A divide-and-conquer based efficient non-dominated sorting approach

Abstract In general, evolutionary algorithms are very prevalent in solving multi-objective optimization problems. Pareto-based multi-objective evolutionary algorithms are popularly used in solving different multi-objective optimization problems. These algorithms work using several steps, non-dominated sorting being the most salient one. However, this non-dominated sorting step is associated with a high computational complexity. In the past, different approaches have been proposed for non-dominated sorting. In this paper, to address the problem of non-dominated sorting, a framework called DCNS (Divide-and-conquer based non-dominated sorting) is developed. Based on this DCNS framework, four different approaches are proposed. The best case time complexity of our proposed DCNS framework is proved to be O ( N log N + M N ) for M ≥ 2 where N is the number of solutions and M is the number of objectives. This best case time complexity is better than the best case time complexities of various other approaches. The number of dominance comparisons performed by the proposed framework is lower than those from other state-of-the-art approaches in different scenarios. The proposed framework has the parallelism property and the scope of parallelism is also discussed.