Three modified versions of differential evolution algorithm for continuous optimization

Abstract

Differential evolution (DE) is one simple and effective evolutionary algorithm (EA) for global optimization. In this paper, three modified versions of the DE to improve its performance, to repair its defect in accurate converging to individual optimal point and to compensate the limited amount of search moves of original DE are proposed. In the first modified version called bidirectional differential evolution (BDE), to generate a new trial point, is used from the bidirectional optimization concept, and in the second modified version called shuffled differential evolution (SDE), population such as shuffled frog leaping (SFL) algorithm is divided in to several memeplexes and each memeplex is improved by the DE algorithm. Finally, in the third modified version of DE called shuffled bidirectional differential evolution (SBDE) to improve each memeplex is used from the proposed BDE algorithm. Three proposed modified versions are applied on two types of DE and six obtained algorithms are compared with original DE and SFL algorithms. Experiments on continuous benchmark functions and non-parametric analysis of obtained results demonstrate that applying bidirectional concept only improves one type of the DE. But the SDE and the SBDE have a better success rate and higher solution precision than original DE and SFL, whereas those are more time consuming on some functions. In a later part of the comparative experiments, a comparison of the proposed algorithms with some modern DE and the other EAs reported in the literature confirms a better or at least comparable performance of our proposed algorithms.

Opposition-based learning in the shuffled differential evolution algorithm

“…Firstly, the focus of the experiments is to compare the performance of the proposed algorithms with the original SDE algorithm proposed by Ahandani et al (2010). Then, a Algorithm 1 (the SOBDE algorithm)…”

“…Ahandani et al (2010) by inspiring from partitioning and shuffling processes employed in the SFL algorithm gave the parallel search ability to the DE algorithms and called them as the SDE. The SDE such as SFL divides the population into several subsets referred to as memeplexes and each memeplex is improved by the DE.…”

“…Limiting the number and variety of search moves prevents exploration of whole search space. Ahandani et al (2010) proposed three modified versions of the DE to repair its defect in accurate converging to individual optimal point and to compensate the limited amount of search moves of original DE. These algorithms carried out several efforts one by one to obtain a fitter offspring so that each search move was different from previously utilized moves.…”

“…These proposed algorithms use a combination of shuffled DE (SDE) proposed by Ahandani et al (2010), and ODE proposed by . On one hand, The SDE diversifies exploratory moves of DE and increases the number of efforts carried out to independently improve each member.…”

The Successive Zooming Genetic Algorithm and Its Applications

“…Optimization techniques range widely from the early gradient techniques 1 to the latest random techniques 16,18,19 including ant colony optimization 13,17 . Gradient techniques are very powerful when applied to smooth well-behaved objective functions, and especially, when applied to a monotonic function with a single optimum.…”