A memetic particle swarm optimization algorithm for multimodal optimization problems Hongfeng Wang a,b,c,⇑ , Ilkyeong Moon b,⇑ , Shenxiang Yang c,d , Dingwei Wang a,c a School of Information Science and Engineering, Northeastern University, Shenyang 110819, China b Department of Industrial Engineering, Pusan National University, Pusan, Republic of Korea c State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China d Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom article info Article history: Received 9 September 2009 Received in revised form 6 March 2011 Accepted 15 February 2012 Available online 24 February 2012 Keywords: Multimodal optimization problem Memetic algorithm Particle swarm optimization Local search Species abstract Recently, multimodal optimization problems (MMOPs) have gained a lot of attention from the evolutionary algorithm (EA) community since many real-world applications are MMOPs and may require EAs to present multiple optimal solutions. In this paper, a memetic algorithm that hybridizes particle swarm optimization (PSO) with a local search (LS) technique, called memetic PSO (MPSO), is proposed for locating multiple global and local optimal solutions in the fitness landscape of MMOPs. Within the framework of the proposed MPSO algorithm, a local PSO model, where the particles adaptively form different species based on their indices in the population to search for different sub-regions in the fitness landscape in parallel, is used for globally rough exploration, and an adaptive LS method, which employs two different LS operators in a cooperative way, is proposed for locally refining exploitation. In addition, a triggered re-initialization scheme, where a species is re-initialized once converged, is introduced into the MPSO algorithm in order to enhance its performance of solving MMOPs. Based on a set of benchmark functions, experiments are carried out to investigate the performance of the MPSO algorithm in comparison with some EAs taken from the literature. The experimental results show the efficiency of the MPSO algorithm for solving MMOPs. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Hard optimization problems, such as constrained optimization problems [5,23], multi-objective optimization problems [7,34,40], and dynamic optimization problems [3,12,38], have always gained a lot of attention due to their universality in scientific and engineering applications. It is noticeable that many real-world optimization problems are multimodal optimi- zation problems (MMOPs) and may require a solving algorithm to provide multiple optimal solutions in the search space. For example, multiple objects always need to be mapped simultaneously in the machine vision application [4]. For this kind of MMOPs, a solving algorithm is required to obtain all global optima and even locate all, or as many as possible, local optima. In recent years, investigating the performance of evolutionary algorithms (EAs) for MMOPs has attracted a growing inter- est from the EA community. However, MMOPs pose serious challenges to traditional EAs since the population tends to con- verge to a single solution. In order to address this problem, a number of approaches have been developed into EAs for solving MMOPs recently. For example, the niche or speciation techniques have been developed to first distribute the individuals on multiple different peaks in the solution space and then allow EAs to exploit those peaks simultaneously. 0020-0255/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2012.02.016 ⇑ Corresponding authors. Address: School of Information Science and Engineering, Northeastern University, Shenyang 110819, China (H. Wang). E-mail addresses: hfwang@mail.neu.edu.cn (H. Wang), ikmoon@pusan.ac.kr (I. Moon). Information Sciences 197 (2012) 38–52 Contents lists available at SciVerse ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins