Search Behavior Analysis of NSGA-III: Dominance-based and Decomposition-based Multi-objective Evolutionary Algorithm
Hisao Ishibuchi, Lie Meng Pang, Cheng Bing Gong · Proceedings of the Genetic and Evolutionary Computation Conference · 2025
In the field of evolutionary multi-objective optimization (EMO), EMO algorithms are often categorized into three types: dominance-based, decomposition-based and indicator-based algorithms. In this categorization, NSGA-III is handled as a decomposition-based algorithm. This is because a single solution is assigned to each of uniformly generated reference vectors as in MOEA/D. However, in a recent survey paper, NSGA-III was categorized in the same group as NSGA-II based on their generation update mechanisms. Another recent study demonstrated that NSGA-III shows a similar search behavior to NSGA-II for combinatorial multi-objective problems. However, for DTLZ test problems, NSGA-III shows almost the same search behavior as MOEA/D. In this paper, we demonstrate that the shape of the Pareto front is the main factor about the search behavior of NSGA-III. If a test problem has a regular (i.e., triangular) Pareto front, NSGA-III shows the same search behavior as MOEA/D. However, if a test problem has an irregular Pareto front (e.g., inverted triangular), NSGA-III shows a similar search behavior to NSGA-II. We also demonstrate that the objective space normalization in NSGA-III is not stable for multi-objective problems with inverted triangular Pareto fronts.