IEEE Proof IEEE TRANSACTIONS ON CYBERNETICS 1 Self-Adaptive Differential Evolution Algorithm With Zoning Evolution of Control Parameters and Adaptive Mutation Strategies Qinqin Fan and Xuefeng Yan Abstract—The performance of the differential evolution (DE) algorithm is significantly affected by the choice of mutation strategies and control parameters. Maintaining the search capa- bility of various control parameter combinations throughout the entire evolution process is also a key issue. A self-adaptive DE algorithm with zoning evolution of control parameters and adap- tive mutation strategies is proposed in this paper. In the proposed algorithm, the mutation strategies are automatically adjusted with population evolution, and the control parameters evolve in their own zoning to self-adapt and discover near optimal val- ues autonomously. The proposed algorithm is compared with five state-of-the-art DE algorithm variants according to a set of benchmark test functions. Furthermore, seven nonparamet- ric statistical tests are implemented to analyze the experimental results. The results indicate that the overall performance of the proposed algorithm is better than those of the five existing improved algorithms. Index Terms—Control parameter adaptation, differential evolution (DE) algorithm, mutation strategy adaptation, zoning evolution. I. I NTRODUCTION D IFFERENTIAL evolution (DE) algorithm proposed by Storn and Price [1] is a competitive and reliable evo- lutionary computing technique for solving a wide vari- ety of complex optimization problems. The optimization performance [2]–[5] of the DE algorithm not only depends on the choice of three control parameters (i.e., muta- tion control parameter F, crossover control parameter CR, and population size NP), but also on the choice of trial vector generation strategies (i.e., mutation and crossover strategies). To improve the algorithm’s performance, several useful empirical guidelines for selecting control parameter settings and mutation strategies have been introduced by many researchers during the past decade. Eiben et al. [6] and Manuscript received December 10, 2013; revised November 16, 2014 and January 21, 2015; accepted January 27, 2015. This work was supported in part by the 973 project of China under Grant 2013CB733600, in part by the National Natural Science Foundation of China under Grant 21176073, in part by the Program for New Century Excellent Talents in University under Grant NCET-09-0346, and in part by the Fundamental Research Funds for the Central Universities. This paper was recommended by Y. Jin. The authors are with the Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China (e-mail: xfyan@ecust.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCYB.2015.2399478 Brest et al. [7] proposed three parameter control techniques (i.e., deterministic, adaptive, and self-adaptive) and an encod- ing technique (i.e., encoding control parameters F and CR into an individual), respectively. However, different optimization problems or particular evolution stages often require chosen mutation strategies and suitable control parameters [8] dur- ing the evolution process; an inappropriate choice of mutation strategies and control parameters may directly influence the algorithm’s performance [9]–[11]. Different control param- eter combinations may also significantly affect algorithm’s search capability. Wang et al. [5] and Mallipeddi et al. [8] employed constant combinations of control parameters (i.e., F and CR values are determined before actual DE usage) to maintain the searching capability of the control parame- ter combinations; however, their proposed methods may be unable to adapt quickly in complex optimization environments. On the basis of these considerations, obtaining the most suitable mutation strategy and reasonable combinations of control parameters at different evolution phases is important to improve DE performance. In this paper, a self-adaptive DE (SDE) algorithm with zoning evolution of control parame- ters and adaptive mutation strategies (ZEPDE) is proposed. In ZEPDE, the number of each mutation strategy can be gradually adjusted via a roulette wheel, and real-time optimal control parameter combinations can be obtained by zoning evolution, which can maintain the control parameter distribution. ZEPDE was compared with five improved DE variants according to 25 CEC2005 and 28 CEC2013 test functions. The remainder of this paper is organized as follows. Section II introduces the basic DE algorithm. Section III reviews the related researches on DE algorithm. Section IV presents the proposed ZEPDE algorithm. Section V reports the experimental results and sensitive analysis of ZEPDE parameters. Finally, the conclusion is summarized in Section VI. To gain better understanding, interested readers can refer to the supplementary file. II. DE ALGORITHM In the evolution process of DE, mutation, crossover, and selection operators are performed. The vector con- taining D optimized variables x 1 , x 2 ,..., x D is denoted by x. x G i = [x G i,1 , x G i,2 ,..., x G i,D ] denotes the ith solution (or individual) in the Gth generation. The population of the Gth generation is denoted by X G = [x G 1 , x G 2 ,..., x G NP ], which 2168-2267 c  2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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