GBOS: Generalized Best Order Sort algorithm for non-dominated sorting

Abstract

Abstract Non-dominated sorting is one of the prominent steps in developing any Pareto-dominance based multi-objective evolutionary algorithm. The computational complexity of any Pareto-dominance based multi-objective evolutionary algorithm primarily depends on this step. Thus, researchers are working on reducing the complexity of this step. Recently, an efficient approach for non-dominated sorting known as Best Order Sort (BOS) has been proposed. This approach is very efficient in terms of the number of comparisons between the solutions. Another advantage of this approach is that while comparing two solutions, the number of objectives which are compared is reduced from the actual number of objectives associated with each solution. However, in spite of these two advantages, this approach is not suitable in its current form for cases in which we have duplicate solutions. This paper generalizes BOS to handle duplicate solutions while retaining both of its advantages. We call this generalized version Generalized Best Order Sort (GBOS). The present work shows that BOS can be generalized to handle its limitation without compromising its time and space complexity.