Mathematical Modeling of Large Multi-Agent Systems

In recent years, considerable interest and enthusiasm have been generated by the prospect of widespread use of intelligent agent-based systems [18]. In particular, a number of researchers have been investigating the design and implementation of systems consisting of multiple agents [26]. The design of successful multiagent systems is, however, a problem of significant magnitude and difficulty. Often multiple, conflicting criteria have to be simultaneously optimized to come up with a cost-effective multiagent system design. Agent system design may involve designing the infrastructure or environment for agent interaction as well as behavioral strategies for individual or multiple agents. Agent behaviors handcrafted offline can be inadequate if possible interactions are overlooked. Genetic algorithms provide us with another tool for designing both individual agent behaviors as well as social rules for multiagent systems. In this chapter we identify different modes for evolving agent groups and present instances of two different approaches: a coevolutionary optimization approach, and an adaptive system approach.KeywordsShared MemoryMultiagent SystemAgent SocietySocial DilemmaQuadrupedal RobotThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Multi-agent systems consist of a number of interacting autonomous agents, each of which is capable of sensing its environment (including other agents) and deciding to act in order to achieve its own objectives. In order to guarantee the overall design objectives of multi-agent systems, the behavior of individual agents and their interactions need to be regulated and coordinated [23,29,30]. The development of multi-agent systems therefore requires programming languages that facilitate the implementation of individual agents as well as mechanisms that control and regulate individual agents' behaviors. It also requires computational tools to test and verify programs that implement multi-agent systems [7].

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results.

The field of multi-agent dynamic systems is an inter-disciplinary research field that has become very popular in the recent years in parallel with the significant interest in the practical applications of such systems in various areas including robotics. In this article we give a relatively short review of this field from the system dynamics and control perspective. We first focus on mathematical modelling of multi-agent systems paying particular attention on the agent dynamics models available in the literature. Then we present a number of problems on coordination and control of multi-agent systems which have gained significant attention recently and various approaches to these problems. Relevant to these problems and approaches, we summarize some of the recent results on stability, robustness, and performance of multi-agent dynamic systems which appeared in the literature. The article is concluded with some remarks on the implementation and application side of the control designs developed for multi-agent systems.

This paper reviews the proposed opponent modeling algorithms within the soccer simulation domain. RoboCup soccer simulation 2D is a rich multi agent environment where opponent modeling plays a crucial role. In multi agent systems with adversarial and cooperative agents, team agents should be adapted to the current environment and opponent in order to propose appropriate and effective counteractions. Predicting the opponent's future behaviors during competition allows for more informed decisions. We divide opponent modeling into two categories of individual agent behaviors and team behaviors. Individual behaviors concern modeling the low-level behaviors of individual opponent agents, however in team behaviors, the high-level strategy of the entire team like formation, offensive and defensive system, is recognized. Several methods have been proposed to create different models of opponents to improve the performance of teams in an essential aspect. In this paper, we review the approaches to the problem of opponent modeling published from 2000 to 2010.

The development of theoretical-based methods for the assessment of multi-agent systems properties is of critical importance. This work is a preliminary investigation on methodologies for modeling, analysis and design of multi-agent systems. Multi-agent systems are regarded as discrete-event dynamic systems and Petri nets are used as a modeling tool to assess the structural properties of the multi-agent system. Our methodology consists of defining a simple multi-agent system based on the abstract architecture for intelligent agents. The abstract architecture is modeled as a discrete-event system using Petri nets and structural analysis of the net provides an assessment of the communication and coordination properties of the multi-agent system. Deadlock avoidance in the multi-agent system is considered as an initial key property, and it is evaluated using liveness and boundedness properties of the Petri net model.

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

Like all systems, multi-agent systems need to be verified during the design cycle. But the test of multi-agent systems is more diffi-cult than the test of classic software. Indeed, it implies to test more than agent functionalities: individual agent behavior, inter-action between agents and global system need to be tested. Sever-al testing methods compensate these difficulties, but do not cover all the aspects of multi-agent systems. In this paper, we compare software testing and multi-agent systems testing and particularly in embedded context. Then major multi-agent system testing techniques are analyzed, with the AEIO facets for multi-agent systems. Finally, we propose a strategy to conduct the testing activity for embedded MAS.

The current economic crisis has provoked an active response from the interdisciplinary scientific community. As a result many papers suggesting what can be improved in understanding of the complex socio-economics systems were published. Some of the most prominent papers on the topic include (Bouchaud, 2009; Farmer and Foley, 2009; Farmer et al, 2012; Helbing, 2010; Pietronero, 2008). These papers share the idea that agent-based modeling is essential for the better understanding of the complex socio-economic systems and consequently better policy making. Yet in order for an agent-based model to be useful it should also be analytically tractable, possess a macroscopic treatment (Cristelli et al, 2012). In this work we shed a new light on our research group's contributions towards understanding of the correspondence between the inter-individual interactions and collective behavior. We also provide some new insights into the implications of the global and local interactions, the leadership and the predator-prey interactions in the complex socio-economic systems.

Multiagent systems in which independent software agents interact with each other to achieve common goals, complete distributed tasks concurrently under autonomous control. Agent communication has been shown to be an important factor in coordinating efficient group behavior in agents. Most research on training or evolving group behavior in multiagent systems used predefined agent communication protocols. Designing agent communication becomes a complex problem in dynamic and large-scale systems. In order to solve this problem, in our previous research we proposed a method applying genetic programming techniques, in particular Automatically Defined Function Genetic Programming (ADF-GP) (K. Mackin and E. Tazaki, 1999), to allow agents to autonomously learn effective agent communication messaging. For this research we take this approach further and combine training of the agent behavior as well as the communication protocol. By training both behavior and communication we expect to further optimize the system performance. A software simulation of a multiagent transaction system is used to observe the effectiveness of the proposed method.

Multiagent systems, in which independent software agents interact with each other to achieve common goals, complete concurrent distributed tasks under autonomous control. Agent Communication has been shown to be an important factor in coordinating efficient group behavior in agents. Most researches on training or evolving group behavior in multiagent systems used predefined agent communication protocols. Designing agent communication becomes a complex problem in dynamic and large‐scale systems. In order to solve this problem, in this paper we propose a new application of existing training methods. By applying Genetic Programming techniques, namely Automatically Defined Function Genetic Programming (ADF‐GP), in combination with pheromone communication features, we allowed the agent system to autonomously learn effective agent communication messaging for coordinated group behavior. A software simulation of a multiagent transaction system aiming at e‐commerce usage will be used to observe the effectiveness of the proposed method in the targeted environment. Using the proposed method, automatic training of a compact and efficient agent communication protocol for the multiagent system was observed.

The complexity of computer systems, networks and applications, as well as the advancements in computer technology, continue to grow at a rapid pace. Mathematical analysis, modeling and optimization have been playing, and continue to play, an important role in research studies to investigate fundamental issues and trade-offs at the core of performance problems in the design and implementation of complex computer systems, networks and applications. On June 20, 2014, the 16th Workshop on MAthematical performance Modeling and Analysis (MAMA 2014) was held in Austin TX, USA, sponsored by ACM SIGMETRICS, and held in conjunction with SIGMETRICS 2014. This workshop seeks to bring together researchers working on the mathematical, methodological and theoretical aspects of performance analysis, modeling and optimization. It is intended to provide a forum at SIGMETRICS conferences for talks on early research in the more mathematical areas of computer performance analysis. These talks tend to be based on very recent research results (including work in progress) or on new research results that will be otherwise submitted only to a journal (or recently have been submitted to a journal). Thus, part of the goal is to complement and supplement the SIGMETRICS Conference program with such talks without removing any theoretical contributions from the main technical program. Furthermore, we continue to experience the desired result of having abstracts from previous MAMA workshops appear as full papers in the main program of subsequent SIGMETRICS and related conferences. All submissions were reviewed by at least 4 members of the program committee, from which a total of 13 were selected for presentation at the MAMA 2014 workshop. This special issue of Performance Evaluation Review includes extended abstracts relating to these presentations (arranged in the order of their presentation), which cover a wide range of topics in the area of mathematical performance analysis, modeling and optimization. The study of Gelenbe examines the backlog of energy and of data packets in a sensor node that harvests energy, computing the properties of energy and data backlogs and discussing system stability. Meyfroyt derives asymptotic results for the coverage ratio under a specific class of spatial stochastic models (Cooperative Sequential Adsorption) and investigates the scalability of the Trickle communication protocol algorithm. The study of Tune and Roughan applies the principle of maximum entropy to develop fast traffic matrix synthesis models, with the future goal of developing realistic spatio-temporal traffic matrices. Bradonjić et al. compare and contrast the capacity, congestion and reliability requirements for alternative connectivity models of large-scale data centers relative to fat trees. The study of Rochman et al. considers the problem of resource placement in network applications, based on a largescale service faced with regionally distributed demands for various resources in cloud computing. Xie and Lui investigate the design and analysis of a rating system and a mechanism to encourage users to participate in crowdsourcing and to incentivize workers to develop high-quality solutions. The study of Asadi et al. formulates a general problem for the joint per-user mode selection, connection activation and resource scheduling of connections using both LTE and WiFi resources within the context of device-todevice communications. Zheng and Tan consider a nonconvex joint rate and power control optimization to achieve egalitarian fairness (max-min weighted fairness) in wireless networks, exploiting the nonlinear Perron-Frobenius theory and nonnegative matrix theory. The study of Goldberg et al. derives an asymptotically optimal control policy for a stochastic capacity problem of dynamically matching supply resources and uncertain demand, based on connections with lost-sales inventory models. Ghaderi et al. investigate a dynamic stochastic bin packing problem, analyzing the fluid limits of the system under an asymptotic best-fit algorithm and showing it asymptotically minimizes the number of servers used in steady state. The study of Tizghadam and Leon-Garcia examines the impact of overlaying or removing a subgraph on the Moore-Penrose inverse of the Laplacian matrix of an existing network topology and proposes an iterative method to find key performance measures. Miyazawa considers a two-node generalized Jackson network in a phase-type setting as a special case of a Markov-modulated twodimensional reflecting random walk and analyzes the tail asymptotics for this reflecting process. The study of Squillante et al. investigates improvement in scalability of search in networks through the use of multiple random walks, deriving bounds on the hitting time to a set of nodes and on various performance metrics.

The five papers in this special issue are based on a selection of top theoretical papers from the ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, which took place at Austin, Texas, in June 2014. As the premier conference on the measurement and modeling of computer systems, the technical program featured papers that covered both theory and applications from a wide variety of areas, including algorithms, communication networks, dynamics and control, optimization, performance analysis, resource allocation and scheduling, and stochastic modeling, among others. The program consisted of 40 papers selected from more than 237 international submissions by a technical program committee of well-established researchers from all over the world. We seek with this special issue to highlight some of the recent theoretical work on the mathematical analysis and modeling of computer systems. The paper of Larranaga, Ayesta, and Verloop deals with a resource allocation problem in a multi-class server with convex holding costs and user impatience under the average cost criterion. Although the optimal policy has a complex dependency on all the input parameters and state information, the authors derive simple index policies obtained by solving a relaxed version of the optimal stochastic control problem and combining results from restless multi-armed bandits and queueing theory.

Swarm-based systems are a class of multi-agent systems (MAS) of particular interest because they exhibit emergent behaviour through self-organisation. They are biology-inspired but find themselves applicable to a wide range of domains, with some of them characterised as mission critical. It is therefore implied that the use of a formal framework and methods would facilitate modelling of a MAS in such a way that the final product is fully tested and safety properties are verified. One way to achieve this is by defining a new formalism to specify MAS, something which could precisely fit the purpose but requires significant period to formally prove the validation power of the method. The alternative is to use existing formal methods thus exploiting their legacy. In this paper, we follow the latter approach. We present OPERAS, an open framework that facilitates formal modelling of MAS through employing existing formal methods. We describe how a particular instance of this framework, namely OPERAS XC , could integrate the most prominent characteristics of finite state machines and biological computation systems, such as X-machines and P Systems respectively. We demonstrate how the resulting method can be used to formally model a swarm system and discuss the flexibility and advantages of this approach.

Most agent architectures implement autonomous agents that use extensive interaction protocols and social laws to control interactions in order to ensure that the correct behaviors result during run-time. These agents, organized into multi-agent systems in which all agents adhere to predefined interaction protocols, are well suited to the analysis, design and implementation of complex systems in environments where it is possible to predict interactions during the analysis and design phases. In these multi-agent systems, intelligence resides in individual autonomous agents, rather than in the collective behavior of the individual agents. These agents are commonly referred to as “next-generation” or intelligent components, which are difficult to implement using current component-based architectures. In most distributed environments, such as the Internet, it is not possible to predict interactions during analysis and design. For a complex system to be able to adapt in such an uncertain and non-deterministic environment, we propose the use of agencies, consisting of simple agents, which use probabilistic reasoning to adapt to their environment. Our agents collectively implement distributed Bayesian networks, used by the agencies to control behaviors in response to environmental states. Each agency is responsible for one or more behaviors, and the agencies are structured into heterarchies according to the topology of the underlying Bayesian networks. We refer to our agents and agencies as “Bayesian agents” and “Bayesian agencies.”