An Efficient Nondominated Sorting Algorithm for Large Number of Fronts

Nondominated sorting is a key operation used in multiobjective evolutionary algorithms (MOEA). Worst case time complexity of this algorithm is O(MN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), where N is the number of solutions and M is the number of objectives. For stochastic algorithms like MOEAs, it is important to devise an algorithm which has better average case performance. In this paper, we propose a new algorithm that makes use of faster scalar sorting algorithm to perform nondominated sorting. It finds partial orders of each solution from all objectives and use these orders to skip unnecessary solution comparisons. We also propose a specific order of objectives that reduces objective comparisons. The proposed method introduces a weighted binary search over the fronts when…