Abstract
Differential evolution (DE) is a robust algorithm of global optimization which has been used for solving many of the real-world applications since it was proposed. However, binomial crossover does not allow for a sufficiently effective search in local space. DE's local search performance is therefore relatively poor. In particular, DE is applied to solve the complex optimization problem. In this case, inefficiency in local research seriously limits its overall performance. To overcome this disadvantage, this paper introduces a new local search scheme based on Hadamard matrix (HLS). The HLS improves the probability of finding the optimal solution through producing multiple offspring in the local space built by the target individual and its descendants. The HLS has been implemented in four classical DE algorithms and jDE, a variant of DE. The experiments are carried out on a set of widely used benchmark functions. For 20 benchmark problems, the four DE schemes using HLS have better results than the corresponding DE schemes, accounting for 80%, 75%, 65%, and 65% respectively. Also, the performance of jDE with HLS is better than that of jDE on 50% test problems. The experimental results and statistical analysis have revealed that HLS could effectively improve the overall performance of DE and jDE.
Highlights
Differential evolution (DE), which was proposed by Storn for solving Chebyshev inequality in 1995 [1], is a well-known numerical optimization algorithm
Over the past two decades, DE has been successfully applied to a variety of fields, such as computer vision [2], dynamic economic dispatch [3], engineering design [4], project scheduling [5], artificial neural networks [6], and complex problems inherent to magnetorheological fluids of interest to the automotive industry, in the framework of extended irreversible thermodynamics [7, 8]
Unlike other population-based evolutionary algorithms, the mutation operator in DE utilizes differential information between individuals in the current population. e mechanism gives DE an obvious edge over other evolutionary algorithms. e binomial crossover, only produces one offspring in the space constructed by the target individual and its descendant. erefore, the trial individual is just only one case of many potential solutions, and other potential solutions are ignored
Summary
Differential evolution (DE), which was proposed by Storn for solving Chebyshev inequality in 1995 [1], is a well-known numerical optimization algorithm. Due to its simple structure, limited number of parameters, an easy implementation, and outstanding optimization performance, DE has drawn great attention of many researchers and engineers since it was proposed. Unlike other population-based evolutionary algorithms, the mutation operator in DE utilizes differential information between individuals in the current population. Is clearly affected the overall performance of DE To fill this gap, we introduced a new scheme of local search based on the Hadamard matrix (HLS) for the sake of improving the overall performance of DE.
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