A hybrid version of differential evolution with two differential mutation operators applied by stages

Abstract

Differential Evolution (DE) is an algorithm capable of solving complex optimization problems with and without constraints. As many of the population-based algorithms, DE is based on operators that evolve a numerical population through search operators. The differential mutation, one of the basic operators in the original version of the algorithm, provides population diversity through the evolution. In this paper we propose an extended version of a previously proposed hybrid DE including know two different mutation operators, which are not applied simultaneously. The first of them, our main contribution, is based on the exploitation of feasible areas to identify promising regions of search space. The second mutation operator is the classic differential mutation and it is applied towards produce a balance between exploration and exploitation as well as to improve the individuals obtained with our operator. An experimental study was performed by considering 18 functions presented for the “Single Objective Constrained Real-Parameter Optimization” of the special session of CEC2010. The results are compared with those obtained by Takahama and Sakai, winners that CEC2010 special session with εDEag algorithm. The obtained results show that our proposed approach is capable of finding solutions of higher quality for scalable problems of dimension 30 whereas the results for dimension 10 remains competitive with εDEag.