A hybrid evolution strategy for mixed discrete continuous constrained problems

Abstract

In this paper, a hybrid evolution strategy is proposed to solve mixed discrete continuous constrained problems. We consider that the functions of the problems are differentiable with respect to the continuous variables but are not with respect to the discrete ones. Evolutionary algorithms are well suited to solve these difficult optimization problems but the number of evaluations is generally very high. The presented hybrid method combines the advantages of evolutionary algorithms for the discrete variables and those of classical gradient-based methods for the continuous variables in order to accelerate the search. The algorithm is based on a dual formulation of the optimization problem. The efficiency of the method is demonstrated through an application to two complex mechanical design problems with mixed-discrete variables.