In evolutionary multi-objective optimization, balancing convergence and diversity remains a challenge and especially for many-objective (three or more objectives) optimization problems (MaOPs). To improve convergence and diversity for MaOPs, we propose a new approach: clustering-ranking evolutionary algorithm (crEA), where the two procedures (clustering and ranking) are implemented sequentially. Clustering incorporates the recently proposed non-dominated sorting genetic algorithm III (NSGA-III), using a series of reference lines as the cluster centroid. The solutions are ranked according to the fitness value, which is considered to be the degree of closeness to the true Pareto front. An environmental selection operation is performed on every cluster to promote both convergence and diversity. The proposed algorithm has been tested extensively on nine widely used benchmark problems from the walking fish group (WFG) as well as combinatorial travelling salesman problem (TSP). An extensive comparison with six state-of-the-art algorithms indicates that the proposed crEA is capable of finding a better approximated and distributed solution set. 
A clustering-ranking method for many-objective optimization