MOEA with Approximate Nondominated Sorting Based on Sum of Normalized Objectives

Pareto based selection techniques are extensively implemented in the multi-objective evolutionary algorithms (MOEAs), to tackle the many-objective optimization problems (MaOPs). In Pareto-dominance based MOEAs (PDMOEAs), nondominated sorting (NDS) plays a prominent role in preserving the elite solutions during mating and environmental selection. Although, NDS is an inevitable procedure in the evolution of PDMOEAs, computational complexity issues enhances the difficulty to adopt NDS approaches. Various methodologies were suggested in literature to overcome complexity issues, but these approaches deteriorate drastically for higher objectives. Recently, an approximate efficient NDS, (AENS) is proposed that utilize three objective comparisons to establish the dominance relation. In this paper, we propose an improved version of AENS, in which maximum two objective comparisons are required to determine the dominance relation. To evaluate the performance of our algorithm, experiments are done on seven different test problems and the experiment results have proved the effectiveness of proposed method in improving the convergence of different MOEAs.