Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics

Mohamed Abouhawwash () and Kalyanmoy Deb ()
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Mohamed Abouhawwash: Mansoura University
Kalyanmoy Deb: Michigan State University

Journal of Heuristics, 2021, vol. 27, issue 4, No 3, 575-614

Abstract: Abstract In a preference-based multi-objective optimization task, the goal is to find a subset of the Pareto-optimal set close to a supplied set of aspiration points. The reference point based non-dominated sorting genetic algorithm (R-NSGA-II) was proposed for such problem-solving tasks. R-NSGA-II aims to finding Pareto-optimal points close, in the sense of Euclidean distance in the objective space, to the supplied aspiration points, instead of finding the entire Pareto-optimal set. In this paper, R-NSGA-II method is modified using recently proposed Karush–Kuhn–Tucker proximity measure (KKTPM) and achievement scalarization function (ASF) metrics, instead of Euclidean distance metric. While a distance measure may not produce desired solutions, KKTPM-based distance measure allows a theoretically-convergent local or global Pareto solutions satisfying KKT optimality conditions and the ASF measure allows Pareto-compliant solutions to be found. A new technique for calculating KKTPM measure of a solution in the presence of an aspiration point is developed in this paper. The proposed modified R-NSGA-II methods are able to solve as many as 10-objective problems as effectively or better than the existing R-NSGA-II algorithm.

Keywords: Decision maker; Evolutionary algorithms; Aspiration point; KKTPM metric; Achievement scalarization function (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10732-021-09470-4

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