A Chaotic Particle Swarm Optimization Exploiting Snap-Back Repellers of a Perturbation-Based System
The particle swarm optimization (PSO) is a population-based optimization technique, where a number of candidate solutions called particles simultaneously move toward the tentative solutions found by particles so far, which are called the personal and glob
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Abstract The particle swarm optimization (PSO) is a population-based optimization technique, where a number of candidate solutions called particles simultaneously move toward the tentative solutions found by particles so far, which are called the personal and global bests, respectively. Since, in the PSO, the exploration ability is important to find a desirable solution, various kinds of methods have been investigated to improve it. In this paper, we propose novel PSOs exploiting a chaotic system derived from the steepest descent method with perturbations to a virtual quartic objective function having its global optima at the personal and global best. In those models, each particle’s position is updated by the proposed chaotic system or the existing update formula. Thus, the proposed PSO can search for solutions without being trapped at any local minima due to the chaoticness. Moreover, we show the sufficient condition of parameter values of the proposed system under which the system is chaotic. Through computational experiments, we confirm the performance of the proposed PSOs by applying it to some global optimization problems.
S. Nakashima (B) · T. Ibuki · K. Tatsumi · T. Tanino Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan e-mail: [email protected] T. Ibuki e-mail: [email protected] K. Tatsumi e-mail: [email protected] T. Tanino e-mail: [email protected] H. Xu et al. (eds.), Optimization and Control Techniques and Applications, 237 Springer Proceedings in Mathematics & Statistics 86, DOI: 10.1007/978-3-662-43404-8_13, © Springer-Verlag Berlin Heidelberg 2014
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1 Introduction The particle swarm optimization (PSO) is a population-based stochastic optimization technique which is inspired by the social behavior of bird flocking or fish schooling [KE95]. In the PSO, a number of candidate solutions called particles are simultaneously updated toward the tentative best solutions called the personal best and global best, respectively, which are found by particles so far. The PSO is a very simple and has a high performance to find desirable solutions, while it is known to suffer from the premature convergence prior to discovering such solutions. Thus, in order to improve the exploration ability, various kinds of improved methods have been investigated [Cle06, PKB07]. Now, we focus on the PSOs exploiting a chaotic system to improve the exploration ability. Those methods often use chaotic sequences to update positions of particles, in which particles search for solutions extensively because of the chaoticness. It has been reported that this kind of PSOs have a wider diversification ability than the original PSO [AAO09]. However, since those methods often use a single kind of well-known function such as the logistic function to generate chaotic sequences for any optimization problems, the sequences are not necessarily suitable to solve the optimization problem. In this paper, we propose a new chaot
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