Reference point based Multi-Objective optimization using evolutionary algorithms

Evolutionary multi-objective optimization (EMO) methodologies have been amply applied to find a representative set of Pareto-optimal solutions in the past decade and beyond. Although there are advantages of knowing the range of each objective for Pareto-optimality and the shape of the Pareto-optimal frontier itself in a problem for an adequate decision-making, the task of choosing a single preferred Pareto-optimal solution is also an important task which has received a lukewarm attention so far. In this paper, we combine one such preference-based strategy with an EMO methodology and demonstrate how, instead of one solution, a preferred set of solutions near the reference points can be found parallely. We propose two approaches for this task: (i) a modified EMO procedure based on the elitist non-dominated sorting GA or NSGA-II [1] and (ii) a predator-prey approach based on original grid based procedure [2]. On two-objective to 10-objective optimization test problems, the modified NSGA-II approach shows its efficacy in finding an adequate set of Pareto-optimal points. On two and three-objective problems, the predator-prey approach also demonstrate its usefulness. Such procedures will provide the decision-maker with a set of solutions near her/his preference so that a better and a more reliable decision can be made.