Quantifying the impact of boundary constraint handling methods on differential evolution

Abstract

Constraint handling is one of the most influential aspects of applying metaheuristics to real-world applications, which can hamper the search progress if treated improperly. In this work, we focus on a particular case - the box constraints, for which many boundary constraint handling methods (BCHMs) have been proposed. We call for the necessity of studying the impact of BCHMs on metaheuristics' performance and behavior, which receives seemingly little attention in the field. We target quantifying such impacts through systematic benchmarking by investigating 28 major variants of Differential Evolution (DE) taken from the modular DE framework (by combining different mutation and crossover operators) and 13 commonly applied BCHMs, resulting in 28 X 13 = 364 algorithm instances after pairing DE variants with BCHMs. After executing the algorithm instances on the well-known BBOB/COCO problem set, we analyze the best-reached objective function value (performance-wise) and the percentage of repaired solutions (behavioral) using statistical ranking methods for each combination of mutation, crossover, and BBOB function group. Our results clearly show that the choice of BCHMs substantially affects the empirical performance as well as the number of generated infeasible solutions, which allows us to provide general guidelines for selecting an appropriate BCHM for a given scenario.