Revisiting Basic Concepts of Dominance Relationship in Non-Dominated Sorting

Non-dominated sorting is one of the essential steps in Pareto dominance-based multi-objective evolutionary algorithms (MOEAs). This sorting is based on the dominance relationship between the points. In this paper, we first explore the dominance relationship in detail and discuss various properties and their proofs. We also revisit some of the fundamental concepts in non-dominated sorting and provide an in-depth analysis of some of the fundamental concepts involved in non-dominated sorting. We establish our claims through some theorems and their proofs.