LONSA: A labeling-oriented non-dominated sorting algorithm for evolutionary many-objective optimization

Multiobjective algorithms are powerful in tackling complex optmization problems mathematically represented by two or more conflicting objective functions and their constraints. Sorting a set of current solutions across non-dominated fronts is the key step for the searching process to finally identify which ones are the best solutions. To perform that step, a high computational effort is demanded, especially if the size of the solution set is huge or the mathematical model corresponds to a many-objective problem. In order to overcome this, a new labeling-oriented algorithm is proposed in this paper to speed up the solution-to-front assignment by avoiding usual dominance tests. Along with this algorithm, called Labeling-Oriented Non-dominated Sorting Algorithm (LONSA), the associated methodology is carefully detailed to clearly explain how the classification of the solution set is successfully achieved. This work presents a comparison between LONSA and other well-known algorithms usually found in the literature. The simulation results have shown a better performance of the proposed algorithm against nine chosen strategies in terms of computational time as well as number of comparisons.