A Self-Adaptive Differential Evolution Algorithm Using Oppositional Solutions and Elitist Sharing

Abstract

Differential evolution (DE) has been applied to solve complex optimization problems. An effective DE algorithm should be convergent and able to jump out of the local optimal solution. Motivated by these considerations, an improved differential evolution is proposed, which is based on the oppositional solution, elite sharing schemes, the heuristic crossover operator and combined with a self-adaptive parameter setting strategy. The algorithm is denoted as SOSESDE. First, in the early stage of evolution, the disturbance oppositional strategy is applied to the worse individuals to increase the search space since the oppositional search strategy will generate redundant offspring by the same genetic operation, which can be avoided by random perturbation. Then, an elite sharing scheme is used for information exchange. In this scheme, the K-means is first used to divide the present population into several subpopulations, and then, the elitist in each subpopulation is taken for mutation operation. In addition, the related parameters $F$ and $CR$ are self-adaptively adjusted based on the results of the Wilcoxon signed-rank test and the probability that a parent is selected for the next generation. Besides, the heuristic crossover operator is constructed by using uniform design method. Finally, 53 benchmark functions are optimized using SOSESDE, and the results are compared with those of various state-of-the-art algorithms. The experiments show that compared to these algorithms, SOSESDE exhibits better performance.