An Agent Based Implementation of Proactive S-Metaheuristics

An Agent Based Implementation of Proactive S-Metaheuristics Mailyn Moreno1, Alejandro Rosete1, and Juán Pavón2 1 Facultad de Ingeniería Informática, Instituto Superior Politécnico “José Antonio Echeverría” (CUJAE), La Habana, Cuba {my,rosete}@ceis.cujae.edu.cu 2 Dep. Ingeniería del Software e Inteligencia Artificial, Universidad Complutense de Madrid, Spain jpavon@fdi.ucm.es Abstract. This paper presents the use of a multi-agent system for the development of proactive S-Metaheuristics (i.e. single-solution based metaheuristics) derived from Record-to-Record Travel (RRT) and Local Search. The basic idea is to implement metaheuristics as agents that operate in the environment of the optimization process with the goal of avoiding stagnation in local optima by adjusting their parameters and neighborhood. Environmental information about previous solutions is used to determine the best operators and parameters. The proactive adjustment of the neighborhood is based on the identification of the best operators using Fitness Distance Correlation (FDC). The proactive adjustment of the parameters is focused on guarantying a minimal level of acceptance of new solutions. Besides, a simple form of combination of both proactive behaviors is introduced. The system has been validated through experimentation with 28 functions on binary strings. Keywords: Metaheuristics, Agents, Proactivity, Local Search, RRT, FDC. 1 Introduction Metaheuristics are popular optimization methods due to their ability to find good solutions (not necessarily optimal) to complex optimization problems in different domains [1]. Local Search (LS) is an important root in the genealogy of metaheuristics [1] that iteratively improves a solution according to the criteria to be optimized. The principal problem of LS is the convergence to local (not global) optima. The existence of local optima is the consequence of two aspects: operators (neighborhood) and acceptance criterion. Many S-Metaheuristics (single-solution based metaheuristics) [1] have been designed to overcome this problem by relaxing the acceptance criterion (some worse solutions are accepted) or by modifying the neighborhood. In all these metaheuristics, several parameters need to be adjusted to get good results. Besides, according to the No Free Lunch (NFL) theorem, it is impossible to demonstrate that one metaheuristic outperforms all the others in all possible problems [2]. Several predictive measures of problem difficulty (e.g. Fitness Distance Correlation J.-S. Pan et al. (Eds.): HAIS 2013, LNAI 8073, pp. 1–10, 2013. © Springer-Verlag Berlin Heidelberg 2013 2 M. Moreno, A. Rosete, and J. Pavón (FDC) [3]) have been proposed to learn which characteristics of a problem make it difficult for certain metaheuristic. This paper is focused is developing proactive S-Metaheuristics that behave proactively (i.e., adjusting themselves the parameters and neighborhood), according to the goals of the optimizer. We use the i* language [5] to model S-Metaheuristics as agents that act in an environment (optimization process) with the goal of achieving a global optimum, while avoiding local optima. This facilitates the identification of goals, and plans to incorporate proactivity. The use of a multi-agent system provides flexibility in the solution as agents can negotiate among them and adjust parameters. The system evolves through a series of iterations by considering previous solutions to detect the best parameter settings and neighborhood structure. Section 2 explains the main concepts of agents and metaheuristics that are relevant to this paper. Section 3 presents the analysis and design of the system model with the i* methodology. This model applies proactive adjustment of parameters and neighborhoods, based on the information gathered from the environment. Section 4 presents an experimental validation of the proactive metaheuristics in 28 functions on 100-bits strings. Section 5 presents the conclusions and discusses possible extensions to this approach. 2 S-Metaheuristics and Agents 2.1 S-Metaheuristics: Parameters, Neighborhoods, and Measures S-Metaheuristics are single-solution based metaheuristics [1], which use the current (single) solution as a reference, in order to generate new solutions by consecutive applications of the operators. All S-Metaheuristics keep the best solution found during the course of the optimization process. The performance of metaheuristics depends highly on the balance between two factors: exploration and exploitation [1]. Random Search (RS) is located in one extreme of exploration, because every new solution is generated without any considerations of the previously generated solutions. Local Search (LS) is in the other extreme, because it generates new solutions as modifications of the best previous solutions. A new solution is only accepted as a reference to generate new ones if it is better than the previous solution. This acceptance criterion can lead to converge to local (not global) optima, where the optimization is stagnated. As local optima are consequence of operators (neighborhood) and acceptance criterion, many S-Metaheuristics have been designed to overcome this issue by relaxing the acceptance criterion, and considering some worse solutions as new references. For example, in Random Walk (RW) every new solution (worse or better) is accepted as reference. Other S-Metaheuristics, such as Record-to-Record Travel (RRT), and Great Deluge Algorithms (GDA) use a moderated acceptance criterion. They accept some worse solutions taking into account the quality of the new solution, and some other aspects and parameters. For instance, RRT accepts worse solutions which are not much worse than the best solution in a certain parameter (Deviation). The parameter Deviation directly affects the performance of RRT, because it controls the balance between exploitation and exploration. For example, RRT with a very high value of deviation is similar to RW. In contrast to the modification of the acceptance