Effect of selection operator on NSGA-III in single, multi, and many-objective optimization

Decomposition-based elitist non-dominated sorting genetic algorithm (NSGA-III) is a recently proposed many-objective optimization algorithm that uses multiple pre-defined yet adaptable reference directions to maintain diversity among its solutions. Designing to solve specifically many-objective problems having four or more objectives, the authors of NSGA-III restricted the population size to be equal to the number of chosen reference directions. This restriction hinders the usage of NSGA-III to single-objective optimization problems, where, by definition, there is only one reference direction. For this reason, a unified algorithm — U-NSGA-III — has been recently proposed to handle this issue. U-NSGA-III is capable of adapting automatically to the dimensionality of the problem in hand through its niching based selection operator. However, the authors of U-NSGA-III abided by this single-fold restriction in all NSGA-III simulations of their study. In this paper we test the possibility of ignoring this restriction of NSGA-III and use multiple population folds to solve single, multi and many-objective problems. Simulations are performed on a variety of constrained and unconstrained single, multi and many-objective problems for this purpose. The strengths and weaknesses of multi-fold NSGA-III compared to those of U-NSGA-III are thoroughly investigated here. The robustness of NSGA-III in each type of problems is also discussed. This study provides a more comprehensive evaluation of the original NSGA-III procedure, which seems to have a wider scope than the original study had foreseen.