An improved NSGA-III algorithm using genetic K-means clustering algorithm

Abstract

The non-dominated sorting genetic algorithm III (NSGA-III) has recently been proposed to solve many-objective optimization problems (MaOPs). While this algorithm achieves good diversity, its convergence is unsatisfactory. In order to improve the convergence, we propose an improved NSGA-III using a genetic K-means clustering algorithm (NSGA-III-GKM), which can also ensure diversity and automatically provide the number and direction vector of the subspaces. Compared with the NSGA-III, the proposed NSGA-III-GKM has two key features. First, the initial reference points are clustered using a GKM clustering algorithm, which realizes automatic learning of the number of clusters. Second, as the reference points are replaced by cluster centers, a penalty-based boundary intersection (PBI) aggregation function is introduced to replace the perpendicular distance. The proposed NSGA-III-GKM and other similar optimization algorithms (NSGA-III, MOEA/D, U-NSGA-III, DC-NSGA-III and B-NSGA-III) are tested on DTLZ test problems and UF test problems. The simulation results demonstrate that the NSGA-III-GKM exhibits better diversity and convergence performance than the other algorithms.