Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation

Abstract

The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the ε constrained differential evolution (εDE), which is the combination of the ε constrained method and differential evolution (DE). It has been shown that the εDE can run very fast and can find very high quality solutions. Also, we proposed the εDE with gradient-based mutation (εDEg), which utilized gradients of constraints in order to solve problems with difficult constraints. In this study, we propose the ε constrained DE with an archive and gradient-based mutation (εDEag). The εDEag utilizes an archive to maintain the diversity of individuals and adopts a new way of selecting the ε level control parameter in the εDEg. The 18 problems, which are given in special session on “Single Objective Constrained RealParameter Optimization” in CEC2010, are solved by the εDEag and the results are shown in this paper.