A hybrid greedy indicator- and Pareto-based many-objective evolutionary algorithm

As most of Multi-Objective Evolutionary Algorithms (MOEAs) scale quite poorly when the number of objective functions increases, new strategies have been proposed to face this limitation. Considered one of the most well-succeeded examples of such new strategies, the third version of Non-dominated Sorting Genetic Algorithm (NSGA-III) uses a set of reference points placed on a normalized hyperplane to solve Many Objective Optimization Problems (MaOPs). Despite the good results of NSGA-III, the shape of the hypersurface can influence the algorithm's performance and it has not been deeply explored in the recent literature. This work aims therefore at proposing a new hybrid algorithm and investigating nonlinear transformations applied to the NSGA-III hyperplane. We categorize our proposed approach as a hybrid MOEA (Indicator- and Pareto-based), and analyze the influence of the modified set of reference points on the proposed algorithm while solving MaOPs. The paper presents as its main contributions: (i) the proposal of a greedy indicator-based variant of NSGA-III that uses math transformations on a subset of chosen reference points; (ii) the use of Vector Guided Adaptation procedure to modify original NSGA-III hyperplane at every few iterations. A set of experiments addressing several benchmark problems is performed to evaluate the performance of the original and adapted NSGA-III versions, and also to compare them with two well known MOEAs, observing both, convergence and diversity of the final Pareto fronts. Based on the analysis of statistical tests, we conclude that the proposed approach is competitive and can provide an interesting alternative to the original NSGA-III conception.

Automated summary

This study proposes a new hybrid algorithm that applies nonlinear transformations to the NSGA-III hyperplane, categorizing it as an indicator- and Pareto-based hybrid MOEA. The influence of the modified set of reference points on solving Many Objective Optimization Problems is analyzed, presenting a competitive alternative to the original NSGA-III conception.