On the Computational Complexity of Efficient Non-dominated Sort Using Binary Search.

Over the years, several approaches have been proposed to solve the problem of non-dominated sorting, which is one of the crucial steps in Pareto dominance-based multi-objective evolutionary algorithms (MOEAs). However, some of these approaches, even though they are correct, lack an in-depth analysis. In this paper, we focus on an approach known as Efficient Non-dominated Sort using Binary Search (ENS-BS) and show that the best case scenario presented in the paper for ENS-BS is not correct. We show this by providing a counter-example where the number of dominance comparisons is less than that reported in the original paper. This is done by obtaining a generic equation and getting the scenario inspired by this equation.