Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary algorithms we introduce, establish Nash Equilibrium in those models, in contrast to the "individual learning" versions which, as we see here, do not imply the convergence of the players' strategies to the Nash outcome. When players use "canonical co-evolutionary genetic algorithms" as learning algorithms, the process of the game is an ergodic Markov Chain, and therefore we analyze simulation results using both the relevant methodology and more general statistical tests, to find that in the "social" case, states leading to NE play are highly frequent at the stationary distribution of the chain, in contrast to the "individual learning" case, when NE is not reached at all in our simulations; to find that the expected Hamming distance of the states at the limiting distribution from the "NE state" is significantly smaller in the "social" than in the "individual learning case"; to estimate the expected time that the "social" algorithms need to get to the "NE state" and verify their robustness and finally to show that a large fraction of the games played are indeed at the Nash Equilibrium.Comment: 18 pages, 4 figure

DARP: Divide Areas Algorithm for Optimal Multi-Robot Coverage Path Planning

This paper deals with the path planning problem of a team of mobile robots, in order to cover an area of interest, with prior-defined obstacles. For the single robot case, also known as single robot coverage path planning (CPP), an (n) optimal methodology has already been proposed and evaluated in the literature, where n is the grid size. The majority of existing algorithms for the multi-robot case (mCPP), utilize the aforementioned algorithm. Due to the complexity, however, of the mCPP, the best the existing mCPP algorithms can perform is at most 16 times the optimal solution, in terms of time needed for the robot team to accomplish the coverage task, while the time required for calculating the solution is polynomial. In the present paper, we propose a new algorithm which converges to the optimal solution, at least in cases where one exists. The proposed technique transforms the original integer programming problem (mCPP) into several single-robot problems (CPP), the solutions of which constitute the optimal mCPP solution, alleviating the original mCPP explosive combinatorial complexity. Although it is not possible to analytically derive bounds regarding the complexity of the proposed algorithm, extensive numerical analysis indicates that the complexity is bounded by polynomial curves for practically sized inputs. In the heart of the proposed approach lies the DARP algorithm, which divides the terrain into a number of equal areas each corresponding to a specific robot, so as to guarantee complete coverage, non-backtracking solution, minimum coverage path, while at the same time does not need any preparatory stage (video demonstration and standalone application are available on-line http://tinyurl.com/DARP-app)

Autonomous trajectory design system for mapping of unknown sea-floors using a team of AUVs

This research develops a new on-line trajectory planning algorithm for a team of Autonomous Underwater Vehicles (AUVs). The goal of the AUVs is to cooperatively explore and map the ocean seafloor. As the morphology of the seabed is unknown and complex, standard non-convex algorithms perform insufficiently. To tackle this, a new simulationbased approach is proposed and numerically evaluated. This approach adapts the Parametrized Cognitive-based Adaptive Optimization (PCAO) algorithm. The algorithm transforms the exploration problem to a parametrized decision-making mechanism whose real-time implementation is feasible. Upon that transformation, this scheme calculates off-line a set of decision making mechanism’s parameters that approximate the - nonpractically feasible - optimal solution. The advantages of the algorithm are significant computational simplicity, scalability, and the fact that it can straightforwardly embed any type of physical constraints and system limitations. In order to train the PCAO controller, two morphologically different seafloors are used. During this training, the algorithm outperforms an unrealistic optimal-one-step-ahead search algorithm. To demonstrate the universality of the controller, the most effective controller is used to map three new morphologically different seafloors. During the latter mapping experiment, the PCAO algorithm outperforms several gradient-descent-like approaches

Large scale nonlinear control system fine-tuning through learning

ISSN:1045-9227ISSN:1941-009

An adaptive algorithm for deploying self-tuning traffic control systems

Currently, a considerable amount of human effort and time is spent for initialization or calibration of operational traffic control systems. Typically, this optimization (fine-tuning) procedure is conducted manually, via trial-and-error, relying on expertise and human judgment and does not always lead to a desirable outcome. This paper presents a new learning/adaptive algorithm that enables automatic fine-tuning of general traffic control systems. The efficiency and online feasibility of the algorithm is investigated through extensive simulation experiments. The fine-tuning problem of three mutually-interacting control modules – each one with its distinct design parameters – of an urban traffic signal control strategy is thoroughly investigated. Simulation results indicate that the learning algorithm can provide efficient automatic fine-tuning, guaranteeing safe and convergent behavior

Simulation and Use of Heuristics for Peripheral Economic Policy

Recent trends in Agent Computational Economics research, envelop a government agent in the model of the economy, whose decisions are based on learning algorithms. In this paper we try to evaluate the performance of simulated annealing in this context, by considering a model proposed earlier in the literature, which has modeled an artificial economy consisting of geographically dispersed companies modeled as agents, that try to maximize their profit, which is yielded by selling an homogeneous product in different cities, with different travel costs. The authors have used an evolutionary algorithm there, for modeling the agents' decision process. Our extension introduces a government agent that tries to affect supply and demand by different taxation coefficients in the different markets, in order to equate the quantities sold in each city. We have studied the situation that occurs when a simulated annealing algorithm and a simple search algorithm is used as the government's learning algorithm, and we have evaluated the comparative performance of the two.

Scalable and Convergent Multi-Robot Passive and Active Sensing

A major barrier preventing the wide employment of mobile networks of robots in tasks such as exploration, mapping, surveillance, and environmental monitoring is the lack of efficient and scalable multi-robot passive and active sensing (estimation) methodologies. The main reason for this is the absence of theoretical and practical tools that can provide computationally tractable methodologies which can deal efficiently with the highly nonlinear and uncertain nature of multi-robot dynamics when employed in the aforementioned tasks. In this paper, a new approach is proposed and analyzed for developing efficient and scalable methodologies for a general class of multi-robot passive and active sensing applications. The proposed approach employs an estimation scheme that switches among linear elements and, as a result, its computational requirements are about the same as those of a linear estimator. The parameters of the switching estimator are calculated off-line using a convex optimization algorithm which is based on optimization and approximation using Sum-of-Squares (SoS) polynomials. As shown by rigorous arguments, the estimation accuracy of the proposed scheme is equal to the optimal estimation accuracy plus a term that is inversely proportional to the number of estimator's switching elements (or, equivalently, to the memory storage capacity of the robots' equipment). The proposed approach can handle various types of constraints such as communication and computational constraints as well as obstacle avoidance and maximum speed constraints and can treat both problems of passive and active sensing in a unified manner. The efficiency of the approach is demonstrated on a 3D active target tracking application employing flying robots