Decomposition into Multi-Objective Fronts: A Pivot-Based Deterministic Non-dominated Sorting Approach

Multi-objective/many-objective optimization genetic algorithm (MOGA) is a technique for conducting a nature-inspired stochastic search of solutions in a multi-objective/many-objective optimization framework. Non-dominated sorting genetic algorithms II and III (NSGA-II and NSGA-III) are examples of MOGA. Incidentally, both of them use fast non-dominated sorting as an indispensable phase of their execution. Because of this, non-dominated sorting stands as an extremely challenging proposition in the relevant research domain. In this paper, we extend an alternative deterministic approach for fast non-dominated sorting, complying with correctness and completeness, a pair of undeniable technical prerequisites. The distinctive aspect of this contribution is its focus on pivots, which enables it to address the complication arising because of dealing with data that has multiple or many objectives. The efficacy of the proposed method is vindicated by its applicability to relevant benchmark data sets available.