An Improved Centroid-Based Boundary Constraint-Handling Method in Differential Evolution for Constrained Optimization

Abstract

Differential Evolution (DE) is a population-based Evolutionary Algorithm (EA) for solving optimization problems over continuous spaces. Many optimization problems are constrained and have a bounded search space from which some vectors leave when the mutation operator of DE is applied. Therefore, it is necessary the use of a boundary constraint-handling method (BCHM) in order to repair the invalid mutant vectors. This paper presents a generalized and improved version of the Centroid BCHM in order to keep the search within the valid ranges of decision variables in constrained numerical optimization problems (CNOPs), which has been tested on a robust and comprehensive set of experiments that include a variant of DE specialized in dealing with CNOPs. This new version, named Centroid [Formula: see text], relocates the mutant vector in the centroid formed by K random vectors and one vector taken from the population that is within or near the feasible region. The results show that this new version has a major impact on the algorithm’s performance, and it is able to promote better final results through the improvement of both, the approach to the feasible region and the ability to generate better solutions.