Nondominated sorting based on sum of objectives

In Pareto-Dominance based multi-objective evolutionary algorithms (PDMOEAs), nondominated sorting (NDS) procedure plays significantly important role in mating and environmental selection of the solutions. However, NDS is computationally expensive as each solution needs to be compared on all objectives with all solutions in the population. Therefore, the complexity increases with increase in the number of objectives (M) and the number of individuals in the population (N). Therefore, designing an efficient NDS algorithm plays a prominent role in reducing the computational complexity of the MOEAs. In this paper, we propose a NDS algorithm that assigns solutions to the fronts in the ascending order of sum of objectives; by comparing with only solutions that are better than the respective solution in the sum of objectives. To demonstrate the effectiveness, we compared the proposed method with the existing efficient nondominated sorting (ENS) algorithm and Corner Sort (CS). The experimental results indicate the effectiveness of the proposed method in reducing the number of comparisons and runtimes as the number of objectives increases.