also results in a compatible success rate. Change of the slope sign before and after the critical point is an interesting feature of this graph. Moreover, rate of slope of improvement changes, with more positive values when more agents are involved, indicating a larger impact of employing policy. Figure 26: Effort comparison for social (SRBR) with various topology and non-social (FBR) strategies for the “with wall + one obs” situation with a varying number of agents 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 7 9 11 13 15 Effort / Agent No social 10%social 30%social 50%social 70%social 100%social 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 7 9 11 13 15 Time No social 10%social 30%social 50%social 70%social 100%social 109 Figure 27: Duration time comparison for social (SRBR) with various topology and non- social (FBR) strategies for the “with wall + one obs” situation with varying number of agents The dynamic process information of when strong social rules are imposed as well as when there are no explicit rules defined between agents are calculated. The measurement result of 23230.66 and 33936.33 respectively is analyzed. The difference between analyzed values is an obvious indicator of the information requirements of the system in order to achieve desire goals in a more efficient manner. Social rules are needed to deal with the regularity of task field. As the designer of CSO systems is knowledgeable of the domain, some rules (or in other words, extra information) are used to instruct agents for better performance. In order to fully investigate the relationship between more complex tasks and the need for social structuring, simulations for the “with wall + two obs” situation is carried out. The task complexity measure for this situation is 38.7 (see Table 7). Here are the screenshots of a simulation of 25 runs for level-1 task, strong social and 9 agents setting: Time Step: 000 Time Step: 004 Time Step: 010 Time Step: 015 Time Step: 021 Time Step: 023 110 Time Step: 025 Time Step: 040 Time Step: 042 Time Step: 044 Time Step: 046 Time Step: 053 Time Step: 055 Time Step: 057 Time Step: 060 Figure 28: Screenshots of a simulation of 25 runs for level-3 task, strong social and 9 agents setting. Figure 29 shows the success rate comparison of two strategies and Figure 30 the comparison of effort and time duration. Figure 29: Success rate comparison for social (SRBR) and non-social (FBR) strategies for the “with wall+ two obs” situation with varying number of agents 0 0.2 0.4 0.6 0.8 1 7 9 11 13 15 Success Rate Social SR NoSocial SR 111 It can be seen from Figure 29 that the success rate for the non-social strategy decreased dramatically even with more agents. However, the social rule based structuring strategy remains 100% successful. Figure 30: Effort and time duration comparison for social (SRBR) and non-social (FBR) strategies for the “with wall+ two obs” situation with varying number of agents For effort comparison, the non-social strategy is always worse than the social one for different agent numbers, as shown in Figure 30. Overall, the efficiency for non-social strategy is worse than that for the social strategy, especially when number of agents is 7 or 15. By comparing Figure 30 with Figure 23, it can be seen that the more complex task “with wall+ two obs” has a greater need for emergent structural complexity. However, when more agents are added into the already social-rule based system, there is not much improvement of time duration and effort. When numbers of agents become 15, social performance declines a little bit. This is because social structuring incurs overhead in task processing as too many interconnections among agents cause interferences. As the number of agents increases, more if-statements in the rule definitions are triggered. This specificity of local social rules causes the system to become less flexible. 0.E+00 1.E+03 2.E+03 3.E+03 7 9 11 13 15 Effort/Agent Social NoSocial 0.0E+00 1.0E+04 2.0E+04 3.0E+04 7 9 11 13 15 Time Social NoSocial 112 When the number of agents decreases, introducing policy to the system structure does not seem to help either with system functionality or with success rate as it reduces the complexity of the overall system. The results reveal the same intuition discussed for level-2 task. Additionally, change of the slope sign and rate before and after the critical point is more explicitly clear in level-3 task compared to level-2 task. On the same line of thought, when the number of agents increases, having policy and using less social rule appear to be more effective while improving the performance (Figure 31, 32 and 33). On the other hand, as the number of agents increases, applying policy to the structure improves the rate of accomplishment after the number of agents hits a certain critical number (as in level-2 task, the critical number is 9 agents). Devising proper social rules and an adequate number of agents is the key. Figure 31: Effort per agent comparison for social (SRBR) with various topology and non- social (FBR) strategies for the “with wall + two obs” situation with varying number of agents 0 500 1000 1500 2000 2500 3000 7 9 11 13 15 Effort/Agent Social 70%social 50%social 30% Social 10%Social NoSocial 113 Figure 32: Duration time comparison for social (SRBR) with various topology and non- social (FBR) strategies for the “with wall + two obs” situation with varying number of agents Figure 33: Success rate comparison for social (SRBR) with various topology and non- social (FBR) strategies for the “with wall + two obs” situation with varying number of agents The dynamic process information is calculated of when strong social rules are imposed as well as when there are no explicit rules defined between agents. The results of measurements are 11214.24 and 178580.57 respectively. The difference between analyzed values is an obvious indicator of the information requirements of the system in 0 5000 10000 15000 20000 25000 30000 7 9 11 13 15 Time Social 70%social 50%social 30% Social 10% Social NoSocial 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate Social 70%social 50%social 30%Social 10%Social NoSocial 114 order to achieve desire goals in a more efficient manner. As mentioned in previous case studies, this result is another proof of necessity of imposing social rules to deal with the regularity of the task field. 5.4.2 Weak Social Rule Result In this section, the effect of rule complexity on the performance of the system is investigated. To explore this scenario, more general rules are introduced for agents to follow. It would be interesting to investigate and understand to which degree complexity of a rule can be influential to system. As stated before, complexity of rules is measured based on the number of conditions described as part of rules. The simple rule algorithm is illustrated in pseudo code in the following. The subsequent variables as: InCross = Agents located cross the box from current push InParal = Agents located in parallel with current push on the other side of the box The rules based on the defined terms is described as follows: If number of agents InCross > 0 [ If field of current agent >= field of InCross [ Move to InCross location proportional to the number of agents in InCross ] ] Figure 34 demonstrates the effort per agent and time spent by agents in no social and weak social settings for level-1 task. The performances have not significantly 115 improved compared to strong social. Since complexity of this task is low, using weak social can be sufficient and can reach the same level of efficiency. Figure 34: Duration time and effort comparison for weak social (SRBR) and non-social (FBR) strategies for the “with wall” situation with varying number of agents Employing policy has been shown in Figure 35 and 36. As the number of agents increases, applying policy can slightly improve the performance. Figure 35: Effort per agent comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall” situation with varying number of agents 0 50 100 150 200 250 300 350 400 7 9 11 13 15 Effort / Agent No social Social 0 500 1000 1500 2000 2500 3000 3500 4000 7 9 11 13 15 Time No social Social 0 50 100 150 200 250 300 350 400 7 9 11 13 15 Effort / Agent No social 10% social 30% social 50% social 70% social Social 116 Figure 36: Duration time comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall” situation with varying number of agents For the following experiments, lets move on to a higher task complexity where it is called level-2 task. Success rate for no social (FBR) and weak social (SRBR) is demonstrated in Figure 37. As expected, social has 100% success rate and exactly like the success rate measured in strong social and same task complexity, when agents are fewer (7, 9) and more (15) no social reaches a high success rate. Figure 37: Success rate comparison for weak social (SRBR) with various policy and non- social (FBR) strategies for the “with wall + one obs” situation with varying number of agents 0 500 1000 1500 2000 2500 3000 3500 4000 4500 7 9 11 13 15 Time No social 10% social 30% social 50% social 70% social Social 0 0.2 0.4 0.6 0.8 1 1.2 7 9 11 13 15 Success Rate No social 100%social 117 As shown in Figure 38 increasing the number of agents after the critical point improves performance in both social and no social scenarios. It is interesting to see that for 7 and 9 agents, weak social does not provide distinguishable advantages over no social. Also, for the 9-agent case, the absence of social rules and structuring has made the system almost as efficient as a system with structuring. In this setting of number of agents and level-2 task complexity, weak social does worse in the critical point (9-agents), and no social does better than the trend followed in other cases. The difference between weak social and no social in this critical point is more noticeable compared to the one of no social and strong social. Since for this specific setting, conducting agents through task field and not applying any social rules seems to be enough guidance with a reasonable performance and without restricting agent’s choice of action, providing any extra information can confuse agents and consequently hurt the system. The more general the rules between agents, the harder to take advantage of added information, resulting in worse performance. For cases where the agent number is much larger than 9, the social structuring strategy appears to be more efficient in terms of both effort and time duration. 0 1000 2000 3000 4000 5000 6000 7000 8000 7 9 11 13 15 Effort / Agent No social 100%social 0 10000 20000 30000 40000 50000 60000 70000 80000 7 9 11 13 15 Time No social 100%social 118 Figure 38: Duration time and effort comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall” situation with varying number of agents According to Figure 39 adding policy to the structure has shown improvement in the success rate of the system after the critical point (9). Figure 39: Success rate comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents Figure 40 and 41 shows the comparison of total effort and time duration for completed (i.e., successful) simulation runs for non-social, social, and various policy strategies. Performance-wise, policy tends to help after the critical point (9-agents), especially in high numbers of agents, the more policy, the better the results. Using policy not only results in a better performance, but it also results in a compatible success rate. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate No social 10%social 30%social 50%social 70%social 100%social 119 Figure 40: Effort per agent comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents Figure 41: Duration time comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + one obs” situation with varying number of agents It can be seen from Figure 42 that the success rate for non-social strategy decreased dramatically even with more agents. For the non-social strategy, for 13 agents, there was no data for comparison and nothing shown in Figure 42 as they could not finish any runs. However, the social rule based structuring strategy remains 100% successful. 0 1000 2000 3000 4000 5000 6000 7000 8000 7 9 11 13 15 Effort / Agent No social 10%social 30%social 50%social 70%social 100%social 0 10000 20000 30000 40000 50000 60000 70000 80000 7 9 11 13 15 Time No social 10%social 30%social 50%social 70%social 100%social 120 Figure 42: Success rate comparison for weak social (SRBR) and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents It is interesting to see that no social can be slightly more efficient in higher task field than having weak social rules. However, their success rate is only 60% maximum; that is pretty low (see Figure 43). Overall, the cost for this added efficiency is more than 50% failure risk, and in some cases 100% failure (13 number of agents). Overall, the efficiency for non-social strategy is much worse than that for the social strategy. Also, it is clear that a small number of agents have a hard time accomplishing the task, regardless of which strategy is used. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate No social 100%social 121 Figure 43: Duration time and effort per agent for weak social (SRBR) and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents On the other hand, applying policy seems to solve all the efficiency problems. It helps with reaching 100% success rate as well as consuming less time and effort for each agent (Figure 44, 45 and 46). Figure 44: Success rate comparison for weak social (SRBR) with various policies and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents 0 2000 4000 6000 8000 10000 7 9 11 13 15 Effort/Agent No social 100%social 0 20000 40000 60000 80000 100000 7 9 11 13 15 Time No social 100%social 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 7 9 11 13 15 Success Rate No social 10%social 30%social 50%social 70%social 100%social 122 Figure 45: Effort per agent comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents Figure 46: Duration time comparison for weak social (SRBR) with various policy and non-social (FBR) strategies for the “with wall + two obs” situation with varying number of agents The reason behind the benefit of adding policy lies in the generality of the rules. Unless there is a comprehensive knowledge about what precisely each agent should do, enforcement of rules will not be constructive. Due to the generality of rule description, it 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 7 9 11 13 15 Effort/Agent No social 10%social 30%social 50%social 70%social 100%social 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 7 9 11 13 15 Time No social 10%social 30%social 50%social 70%social 100%social 123 becomes unnecessary for agents to completely follow the rules. Based on the Figure 44, even rarely following this general rule can tremendously improve the success rate. The presented results illustrate the importance of assigning proper social rules among agents to reach a higher level of efficiency. The main purpose of applying social rules is to resolve possible conflicts, and this fact is captured more in the complex rule set which proposes more suitable social rules and consequently a better performance. In the least profitable design of self-organizing social rules, counteracting or resolving the contrary torque is the main concern, while realizing the fact that improving the system through assisting other agents, especially the ones with higher priority and in this case having lower field, can be more beneficial. 5.5 Comparison of Strong Social and Weak Social In this section, the focus is on the differences between weak social and strong social in different setting of task level. 5.5.1 Level-1 Task The percentage improvements of strong social with respect to weak social for level-1 task is shown in Figure 47, and 10% strong social versus weak social in Figure 48. The improvement does not follow a specific trend and is not very explicit. In case of measures of agents’ effort, strong social mostly does slightly better than weak social. On the other hand, in terms of time duration, weak social finishes the level-1 job generally faster than strong social. It is mainly because there are more calculations involved in strong social that causes the system to ponder more in each step. 124 Figure 47: Percentage improvements of performance of strong social with respect to weak social for level-1 task Figure 48: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-1 task. 5.5.2 Level-2 Task The percentage improvements of strong social with respect to weak social for level-2 task is shown in Figure 49. Incorporating strong social shows better performance compare to weak social when task becomes even more complex. Distance from a specific number of agents reduces the difference between strong social and weak social (11 -‐10 -‐5 0 5 10 7 9 11 13 15 Effort / Agent Percentage of Improvement -‐14 -‐12 -‐10 -‐8 -‐6 -‐4 -‐2 0 2 7 9 11 13 15 Time Percentage of Improvement -‐4 -‐2 0 2 4 6 8 10 7 9 11 13 15 Effort / Agent Percentage of Improvement in 10% Social -‐4 -‐2 0 2 4 6 8 7 9 11 13 15 Time Percentage of Improvement in 10% Social 125 agents). As mentioned before, adding more agents to the system in the level-2 task does not help significantly with strong social as oppose to weak social where it’s performance improves noticeably after the critical point (9 agents). Considering these two facts results in the following illustrated graph. Differences between complex and weak social increase until the point where the time duration and effort consumption decays faster in weak social compared to strong social. Both the overhead in strong social while more number of agents are involved as well as the positive effect of adding more social when using weak social are the main basis of this bell shape. Figure 49: Percentage improvements of performance of strong social with respect to weak social for level-3 task In the critical point, 10% weak social outperforms strong social, and in the other settings, strong social offers a better performance level (Figure 50). 0 10 20 30 40 50 60 70 7 9 11 13 15 Effort / Agent Percentage of Improvement -‐20 -‐10 0 10 20 30 40 50 60 7 9 11 13 15 Time Percentage of Improvement 126 Figure 50: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-3 task. 5.5.3 Level-3 Task The percentage improvements of strong social with respect to weak social for level-3 task is shown in Figure 51. Incorporating strong social shows better performance compared to weak social when the task becomes even more complex. As weak social provides a very general description for agents to regulate their actions independent of the specifics of the situation, it can hurt the performance of the system even in comparison with using no social strategy. It is clearly demonstrated in Figure 51 that having more specific social rules in essential for better performance both in terms of time duration and effort consumed. -‐5 0 5 10 15 20 25 30 7 9 11 13 15 Effort /Agent Percentage of Improvement in 10% Social -‐5 0 5 10 15 20 25 30 7 9 11 13 15 Time Percentage of Improvement in 10% Social 127 Figure 51: Percentage improvements of performance of strong social with respect to weak social for level-3 task. In 10% social, for most numbers of agents, as illustrated in Figure 52, strong social outperforms weak social. There are slight decreases in two settings of number of agents, 11 and 13. There is not a general trend in the change of performance based on change in the number of agents. Figure 52: Percentage improvements of performance of 10% strong social with respect to 10% weak social for level-3 task. -‐10 10 30 50 70 90 7 9 11 13 15 Effort / Agent Percentage of Improvement -‐10 10 30 50 70 90 7 9 11 13 15 Time Percentage of Improvement -‐10 0 10 20 30 40 50 7 9 11 13 15 Effort / Agent Percentage of Improvement in 10% Social -‐20 -‐10 0 10 20 30 40 50 60 7 9 11 13 15 Time Percentage of Improvement in 10% Social 128 5.6 Discussion and Conclusions As domain tasks become more complex, engineered systems become more complex by moving from rigid and tightly organized formations into those of more components and more interactions. A potential issue with this top-down or ordered-to- disorder approach is the unintended and unknown interactions that may cause failure of the whole system. An alternative approach is to start with simple and disorganized agents and then move bottom-up and disordered-to-ordered by devising dynamic structures through self-organization. In this research, the sources of task complexity in explored by defining various complexity types and investigated how social rule based behavior regulation can be applied to allow dynamic structures, hence system complexity, to emerge from self-interested agents. The case study results have demonstrated the effectiveness of the proposed approach and shed some useful insights. • Increasing complexity from disorder can be achieved through adding more agents or devising structures. However, the former only has limited effect. When tasks become more complex, adding agents can hardly reach 100% success rate and the efficiency for the successful runs is low. On the other hand, devising dynamic structures can make the system more adaptable. Not only is the successful rate always 100%, but also the efficiency is well maintained with changing task complexity (from “with wall” to “with wall+ obs” and then to “with wall+ two obs”) and varying number of agents. This result is consistent with Huberman and Hogg’s (1986) conjecture that higher structural complexity makes a system more adaptable. 129 • When a relatively disordered system can complete a task by a certain policy, for this completed task, its efficiency can be better than structured systems; this happens only for a large number of agents. The reason behind this observation is that dynamic social structuring incurs overhead in task processing as too many interconnections among agents cause interferences. As the number of agents increases, more if statements in the rule definitions are triggered. This specificity of local social rules causes the system to become less flexible. However, lack of structure and disorder can be very poor performance-wise and is based on the high risk of failures. Applying a small percentage of policy to no social strategy can be a solution to embed complexity as well as redeeming the less quality caused by adding more agents. • There can be tipping points of matching between the task complexity and system complexity where the difference of having social structuring and lack of social structuring is negligible. This tipping point phenomenon is due to the mismatch between the highly complex task and not-so-complex system. The rate by which social structuring affects the system performance as the number of agents increases is slow, reflecting the fact that regularity of social rules is causing an overhead when more agents are involved, resulting in less complexity of the overall system. This also describes the usefulness of applying policy to enhance performance after the tipping point. • As tasks complexity increases, the impact of adding more agents becomes less noticeable and almost ignorable especially when social rules are employed while applying policy not only performs better, but it also results in a compatible success rate. The rate of slope of improvement changes both in simple and strong social, with 130 more positive values when more agents are involved, indicating a larger impact of employing policy. When implying weak social, adding policy is always beneficial, which implies the un-necessity of enforcing rules. The intuition behind these results implies that full execution of rules can be destructive unless there is a comprehensive knowledge about what precisely each agent needs to do. Even rarely following this general rule can tremendously improve the success rate. • The generality of description in weak social for the purpose of action regulation of agents independent of the specifics of the situation can hurt the performance of system. Having more specific social rules is demonstrated to be essential, specifically in higher-level tasks to gain better performance in terms of time duration and effort consumed. However, the stated importance diminishes as more agents are added to the system. • Increasing the number of agents helps more with no social, and when the number of agents exceeds some amount (25 agents), the difference between social and no-social and the various ranges of social strength fade away and become less noticeable. The randomness added to the system due to participation of more entities overcomes any relationship defined between agents. • The analyzed values for dynamic process information are an obvious indicator of the difference between information requirements by the agents when social rules are imposed and in the absence of rules in order to achieve desire goals in a more efficient manner. Social rules are needed to deal with the regularity of task field. From a design point of view, functional requirements often contradict with uniform definition of task fields. Since there is no uniform way of describing task field, social 131 field can dynamically affect the strength and distributions of conducting fields for agents. As the designer of CSO systems and knowledgeable of the domain, some rules (or in other words, extra information) can be devised to instruct agents for better performance. 5.7 Hypothesis Revisit In this section, the previous hypotheses, which were addressed earlier in this thesis, are revisited. The first hypothesis targets the importance of dynamical social structuring in order to get higher efficiency. This importance hypothesis is true; however, it can be situation dependent. Based on the noted results and conclusion, there are ways to increase complexity of the system other than introducing social structuring, like adding more agents to the system. Although it still depends on the complexity of the task, if complexity goes beyond a threshold, even adding more agents can not simply increase effectiveness as the success rate becomes a higher risk. The second hypothesis demonstrated that social structuring can be designed, which is true; however since not enough information is gathered due to lack of investigation of different possible types of tasks, the methodology through which social structuring should be designed has not been developed yet. Therefore, it can be part of future work to perform systematic design of rules/relations among agents. 132 6 Contributions and Future Directions The effectiveness of the social rule based self-organizing approach has been examined in order to build effective CSO systems to deal with more complex and realistic tasks. As task requirements become more complicated and the system is confronted with inevitable constraints, and uncertainties, applying previous CSO design methods may result in an incomplete task. The relations between task complexity and the complexity needed to be embedded in the system either through social rules/relations or through changing of the system setting is uncovered. Social rules and relations can play an important role in minimizing conflict and providing cooperation among agent by being a mediator to regulate and confines the possible agent actions that lead to emergence of a suitable structure. I have shown that this new approach is beneficial for CSO systems and can guarantee task accomplishments by maintaining and applying the designed coordination mechanism in the system. Concluding this dissertation, the contributions of this research are stated below followed by future research directions. 6.1 Contributions • Two-field Framework for Cellular Self-Organizing Systems: Drawing on the natural idea of fields, a two-field based model is proposed to characterize the task domain and to guide agents’ self-organizing behavior. The task field captures the task environment while the social field arises from agent–agent relations and rules. The combined effect of these two fields, sensed by agents individually, determines the behavior of each agent, while the system-level behavior emerges from the actions of and interactions among the agents. The proposed two-field model was able to capture 133 important features of self-organizing mechanisms by which agents could form task- based structures to fulfill functional requirements. A deeper understanding of complex adaptive systems, specifically design of a more sophisticated CSO framework, capable of dealing with more complex tasks in an unpredictable environment, is revealed in this research, which will ultimately enable us to improve the adaptive system design processes. • Task Complexity Model: to demonstrate that more complex tasks require more complex systems; a measure of task complexity is needed. In this research, the task complexity is defined based on three components: action and action relation complexity, object and object relation complexity, and dynamic complexity. Tasks can be viewed as a number of functions and different objects involved. As the number of distinguishable verbs associated with a task increases, the skills and information needed for the task also increase. In addition to the number of actions, there can be various relationships between these actions that must be maintained for the completion of the task. The characteristics of the objects involved in a task as well as the number of objects and relations between objects, contribute to the task complexity. • Social Rule Based Regulator for Cellular Self-Organizing Systems and Social Complexity Model: In this research, the concept of “social structure” was introduced to capture explicit/direct interactions among agents and “social rules” were applied to facilitate dynamical social structuring among agents. A new self-organizing method was introduced by designing local rules of interaction among mCells in such a way that allow promoting cooperation and avoiding conflict. Social field adds another layer to the design of CSO systems as a helpful mechanism to secure unity in the 134 system. The social complexity measure of agents is defined based on their connectivity graph that originates from social rules as well as rule complexity based on the number of conditions determined in the rule definition. The structure, if managed properly, can result in having simple agents exhibit complex behaviors and help sophisticated agents reduce the complexity of their reasoning. Lack of structure and disorder can be very poor performance-wise and be the basis for a high risk of failures. • Impact of the population size: Based on the simulation findings and derived complexity measure of system, there can be some tipping points that cause a shift in the normal trend of increased complexity by having more intelligent entities. Therefore, adding more agents does not always increase the system complexity in a sense that even if the performance measures of the system increase by having more agents, there might be a risk of failure for that setting. This tipping point is problem or task dependent in a way that all descriptive parameters can make a difference. On average, when some rules are built in the system, except for the extreme tipping points which are normally independent of any relationship defined among agents, having more agents can enhance system level efficiency until the point where combinations of number of agents, specific rules and conditions among them create overhead. This trend can also be seen in cases where policy is applied and generally policy has a smoothing impact on the rate of performance change with respect to the number of agents. • Impact of the specificity of rules: Social rules can be general or task specific. When rules are more specific, as the number of agents involved increases, more “if 135 statements” in the rule definitions are triggered. This specificity of local social rules causes process overhead for the system and makes it less flexible. Applying a small percentage of adoption rate can be a solution to embed complexity as well as redeeming the decrease in efficiency caused by adding a high numbers of agents. On the other hand, unless there is a comprehensive knowledge about what precisely each agent should do, enforcement of rules will not be constructive. If rules have general description, it becomes unnecessary for agents to completely follow the rules. Having more specific social rules is essential, specifically in higher-level tasks to gain better performance. Although, the stated importance diminishes as more agents are added to the system. • Impact of the rule adoption rate: Applying policy becomes very handy when more agents are involved in the system. The main reason behind implementing the adoption rate is to control the unknown interactions that might occur especially when the number of agents increases as the main factor to increase the possibility of unwanted interactions. The more general the rules, the better impact of applying policy independent of number of agents. To maintain or even improve the efficiency level of the system in the presence of rules/relations between agents, either a more specific rule is needed to capture various possible conflicts or less policy can result in a desirable performance. A major limitation with this work is the lack of task variety. In order to draw broader conclusions, one should explore the properties of various types of task complexity and their demands for corresponding types of structural complexity of the CSO systems. In this thesis, only the box-pushing task in various settings was explored, 136 and the influence of different task types or other parameters affecting the system has not been investigated, and the overall performance of SRBR needs to be more broadly assessed. The future work needs to include more close-to-real engineering tasks and gradually make CSO systems more real and practically functional. 6.2 Future Work The future work is the research direction for which this dissertation will lay the groundwork and leads to a lot of future opportunities to be explored. These are areas that due to time and workload constraints remain untouched. • The exploration presented in this thesis needs to be carried out against a variety of different types of tasks. The same measures and models should be applicable to these different tasks. • Future work may include improving the framework through introducing new concepts. To evaluate satisfaction of agents both at the individual and the system level, a new function can be developed. Proposing new ways of creating social field when agents have limitations in their communication can be very beneficial. Also, a more advanced dynamics of objects may need to be considered to better capture the real- world mechanical system. • Furthermore, learning capability can be added to the agents, although it would cause an increase in complexity of the agents themselves. Learning can be involved in assigning probabilities to available behaviors in certain situations. For example, choosing an action proportional to the energy consumption for that particular action 137 might not always be valuable for the overall system. Therefore, there could be a learning mechanism for agents to keep track of their decisions along the way and learn to not only consider energy consumption but also evaluate their action selection based on other parameters in the system, their past experience, and the rewards associated with them. In addition, learning can be embedded in designing social rules that could lead to a system that would self-generate proper social rules depending on the criteria. • To this point, only homogenous systems have been explored. While this current approach is unable to explore heterogeneous mCells due to time limitations, exploring different levels of heterogeneity would benefit future research. Mechanical cells can be mechanically and physically different and have different capabilities and behavior capacities. Introducing distinctive behaviors for mCells may give rise to expanded collaborative capacity and consequently result in higher complexity. Increasing the behavior space for mCells can cause an increase in types of interaction and introduce new levels of communication. • One last area for exploration is an investigation into how probability and uncertainty can be incorporated into the communication phase. Developing asynchronous communication, which negatively influences proper reactions of cells to the received information, will allow for the development of methods closer to real world. As in gradient-based interaction and communication, where chemicals and information are exposed to evasion and noise, considering incomplete transfers of information among agents is an interesting new avenue of research and provides a further understanding of the coordination process. 138 7 References Arkin, R. C. 1995. “Reactive Robotic Systems.” The Handbook of Brain Theory and Neural Networks, 793–96. ———. 1998. Behavior-Based Robotics. MIT press. http://books.google.com/books?hl=en&lr=&id=mRWT6alZt9oC&oi=fnd&pg=PR 11&dq=(Arkin,+1995)+where+animal+models+have+been+studied&ots=43Zvc mN7oE&sig=ieGFBOKrPXUnzg5q6y1g7-GSFTA. Arkin, R. C., and T. Balch. 1998. “Cooperative Multiagent Robotic Systems.” Artificial Intelligence and Mobile Robots. MIT/AAAI Press, Cambridge, MA. http://www.cs.cmu.edu/afs/.cs.cmu.edu/Web/People/motionplanning/papers/sbp_ papers/integrated1/balch_coop_formations.pdf. Ashby, W. R. 1956. An Introduction to Cybernetics. Taylor & Francis. http://books.google.com/books?hl=en&lr=&id=YSkOAAAAQAAJ&oi=fnd&pg= PR5&dq=An+Introduction+to+Cybernetics.&ots=_Lfpvisuuq&sig=9p21__L0SP dIZ8xCt6SiqJdDoLQ. Bak, Per. 1996. “How Nature Works. The Science of Organized Criticality.” New York: Copernicus and Springer-Verlag. Bak, Per, Chao Tang, and Kurt Wiesenfeld. 1987. “Self-Organized Criticality: An Explanation of the 1/f Noise.” Physical Review Letters 59 (4): 381. Balch, T., and L. E. Parker. 2002. Robot Teams: From Diversity to Polymorphism. AK Peters, Ltd. http://dl.acm.org/citation.cfm?id=582767. Barber, K. S., A. Goel, and C. E. Martin. 2000. “Dynamic Adaptive Autonomy in Multi- Agent Systems.” Journal of Experimental & Theoretical Artificial Intelligence 12 (2): 129–47. Bar-Yam, Y. 2003. “Dynamics of Complex Systems.” http://www.citeulike.org/group/2050/article/1526297. Bar-Yam, Yaneer. 2006. “Multiscale Analysis and Evolutionary Engineering.” In Complex Engineered Systems: Science Meets Technology, 23–39. Springer Complexity. Berlin ; New York: Springer. Beer, S. 1966. Diagnosing the System for Organisations. John Willey. https://textweb.livjm.ac.uk/cmp/cmp_docs/6045COMP_Business_Systems_- _Analysis_and_Evolution.pdf. ———. 1984. “The Viable System Model: Its Provenance, Development, Methodology and Pathology.” Journal of the Operational Research Society, 7–25. Bonabeau, E., M. Dorigo, and G. Theraulaz. 1999. Swarm Intelligence: From Natural to Artificial Systems. 1. Oxford University Press, USA. http://books.google.com/books?hl=en&lr=&id=fcTcHvSsRMYC&oi=fnd&pg=P R11&dq=Swarm+Intelligence:+From+Natural+to+Artificial+Systems.&ots=48G kniLIxP&sig=qJrR5OQZLXyP-RmNS9ytC4LJMSE. Bonchev, D. 2003a. “Shannon’s Information and Complexity.” Complexity in Chemistry. Introduction and Fundamentals, D. Bonchev and D H. Rouvray (eds.), Taylor and Francis, London, 157–87. ———. 2003b. “On the Complexity of Directed Biological Networks.” SAR and QSAR in Environmental Research 14 (3): 199–214. 139 Bonchev, Danail. 2004. “Complexity Analysis of Yeast Proteome Network.” Chemistry & Biodiversity 1 (2): 312–26. Bonchev, Danail, Danail Bon\vcev, Bulgarien Chemiker, Danail Bon\vcev, Danail Bon\vcev, and Bulgaria Chemist. 1983. Information Theoretic Indices for Characterization of Chemical Structures. Vol. 5. Research Studies Press Chichester. http://www.getcited.org/pub/102219522. Bonchev, Danail, and Dennis H. Rouvray. 2005. Complexity in Chemistry, Biology, and Ecology. Springer. http://link.springer.com/content/pdf/10.1007/b136300.pdf. Bonchev, D. G., and Dennis H. Rouvray. 2003. Complexity: Introduction and Fundamentals. Vol. 7. CRC Press. http://books.google.com/books?hl=en&lr=&id=hYD- Pr9_2pAC&oi=fnd&pg=PR7&dq=complexity:+introduction+and+fundamentals &ots=aqEG7LyweG&sig=-2Ld8cNsxH1bigsaG7bSYWKnfn8. Brooks, C. H., and E. H. Durfee. 2003. “Congregation Formation in Multiagent Systems.” Autonomous Agents and Multi-Agent Systems 7 (1): 145–70. Brooks, R. 1986. “A Robust Layered Control System for a Mobile Robot.” Robotics and Automation, IEEE Journal of 2 (1): 14–23. Buice, Michael A., and Jack D. Cowan. 2009. “Statistical Mechanics of the Neocortex.” Progress in Biophysics and Molecular Biology 99 (2): 53–86. Campbell, D. J. 1988. “Task Complexity: A Review and Analysis.” Academy of Management Review 13 (1): 40–52. Chen, Chang, and Yan Jin. 2011. “A Behavior Based Approach to Cellular Self- Organizing Systems Design.” In . http://link.aip.org/link/abstract/ASMECP/v2011/i54860/p95/s1. Chiang, Winston, and Yan Jin. 2011. “Toward a Meta-Model of Behavioral Interaction for Designing Complex Adaptive Systems.” In , 1077–88. ASME. doi:10.1115/DETC2011-48821. Cools, Seung-Bae, Carlos Gershenson, and Bart D’Hooghe. 2008. “Self-Organizing Traffic Lights: A Realistic Simulation.” In Advances in Applied Self-Organizing Systems, 41–50. Springer. http://link.springer.com/content/pdf/10.1007/978-1- 84628-982-8_3.pdf. Corkill, D. D., and S. E. Lander. 1998. “Diversity in Agent Organizations.” Object Magazine 8 (4): 41–47. Davis, R., and R. G. Smith. 1983. “Negotiation as a Metaphor for Distributed Problem Solving.” Artificial Intelligence 20 (1): 63–109. Deneubourg, J. L., S. Goss, N. Franks, A. Sendova-Franks, C. Detrain, and L. Chrétien. 1991. “The Dynamics of Collective Sorting Robot-like Ants and Ant-like Robots.” In Proceedings of the First International Conference on Simulation of Adaptive Behavior on From Animals to Animats, 356–63. http://www.ulb.ac.be/sciences/use/publications/Claire/11.pdf. Di Marzo Serugendo, G., N. Foukia, S. Hassas, A. Karageorgos, S. Mostéfaoui, O. Rana, M. Ulieru, P. Valckenaers, and C. Van Aart. 2004. “Self-Organisation: Paradigms and Applications.” Engineering Self-Organising Systems, 1–19. Doursat, René. 2011. “The Myriads of Alife: Importing Complex Systems and Self- Organization into Engineering.” In Artificial Life (ALIFE), 2011 IEEE Symposium on, 1–8. IEEE. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5954671. 140 Durfee, E. H., V. R. Lesser, and D. D. Corkill. 1987. “Coherent Cooperation among Communicating Problem Solvers.” Computers, IEEE Transactions on 100 (11): 1275–91. Fax, J. A., and R. M. Murray. 2004. “Information Flow and Cooperative Control of Vehicle Formations.” Automatic Control, IEEE Transactions on 49 (9): 1465–76. Fox, S. W. 1971. “Chemical Origins of Cells, Part 2.” Chemical and Engineering News. Friston, Karl J., and Raymond J. Dolan. 2010. “Computational and Dynamic Models in Neuroimaging.” Neuroimage 52 (3): 752–65. Galbraith, J. R. 1973. Designing Complex Organizations. Addison-Wesley Longman Publishing Co., Inc. http://dl.acm.org/citation.cfm?id=540368. ———. 1977. Organization Design. Addison-Wesley Reading, MA. http://hevra.haifa.ac.il/~soc/lecturers/samuel/files/651256217022.pdf. Gardner, M. 1970. “Mathematical Games: The Fantastic Combinations of John Conway’s New Solitaire Game ‘life.’” Scientific American 223 (4): 120–23. Gasser, L. 1991. “Social Conceptions of Knowledge and Action: DAI Foundations and Open Systems Semantics.” Artificial Intelligence 47 (1): 107–38. Glansdorff, P., and I. Prigogine. 1971. “Thermodynamic Theory of Structure, Stability and Fluctuations.” http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=372427. Goldberg, D., V. Cicirello, M. B. Dias, R. Simmons, S. Smith, and A. Stentz. 2003. “Task Allocation Using a Distributed Market-Based Planning Mechanism.” In International Conference on Autonomous Agents: Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems, 14:996–97. http://www.cs.cmu.edu/~FIRE/papers/aamas03-submit.ps.gz. Goto, H., Y. Hasegawa, and M. Tanaka. 2007. “Efficient Scheduling Focusing on the Duality of MPL Representation.” In Computational Intelligence in Scheduling, 2007. SCIS’07. IEEE Symposium on, 57–64. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4218597. Hackman, J. R. 1969. “Toward Understanding the Role of Tasks in Behavioral Research.” Acta Psychologica 31: 97–128. ———. 1987. “The Design of Work Teams.” Handbook of Organizational Behavior 315: 342. Haken, Hermann. 1983. “Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organisation in Physics.” Chemistry, and Biology 3. Halley, John M. 1996. “Ecology, Evolution and 1f-Noise.” Trends in Ecology & Evolution 11 (1): 33–37. Hanken, H. 1983. “Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices.” Springer. Heylighen, F. 2001. “The Science of Self-Organization and Adaptivity.” The Encyclopedia of Life Support Systems 5 (3): 253–80. Heylighen, F., and D. T. Campbell. 1995. “Selection of Organization at the Social Level: Obstacles and Facilitators of Metasystem Transitions.” World Futures: Journal of General Evolution 45 (1-4): 181–212. Horling, B., and V. Lesser. 2004. “A Survey of Multi-Agent Organizational Paradigms.” The Knowledge Engineering Review 19 (4): 281–316. 141 Horling, B., R. Mailler, and V. Lesser. 2004. “A Case Study of Organizational Effects in a Distributed Sensor Network.” In Intelligent Agent Technology, 2004.(IAT 2004). Proceedings. IEEE/WIC/ACM International Conference on, 51–57. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1342923. Hoschke, N., C. J. Lewis, D. C. Price, D. A. Scott, V. Gerasimov, and P. Wang. 2008. “A Self-Organizing Sensing System for Structural Health Monitoring of Aerospace Vehicles.” In Advances in Applied Self-Organizing Systems, 51–76. Springer. http://link.springer.com/content/pdf/10.1007/978-1-84628-982-8_4.pdf. Jiang, Y. C., and J. C. Jiang. 2005. “A Multi-Agent Coordination Model for the Variation of Underlying Network Topology.” Expert Systems with Applications 29 (2): 372–82. Jiang, Y., and J. Jiang. 2009. “Contextual Resource Negotiation-Based Task Allocation and Load Balancing in Complex Software Systems.” Parallel and Distributed Systems, IEEE Transactions on 20 (5): 641–53. Jin, Y., and C. Chen. 2013. “Field Based Behavior Regulation for Self-Organization in Cellular Systems.” Accessed January 14. http://mason.gmu.edu/~jgero/conferences/dcc12/DCC12DigitalProceedings/Digit al%20pdf/Jin.pdf. Jin, Y., and R. E. Levitt. 1996. “The Virtual Design Team: A Computational Model of Project Organizations.” Computational & Mathematical Organization Theory 2 (3): 171–95. Kauffman, S. 2000. Investigations. Oxford University Press, Oxford. Kauffman, Stuart A., and Sonke Johnsen. 1991. “Coevolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Coevolutionary Avalanches.” Journal of Theoretical Biology 149 (4): 467–505. Kitzbichler, Manfred G., Marie L. Smith, Søren R. Christensen, and Ed Bullmore. 2009. “Broadband Criticality of Human Brain Network Synchronization.” PLoS Computational Biology 5 (3): e1000314. Kraus, S. 1997. “Negotiation and Cooperation in Multi-Agent Environments.” Artificial Intelligence 94 (1): 79–97. Kube, C. R., and H. Zhang. 1992. “Collective Robotic Intelligence.” In Proceedings of the Second International Conference on Simulation of Adaptive Behaviors, 460– 68. http://books.google.com/books?hl=en&lr=&id=teHhVHk3a54C&oi=fnd&pg=PA 460&dq=Collective+robotic+intelligence&ots=h_th2xVr6o&sig=TaaA__Jz6weq AQn0uyOt-uztpOA. Lesser, V., C. L. Ortiz, and M. Tambe. 2003. Distributed Sensor Networks: A Multiagent Perspective. Vol. 9. Springer. http://books.google.com/books?hl=en&lr=&id=wNnLYHAkKn4C&oi=fnd&pg= PR11&dq=%5B3%5D+Lesser,+V.,+Ortiz,+C.+and+Tambe,+M.+(2003)+Distrib uted+Sensor+Networks:+A+Multiagent+Perspective.+Springer.&ots=o8u28subD f&sig=2aWCiD_pN6G-qTt_rs0PUo5PvAM. Lesser, V. R. 1998. “Reflections on the Nature of Multi-Agent Coordination and Its Implications for an Agent Architecture.” Autonomous Agents and Multi-Agent Systems 1 (1): 89–111. Lewin, R. 1982. “Biology Is Not Postage Stamp Collecting.” Science 216 (4547): 718–20. 142 Li, Bai-Lian, Hsin-i Wu, and Guangzhou Zou. 2000. “Self-Thinning Rule: A Causal Interpretation from Ecological Field Theory.” Ecological Modelling 132 (1): 167– 73. Lucidarme, P., O. Simonin, and A. Liégeois. 2002. “Implementation and Evaluation of a Satisfaction/altruism Based Architecture for Multi-Robot Systems.” In Robotics and Automation, 2002. Proceedings. ICRA’02. IEEE International Conference on, 1:1007–12. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1013487. Lysaght, R. J., S. G. Hill, A. O. Dick, B. D. Plamondon, and P. M. Linton. 1989. Operator Workload: Comprehensive Review and Evaluation of Operator Workload Methodologies. DTIC Document. http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD A212879. Mataric, M. J. 1997. “Behaviour-Based Control: Examples from Navigation, Learning, and Group Behaviour.” Journal of Experimental & Theoretical Artificial Intelligence 9 (2-3): 323–36. Matson, E., and S. DeLoach. 2003. Using Dynamic Capability Evaluation to Organize a Team of Cooperative, Autonomous Robots. DTIC Document. http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD A451686. Miller, Julian F., Dominic Job, and Vesselin K. Vassilev. 2000. “Principles in the Evolutionary Design of Digital circuits—Part I.” Genetic Programming and Evolvable Machines 1 (1-2): 7–35. Milne, Bruce T. 1998. “Motivation and Benefits of Complex Systems Approaches in Ecology.” Ecosystems 1 (5): 449–56. Mina, A. A., D. Braha, and Y. Bar-Yam. 2006. “Complex Engineered Systems: A New Paradigm.” Complex Engineered Systems, 1–21. Morton, R. D., G. A. Bekey, and C. M. Clark. 2009. “Altruistic Task Allocation despite Unbalanced Relationships within Multi-Robot Communities.” In Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on, 5849–54. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5354072. MOTIVATIONS, I. 2005. “Self-Organization in Distributed Systems Engineering: Introduction to the Special Issue.” IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS 35 (3): 313. Nagpal, R. 1922. “Programmable Self-Assembly: Constructing Global Shape Using Biologically-Inspired Local Interactions and Origami Mathematics.” MASSACHUSETTS INSTITUTE OF TECHNOLOGY. http://pdos.csail.mit.edu/~micahbro/junk/nagpal-thesis[2].pdf. ———. 2002. “Programmable Self-Assembly Using Biologically-Inspired Multiagent Control.” In Proceedings of the First International Joint Conference on Autonomous Agents and Multiagent Systems: Part 1, 418–25. http://dl.acm.org/citation.cfm?id=544839. Pahl, G., and W. Beitz. Engineering Design. 1996. Springer-Verlag, London. Parker, L. E. 1998. “ALLIANCE: An Architecture for Fault Tolerant Multirobot Cooperation.” Robotics and Automation, IEEE Transactions on 14 (2): 220–40. Parsons, T. 1991. The Social System. Psychology Press. http://books.google.com/books?hl=en&lr=&id=FEWj6qIiXcQC&oi=fnd&pg=PP 143 1&dq=The+social+system&ots=Zi7qxbR0GT&sig=xXJoASvV0b4emxt6Xnlab_ 2cBLQ. Prevas, K. C., C. Unsal, M. O. Efe, and P. K. Khosla. 2002. “A Hierarchical Motion Planning Strategy for a Uniform Self-Reconfigurable Modular Robotic System.” In Robotics and Automation, 2002. Proceedings. ICRA’02. IEEE International Conference on, 1:787–92. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1013454. Prigogine, Ilya. 1997. The End of Certainty. Simon and Schuster. http://books.google.com/books?hl=en&lr=&id=- VI8093PJuUC&oi=fnd&pg=PR7&dq=The+End+of+Certainty:&ots=v1dV- vUOW6&sig=_Ds6G5cnKiTP8T4A-UKS-He_y6A. Prokopenko, Mikhail. 2008. Advances in Applied Self-Organizing Systems. Springer. http://link.springer.com/content/pdf/10.1007/978-1-84628-982-8.pdf. Prokopenko, Mikhail, Fabio Boschetti, and Alex J. Ryan. 2007. “An Information- Theoretic Primer on Complexity, Self-Organisation and Emergence.” Advances in Complex Systems. http://prokopenko.net/Publications/Agents/ITprimer-Nov- 2007.pdf. Randi, Milan, and Dejan Plav. 2002. “On the Concept of Molecular Complexity.” Croat. Chem. Acta 75: 107–16. Ravasz, E., and A. L. Barabási. 2003. “Hierarchical Organization in Complex Networks.” Physical Review E 67 (2): 026112. Reich, Y. 1995. “The Study of Design Research Methodology.” TRANSACTIONS- AMERICAN SOCIETY OF MECHANICAL ENGINEERS JOURNAL OF MECHANICAL DESIGN 117: 211–211. Reynolds, C. W. 1987. “Flocks, Herds and Schools: A Distributed Behavioral Model.” In ACM SIGGRAPH Computer Graphics, 21:25–34. http://dl.acm.org/citation.cfm?id=37406. Romelaer, P. 2002. “Organization: A Diagnosis Method.” http://basepub.dauphine.fr/handle/123456789/3437. Rus, D., and M. Vona. 1999. “Self-Reconfiguration Planning with Compressible Unit Modules.” In Robotics and Automation, 1999. Proceedings. 1999 IEEE International Conference on, 4:2513–20. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=773975. ———. 2000. “A Physical Implementation of the Self-Reconfiguring Crystalline Robot.” In Robotics and Automation, 2000. Proceedings. ICRA’00. IEEE International Conference on, 2:1726–33. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=844845. Russell Carpenter, J. 2002. “Decentralized Control of Satellite Formations.” International Journal of Robust and Nonlinear Control 12 (2-3): 141–61. Scott, W. 1992. Richard: Organizations-Rational, Natural, and Open Systems. Prentice Hall. Shen, W. M., C. M. Chuong, and P. Will. 2002. “Simulating Self-Organization for Multi- Robot Systems.” In Intelligent Robots and Systems, 2002. IEEE/RSJ International Conference on, 3:2776–81. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1041690. 144 Shen, W. M., M. Krivokon, H. Chiu, J. Everist, M. Rubenstein, and J. Venkatesh. 2006. “Multimode Locomotion via SuperBot Reconfigurable Robots.” Autonomous Robots 20 (2): 165–77. Shen, W. M., P. Will, A. Galstyan, and C. M. Chuong. 2004. “Hormone-Inspired Self- Organization and Distributed Control of Robotic Swarms.” Autonomous Robots 17 (1): 93–105. Sheridan, T. B., and R. W. Simpson. 1979. Toward the Definition and Measurement of the Mental Workload of Transport Pilots. Cambridge, Mass.: Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, Flight Transportation Laboratory,[1979]. http://dspace.mit.edu/handle/1721.1/67913. Simon, H. A. 1962. “The Architecture of Complexity.” Proceedings of the American Philosophical Society, 467–82. Simonin, O., and J. Ferber. 2000. “Modeling Self Satisfaction and Altruism to Handle Action Selection and Reactive Cooperation.” In The Sixth International Conference on the Simulation of Adaptative Behavior FROM ANIMALS TO ANIMATS, 6:314–23. http://www.loria.fr/~simoniol/OSimonin/travaux/SimoninFerberSAB2000.pdf. So, Y., and E. H. Durfee. 1998. Designing Organizations for Computational Agents, Simulating Organizations: Computational Models of Institutions and Groups. MIT Press, Cambridge, MA. Sproull, L., and S. Kiesler. 1992. Connections: New Ways of Working in the Networked Organization. MIT press. http://books.google.com/books?hl=en&lr=&id=xAviIJ- D- 1EC&oi=fnd&pg=PR9&dq=:++New++ways++of++working++in++the++networ ked+organization&ots=fJ9v964Y_I&sig=xG4YiWXVFEnnsm4F2R6f0xiuOis. Stoy, K., and R. Nagpal. 2007. “Self-Reconfiguration Using Directed Growth.” Distributed Autonomous Robotic Systems 6, 3–12. Suh, N. P. 1990. The Principles of Design. Vol. 990. Oxford University Press New York. http://www.maelabs.ucsd.edu/mae156/A_New/Resources/Design- Process/Axiomatic_Design/Axiomatic_Text_Excerpts.pdf. ———. 2001. “Axiomatic Design: Advances and Applications (The Oxford Series on Advanced Manufacturing).” http://www.citeulike.org/group/300/article/225343. Tang, Y., S. Parsons, and E. Sklar. 2007. “Modeling Human Education Data: From Equation-Based Modeling to Agent-Based Modeling.” Multi-Agent-Based Simulation VII, 41–56. Thompson, J. D. 1967. Organizations in Action: Social Science Bases of Administrative Theory. Transaction Pub. http://books.google.com/books?hl=en&lr=&id=YhHo7aHmBGMC&oi=fnd&pg= PA2&dq=Organizations+in+Action:+Social+Sciences+Bases+in+Administrative +Theory&ots=j_O5a-Ml-S&sig=LU34PBWB9DNeGvEkpcgTPjEnXAY. Tomiyama, T. 1995. “A Design Process Model That Unifies General Design Theory and Empirical Findings.” In Proceedings of the 1995 Design Engineering Technical Conferences, 2:329–40. Tomiyama, T., and H. Yoshikawa. 1986. “Extended General Design Theory.” http://www.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&rec id=N8632162AH. 145 Tynan, R., G. M. P. O’Hare, and A. Ruzzelli. 2006. “Multi-Agent System Methodology for Wireless Sensor Networks.” Multiagent and Grid Systems 2 (4): 491–503. Ünsal, C., H. Kili\cc\ccöte, M. E. Patton, and P. Khosla. 2000. “Motion Planning for a Modular Self-Reconfiguring Robotic System.” http://repository.cmu.edu/isr/541/. Vassilvitskii, S., M. Yim, and J. Suh. 2002. “A Complete, Local and Parallel Reconfiguration Algorithm for Cube Style Modular Robots.” In Robotics and Automation, 2002. Proceedings. ICRA’02. IEEE International Conference on, 1:117–22. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1013348. Viroli, M., M. Casadei, and A. Omicini. 2009. “A Framework for Modelling and Implementing Self-Organising Coordination.” In Proceedings of the 2009 ACM Symposium on Applied Computing, 1353–60. http://dl.acm.org/citation.cfm?id=1529585. Weiss, G. 2000. Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence. MIT press. http://books.google.com/books?hl=en&lr=&id=JYcznFCN3xcC&oi=fnd&pg=PR 19&dq=Multiagent+Systems:+A+Modern+Approach+to+Distributed+Artificial+I ntelligence.&ots=IG3YqGRmYt&sig=8iGRDlfXh-cUzFAHZ_OXGLrOHg0. Werfel, J. 2006. “Anthills Built to Order: Automating Construction with Artificial Swarms.” http://dspace.mit.edu/handle/1721.1/33791. Wilensky, U. 1999. “${$NetLogo$}$.” http://www.citeulike.org/group/2050/article/1283125. ———. 2001. “Modeling Nature’s Emergent Patterns with Multi-Agent Languages.” In Proceedings of EuroLogo. http://ccl.northwestern.edu/papers/MEE/. Williams, E. L. 1981. Thermodynamics and the Development of Order. Creation Research Society Books. http://www.getcited.org/pub/102249995. Wolfram, S. 2002. “A New Kind of Science.” http://austms.org.au/Jobs/Reviews2.html. Wood, R. E. 1986. “Task Complexity: Definition of the Construct.” Organizational Behavior and Human Decision Processes 37 (1): 60–82. Wooldridge, M. 2002. An Introduction to Multiagent Systems. Wiley. http://books.google.com/books?hl=en&lr=&id=C4_9riKP2kQC&oi=fnd&pg=PR 7&dq=Michael+Wooldridge+2002&ots=ovdu9A3272&sig=4xJkTlk9AYe8VCaa 13ZS2oarUoU. Yim, M. 1993. “A Reconfigurable Modular Robot with Many Modes of Locomotion.” In Proc. of Intl. Conf. on Advanced Mechatronics, 283–88. ———. 1994. “New Locomotion Gaits.” In Robotics and Automation, 1994. Proceedings., 1994 IEEE International Conference on, 2508–14. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=351134. Yim, M., Y. Zhang, and D. Duff. 2002. “Modular Robots.” Spectrum, IEEE 39 (2): 30– 34. Yoshikawa, H. 1981. “General Design Theory and a CAD System.” Man-Machine Communications inCAD/CAM. http://ci.nii.ac.jp/naid/10016110833/. Zouein, G., C. Chen, and Y. Jin. 2010. “Create Adaptive Systems through ‘DNA’ Guided Cellular Formation.” Design Creativity 2010, 149.
Abstract (if available)
Abstract
Conventional mechanical systems composed of various modules and parts are often inherently inadequate for dealing with unpredictable changing situations. Taking advantage of the flexibility of multi‐agent systems, a cellular self‐organizing (CSO) systems approach has been proposed, in which mechanical cells or agents self‐organize as the environment and tasks change based on a set of predefined rules. To enable CSO systems to deal with more realistic tasks, a two‐field mechanism is introduced to describe task and agent complexities and to investigate how social rules among agents can influence CSO system performance with increasing task complexity. A ""by emergence"" approach is presented to guide self‐organization in the system. Besides allowing agents to follow the attractors of their perceived task fields, the concept of ""social structure"" is introduced to capture explicit and direct interactions among agents and apply ""social rules"" to facilitate dynamical social structuring among agents. To further increase the level of order, a decision mechanism is proposed for agents to correlate their actions for better overall system performance. Proper interactions of mCells lead to the emergence of social structures that are closely interrelated with the task specifications. The simulation results of case studies based on the proposed mechanism provide insights into task‐driven dynamic structures and their effect on the behavior, and consequently the function, of CSO systems. In order to gain detail understanding and explore interplay between task and social structuring components, I investigated different aspect of social structuring including the impact of the population size, specificity of rules and rule adoption rate on the system performance.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
A meta-interaction model for designing cellular self-organizing systems
PDF
Behavioral modeling and computational synthesis of self-organizing systems
PDF
Building cellular self-organizing system (CSO): a behavior regulation based approach
PDF
Reward shaping and social learning in self- organizing systems through multi-agent reinforcement learning
PDF
A social-cognitive approach to modeling design thinking styles
PDF
Transfer reinforcement learning for autonomous collision avoidance
PDF
Nonlinear control of flexible rotating system with varying velocity
PDF
A biologically inspired DNA-based cellular approach to developing complex adaptive systems
PDF
A synthesis approach to manage complexity in software systems design
PDF
An approach to dynamic modeling of percussive mechanisms
PDF
On the synthesis of controls for general nonlinear constrained mechanical systems
PDF
Dynamic analysis and control of one-dimensional distributed parameter systems
PDF
Mathematical characterizations of microbial communities: analysis and implications
PDF
Design, modeling and analysis of piezoelectric forceps actuator
PDF
Modeling and dynamic analysis of coupled structure-moving subsystem problem
PDF
Nonlinear dynamics and nonlinear dynamical systems
PDF
Control of spacecraft with flexible structures using pulse-modulated thrusters
PDF
Control of two-wheel mobile platform with application to power wheelchairs
PDF
Large-scale path planning and maneuvering with local information for autonomous systems
PDF
Using nonlinear feedback control to model human landing mechanics
Asset Metadata
Creator
Khani, Newsha
(author)
Core Title
Dynamic social structuring in cellular self-organizing systems
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
02/13/2015
Defense Date
11/25/2014
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
complex systems,complexity,design synthesis,entropy,intelligence,OAI-PMH Harvest,organization,self‐organization,social field,social structuring
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Jin, Yan (
committee chair
), Flashner, Henryk (
committee member
), Meshkati, Najmedin (
committee member
), Shiflett, Geoffrey R. (
committee member
)
Creator Email
niusha.khani@gmail.com,nkhani@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c3-533197
Unique identifier
UC11297815
Identifier
etd-KhaniNewsh-3188.pdf (filename),usctheses-c3-533197 (legacy record id)
Legacy Identifier
etd-KhaniNewsh-3188.pdf
Dmrecord
533197
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Khani, Newsha
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
complex systems
complexity
design synthesis
entropy
intelligence
organization
self‐organization
social field
social structuring