Memetic Differential Evolution with an Improved Contraction Criterion.

Lei Peng,Guangming Dai,Yanyun Zhang,Maocai Wang

doi:10.1155/2017/1395025

Lei Peng, Guangming Dai + Show 2 more

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https://doi.org/10.1155/2017/1395025

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Abstract

Memetic algorithms with an appropriate trade-off between the exploration and exploitation can obtain very good results in continuous optimization. In this paper, we present an improved memetic differential evolution algorithm for solving global optimization problems. The proposed approach, called memetic DE (MDE), hybridizes differential evolution (DE) with a local search (LS) operator and periodic reinitialization to balance the exploration and exploitation. A new contraction criterion, which is based on the improved maximum distance in objective space, is proposed to decide when the local search starts. The proposed algorithm is compared with six well-known evolutionary algorithms on twenty-one benchmark functions, and the experimental results are analyzed with two kinds of nonparametric statistical tests. Moreover, sensitivity analyses for parameters in MDE are also made. Experimental results have demonstrated the competitive performance of the proposed method with respect to the six compared algorithms.

Highlights

In 1989, the name of “memetic algorithms” (MAs) [1] was introduced for the first time
(1) Generate the initial population P, define xi as the ith individual in P, M is the population size, NFEs is the number of function evaluations in each run, Max_GEN is the maximum generation, Max_NFEs is the number of max function evaluation, D is the number of decision variable, F is the mutation factor, CR is crossover rate
M is the population size, NFEs is the number of function evaluations in each run, Max_GEN is the maximum generation, Max_NFEs is the number of max function evaluation, Dis the number of decision variable, F is the mutation factor, CR is crossover rate, ρ1 and ρ2 are the contraction criterion, Flag is the restart mark

Summary

Introduction

In 1989, the name of “memetic algorithms” (MAs) [1] was introduced for the first time. In the last two decades, MAs gradually became one of the recent growing areas of research in evolutionary computation They combine various evolutionary algorithms (EAs) with different LS methods to balance exploration and exploitation. Differential evolution was first proposed by Storn and Price [7] in 1995 to solve global numerical optimization problems over continuous search spaces. It shares some similarities with other EAs. For example, DE works with a population of solutions, called vectors; it uses recombination and mutation operators to generate new vectors and, it has a replacement process to discard the less fit vectors. In the past few decades, DE has been successfully used in many real-world applications, such as space trajectory design [8,9,10], hydrothermal optimization [11], underwater glider path planning [12], and vehicle routing problem [13]

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