MBOS: Modified Best Order Sort Algorithm for Performing Non-Dominated Sorting

Abstract

The current paper aims to improve an efficient algorithm for solving the problem of non-dominated sorting which is one of the dominant steps of any Pareto based multi/many objective optimization algorithms. Recent years witnessed a large number of attempts in developing some solution frameworks for the problem of non-dominated sorting. One such recent approach is ‘Best Order Sort’ which is efficient with respect to the number of dominance comparisons. However, this approach does not perform well in the presence of duplicate solutions. In this paper attempts have been made to modify the ‘Best Order Sort’ and we call this modified version as ‘Modified Best Order Sort’ to remove the above mentioned limitation. The modified best order sort algorithm has been thoroughly analyzed in different scenarios. Current work shows that ‘Best Order Sort’ can be generalized without affecting its best and the worst case time complexities.