NSLS with the Clustering-Based Entropy Selection for Many-Objective Optimization Problems

The multi-objective optimization algorithm based on nondominated sorting and local search (NSLS) has shown great competitiveness in the most multi-objective optimization problems. NSLS can obtain the Pareto-optimal front with better distribution and convergence than other traditional multi-objective optimization algorithms. However, the performance of NSLS degrades rapidly when facing the many-objective optimization problems (MaOPs). This paper proposes another version of NSLS, named NSLS with the Clustering-based Entropy Selection (NSLS-CE), which replaces the farthest-candidate approach with the clustering-based entropy selection approach. The concept of clustering-based entropy is proposed to measure the distribution of populations, which is implemented by the k-means clustering algorithm. Besides, to reduce the time complexity of the proposed clustering-based entropy selection approach, we apply the thermodynamic component replacement strategy. In order to prove the efficacy of NSLS-CE for solving MaOPs, the experiment is carried out on eighteen instances with three different objective numbers. The experimental results indicate that NSLS-CE can obtain Pareto solutions with better convergence and better distribution than NSLS.