Impact of selection methods on the diversity of many-objective Pareto set approximations

Selection methods are a key component of all multi-objective and, consequently, many-objective optimisation evolutionary algorithms. They must perform two main tasks simultaneously. First of all, they must select individuals that are as close as possible to the Pareto optimal front (convergence). Second, but not less important, they must help the evolutionary approach to provide a diverse population. In this paper, we carry out a comprehensive analysis of state-of-the-art selection methods with different features aimed to determine the impact that this component has on the diversity preserved by well-known multi-objective optimisers when dealing with many-objective problems. The algorithms considered herein, which incorporate Pareto-based and indicator-based selection schemes, are analysed through their application to the Walking Fish Group (WFG) test suite taking into account an increasing number of objective functions. Algorithmic approaches are assessed via a set of performance indicators specifically proposed for measuring the diversity of a solution set, such as the Diversity Measure and the Diversity Comparison Indicator. Hypervolume, which measures convergence in addition to diversity, is also used for comparison purposes. The experimental evaluation points out that the reference-point-based selection scheme of the Non-dominated Sorting Genetic Algorithm III (NSGA-III) and a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), where the crowding distance is replaced by the Euclidean distance, yield the best results.