Advances in Computer Science and its Applications 5 Vol. 1, No. 1, March 2012 Copyright © World Science Publisher, United States www.worldsciencepublisher.org A Robust Hybrid Restarted Simulated Annealing Particle Swarm Optimization Technique Yudong Zhang, Lenan Wu School of Information Science and Engineering, Southeast University, Nanjing, China zhangyudongnuaa@gmail.com, wuln@seu.edu.cn Abstract: Global optimization is a hot topic of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions. In this paper we proposed a hybrid restarted simulated annealing particle swarm optimization (RSAPSO) technique to find global minima more efficiently and robustly. The proposed RSAPSO combines the global search ability of PSO and the local search ability of RSA, and offsets the weaknesses of each other. The four benchmark functions demonstrate the superiority of our algorithm. Keywords: global search, local search, simulated annealing, particle swarm optimization. 1 Introduction Particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality [1]. It is commonly known as metaheuristic method as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. PSO does not use the gradient of the problem being optimized, which means PSO does not require for the optimization problem to be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. PSO can therefore also be used on optimization problems that are partially irregular, noisy, adaptive, etc [2]. PSO is widely applied in various fields. Lin et al. [3] proposed an immune PSO with functional link based neuro-fuzzy network for image backlight compensation. Fan et al. [4] integrates the PSO and entropy matching estimator to seek the optimal parameter of the generalized Gaussian distribution mixture model. Zahara et al. [5] used PSO to obtain the optimal thresholding of multi- level image segmentation. Zhang et al. [6] proposed an adaptive chaotic PSO for magnetic resonance brain image classification. Samanta et al. [7] integrated PSO to artificial neural networks (ANN) and support vector machine (SVM) for machinery fault detection, and demonstrated the results of PSO is superior to the ones of genetic algorithm. Zhang et al. [8] proposed a neural network by PSO for remote-sensing image classification. Unfortunately, PSO is easy to be trapped into local minima and its calculation efficiency is low. In the worst case, when the best solution found by the group and the particles are all located at the same local minimum, it is almost impossible for particles to jump out and do further searching due to the velocity update equation [9]. The reason lies in the fact that PSO is powerful of global search but weak on local search. Therefore, our strategy is to introduce in a local search which is applied during each update cycle. In this study, simulated annealing (SA) was chosen as the local search method. SA comes from annealing in metallurgy [10], a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects [11]. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one [12]. Moreover, we introduced in the restarted simulated annealing (RSA) technique to improve the performance of SA. The hybrid algorithm combines both global search provided by PSO and local search provided by RSA [13]. The structure of the rest of the paper is organized as follows: Next section 2 introduces the basic principles and procedures of PSO; Section 3 gives detailed description of RSA; Section 4 proposes the RSAPSO technique with particular explanation of every step; Experiments in section 5 demonstrate the RSAPSO outperforms GA, SA, and PSO; Final section 0 concludes the paper. 2 Particle Swarm Optimization PSO is a population based stochastic optimization technique, which simulates the social behavior of a swarm of bird, flocking bees, and fish schooling. By randomly initializing the algorithm with candidate solutions, the PSO successfully leads to a global optimum. This is achieved by an iterative procedure based on the processes of movement and intelligence in an evolutionary system. Fig. 1 shows the flow chart of a PSO algorithm.