An Ensemble of S-energy Based Mating Restrictions for Multi-Objective Evolutionary Algorithms

Abstract

Mating restrictions are a mechanism adopted by multi-objective evolutionary algorithms to improve the solution of multi-objective optimization problems (MOPs) by establishing a strategy to mate individuals during the reproduction step of the algorithm. Several mating restrictions have been proposed for MOEAs to solve MOPs having two and three objective functions. However, in the case of many-objective optimization problems (four or more objectives), only a few mating restriction schemes have been proposed so far. The Riesz S-energy is a performance indicator which can be used to evaluate population's diversity, and it is able to provide useful neighborhood information from individuals in MOPs with any number of objectives. This feature has been used in some of our previous work to propose a few different mating restriction schemes based on the s-energy indicator. In this paper, we propose the use of an ensemble of four of these mating restriction mechanisms, which is implemented within the NSGA-III to assess its performance. The ensemble's behavior is guided by two measurements of each mating restriction performance throughout the algorithm's execution. We performed an experimental validation of this ensemble in MOPs with up to seven objective functions, and compared the results obtained using the hypervolume, the s-energy, and the inverted generational distance performance indicators. The results obtained show that the use of our mating restrictions ensemble outperforms the original NSGA-III in most of the test instances adopted.