Differential Evolution Enhanced by Neighborhood Search Hui Wang, Zhijian Wu and Shahryar Rahnamayan Abstract— This paper presents a novel Differential Evolution (DE) algorithm, called DE enhanced by neighborhood search (DENS), which differs from pervious works of utilizing the neighborhood search in DE, such as DE with neighborhood search (NSDE) and self-adaptive DE with neighborhood search (SaNSDE). In DENS, we focus on searching the neighbors of individuals, while the latter two algorithms (NSDE and SaNSDE) work on the adaption of the control parameters F and CR. The proposed algorithm consists of two following main steps. First, for each individual, we create two trial individuals by local and global neighborhood search strategies. Second, we select the fittest one among the current individual and the two created trial individuals as a new current individual. Experi- mental studies on a comprehensive set of benchmark functions show that DENS achieves better results for a majority of test cases, when comparing with some other similar evolutionary algorithms. Index Terms— Differential evolution, neighborhood search, local search, global optimization. I. I NTRODUCTION Differential Evolution (DE), proposed by Price and Storn [1], is an effective, robust, and simple global optimization algorithm. According to frequently reported experimental studies, DE has shown better performance than many other evolutionary algorithm (EAs) in terms of convergence speed and robustness over several benchmark functions and real- world problems [2]. Since the development of DE, many improved versions have been proposed. Based on the improved mechanisms, we can divide them into three categories as follows. 1) Adaptive Parameter Control: The classical DE algo- rithm only has three control parameters N p (population size), CR and F , which greatly affect performance of DE. The values of these parameters highly determine the quality of the obtained solution and the efficiency of the search [3]. Choosing appropriate parameter val- ues is a problem dependent task and requires previous experience and knowledge of the user. To tackle this problem, some adaptive parameter control strategies have been proposed, such as fuzzy DE (FADE) [4] self-adaptive DE (SaDE) [5], [6], self-adapting control parameters in DE (jDE) [3], DE with neighborhood search (NSDE) [7] and self-adaptive DE with neigh- borhood search (SaNSDE) [8]. Hui Wang and Zhijian Wu are with the State Key Laboratory of Software Engineering, Wuhan University, Wuhan, 430072 China (e-mail: wanghui cug@yahoo.com.cn; zjwu9551@sina.com). Shahryar Rahnamayan is with Faculty of Engineering and Ap- plied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, ON L1H 7K4, Canada (e-mail: shahryar.rahnamayan@uoit.ca). 2) Modified Mutation Strategies: The DE algorithm has two important operators (besides the selection), muta- tion and crossover. The former is determined by the mutation strategies, and the latter is dominated by the crossover probability CR and crossover strategy. Besides the improvement of the control parameters, some modifications of the mutation strategies could also improve the performance of DE. DE/current-to- pbest [9] and DE/target-to-best/1 [10] are some exam- ples among others. 3) Hybrid Strategies: Recently, some new works have been introduced by combining the classical DE with the concepts of machine learning and some successful search techniques. These new improved DE variants are called hybrid DE, such as opposition-based DE (ODE) [11], [12], [13], [14], DE with adaptive local search (DEahcSPX) [15], and DE based on generalized opposition-based learning (GODE) [16]. In this paper, we present a novel DE algorithm, called DE enhanced by neighborhood search (DENS), to improve the performance of the standard DE. In order to verify the perfor- mance of DENS, current work provides a comparative study of DENS and other similar DE variants on a comprehensive set of benchmark functions. The rest of the paper is organized as follows. In Section II, the classical DE algorithm is briefly reviewed. The proposed approach, DENS, is presented in Section III. In Section IV, the test functions, parameter settings and the comparison of DENS with other similar algorithms are provided. Finally, the work is summarized and concluded in Section V. II. A BRIEF REVIEW OF DIFFERENTIAL EVOLUTION DE is a population-based stochastic search algorithm, and has been successfully applied to solve complex problems including linear and nonlinear, unimodal and multimodal functions. It has been investigated that DE is faster and more robust on majority of functions than many other evolutionary algorithms [2]. There are several variants of DE [1], where the most popular variant is indicated by “DE/rand/1/bin” which is called classical version. The proposed algorithm is also based on this DE scheme. Let us assume that X i,G (i =1, 2,...,N p ) is the ith individual in population P (G), where N p is the population size, G is the generation index, and P (G) is the population in the Gth generation. The main idea of DE is to generate trial vectors. Mutation and crossover are used to produce new trial vectors, and selection determines which of the vectors will be successfully selected into the next generation. 978-1-4244-8126-2/10/$26.00 ©2010 IEEE