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

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.