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

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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.

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  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Mohamed Abouhawwash

  2. Department of Electrical and Computer Engineering Computational Optimization and Innovation (COIN) Laboratory, Michigan State University, East Lansing, MI, 48824, USA

    Mohamed Abouhawwash & Kalyanmoy Deb

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Abouhawwash, M., Deb, K. Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics. J Heuristics 27, 575–614 (2021). https://doi.org/10.1007/s10732-021-09470-4

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