k-Pareto Optimality-Based Sorting with Maximization of Choice and Its Application to Genetic Optimization

• Published in: Algorithms Vol. 15; no. 11; p. 420
• Main Authors: Ruppert, Jean, Aleksandrova, Marharyta, Engel, Thomas
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-11-2022
• Subjects: Evolutionary algorithms; Genetic algorithms; Knapsack problem; linear extension of multidimensional sorting; multi-objective optimization; Multiple objective analysis; Objectives; Optimization; Optimization techniques; Pareto optimum; Statistical analysis; topological sorting
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a15110420

Deterioration of the searchability of Pareto dominance-based, many-objective evolutionary optimization algorithms is a well-known problem. Alternative solutions, such as scalarization-based and indicator-based approaches, have been proposed in the literature. However, Pareto dominance-based algorithms are still widely used. In this paper, we propose to redefine the calculation of Pareto-dominance. Instead of assigning solutions to non-dominated fronts, they are ranked according to the measure of dominating solutions referred to as k-Pareto optimality. In the case of probability measures, such re-definition results in an elegant and fast approximate procedure. Through experimental results on the many-objective 0/1 knapsack problem, we demonstrate the advantages of the proposed approach: (1) the approximate calculation procedure is much faster than the standard sorting by Pareto dominance; (2) it allows for achieving higher hypervolume values for both multi-objective (two objectives) and many-objective (25 objectives) optimization; (3) in the case of many-objective optimization, the increased ability to differentiate between solutions results in a better compared to NSGA-II and NSGA-III. Apart from the numerical improvements, the probabilistic procedure can be considered as a linear extension of multidimentional topological sorting. It produces almost no ties and, as opposed to other popular linear extensions, has an intuitive interpretation.