Applied Soft Computing 13 (2013) 390–401 Contents lists available at SciVerse ScienceDirect Applied Soft Computing j ourna l ho me p age: www.elsevier.com/l ocate/asoc A differential evolution algorithm with intersect mutation operator Yinzhi Zhou, Xinyu Li, Liang Gao ∗ State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan 430074, PR China a r t i c l e i n f o Article history: Received 3 May 2011 Received in revised form 6 April 2012 Accepted 4 August 2012 Available online 25 August 2012 Keywords: Differential evolution (DE) Intersect mutation operation Global search Local search a b s t r a c t This paper proposes a novel differential evolution (DE) algorithm with intersect mutation operation called intersect mutation differential evolution (IMDE) algorithm. Instead of focusing on setting proper param- eters, in IMDE algorithm, all individuals are divided into the better part and the worse part according to their fitness. And then, the novel mutation and crossover operations have been developed to generate the new individuals. Finally, a set of famous benchmark functions have been used to test and evalu- ate the performance of the proposed IMDE. The experimental results show that the proposed algorithm is better than, or at least comparable to the self-adaptive DE (JDE), which is proven to be better than the standard DE algorithm. In further study, the IMDE algorithm has also been compared with several improved Particle Swarm Optimization (PSO) algorithms, Artificial Bee Colony (ABC) algorithm and Bee Swarm Optimization (BSO) algorithm. And the IMDE algorithm outperforms these algorithms. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Differential evolution (DE) is a simple yet powerful evolutionary algorithm (EA) first introduced by Storn and Price [1]. With the advantages of simplicity, fast convergence and less parameter, DE has been used in many areas, such as scheduling [2,3], structural optimization [4], satellite image registration [5], biogeography [6], and so on [7–9]. Just like some other EAs, DE consists of three main operations: mutation, crossover and selection, and three important parame- ters: NP (number of individuals), F (mutation parameter) and CR (crossover parameter). Since DE was firstly introduced in 1997 [1], many researchers have focused on the setting of these three param- eters. Mutation parameter F controls the disturbance caused by the difference between two randomly selected individuals. So it is a crucial factor for the population diversity. If F is too small, DE may lose the ability of converging to global optimum. Zaharie [10] pre- sented an important result in which F should never be smaller than F crit where F crit =  1 - CR/2 NP (1) Crossover parameter CR controls how many variables of trail vector belong to target vector, i.e. the distance between trail vector and target vector. So, CR influences the convergence speed. Rönkkö- nen and Kukkonen [11] stated that CR should be smaller than 0.2 ∗ Corresponding author. E-mail address: gaoliang@mail.hust.edu.cn (L. Gao). when DE was used to solve the separable functions and larger than 0.9 for solving the non-separable ones. There are quite different conclusions about the best setting of F and CR. Storn and Price [12,13] stated that they are not difficult to set, and the value of F should be in the range [0.4, 1] and NP should be between 5n and 10n, where n is the number of variables. However, Gämperle [14] reported that the values of F, CR and NP can be quite difficult to find, and some functions are sensitive to the proper setting of these parameters. He suggested that the value of NP should be between 3n and 8n, and F should be 0.6, while CR should be in the range [0.3, 1.0]. Wang and Huang [15] also analyzed the probability distribution of the population changed by mutation, selection and crossover operations. They provided some guidelines about the setting of parameters in accordance with the theoretical analysis. Some researchers tried to adapt the values adjustable to vari- able problems and have developed several improved DE algorithms with adaptive control parameters. Since the setting of proper F and CR values varies restricted to the problems, strategies and other application environment, Zaharie [16] proposed an adaptive DE algorithm named ADE with a variable population. He found that the convergence rate pertains to the decreasing rate of population vari- ance. Therefore a parameter was applied to control the decreasing rate of population variance. Liu and Lampinen [17] presented a new fuzzy adaptive DE algorithm named FADE. They used fuzzy logic controllers to adapt F and CR. The experiment results showed that the FADE algorithm converged much faster than the traditional DE particularly when the dimensionality of the problem is high or the problem concerned is complicated. Brest et al. [18] presented a self-adaptive DE algorithm called JDE. They set F and CR as random numbers with certain ranges or as the values of latest generation 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2012.08.014