An Empirical Study on the Use of the S-energy Performance Indicator in Mating Restriction Schemes for Multi-Objective Optimizers

Abstract

Mating restrictions have been used to improve the performance of Multi-Objective Evolutionary Algorithms (MOEAs) by altering the way in which parents are selected in the recombination step. Originally proposed for single-objective optimization, mating restrictions have been implemented in different MOEAs obtaining mixed results. However, the role of mating restrictions in diversity management/maintenance and in the proper balance between exploration and exploitation within MOEAs has not been studied in sufficient detail in spite of its evident importance. In this paper, we present an empirical study on the impact of three new mating restrictions based on the s-energy performance indicator. When obtaining each individual’s contribution to the total s-energy, we implicitly obtain vicinity information, since a high contribution means that an individual is relatively close to at least some other individual, i.e., it is in a crowded region. Conversely, an individual with a low contribution is in a non-crowded region. Using this information we explore different strategies aiming to improve the diversity of the population during its execution, as well as exploiting the least crowded regions of the objective space. One of the main advantages of our proposal are both its simplicity and its ability to scale up (in objective function space). We evaluate the impact of our proposals by implementing them in NSGA-III and comparing the obtained results with respect to those of the original algorithm. Our experimental results show that the use of mating restrictions does provide improvements in most of the test instances adopted for some of our proposed strategies.