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 solutions near the reference points can be found parallely. We propose a modified EMO procedure based on the elitist non-dominated sorting GAor NSGA-II. On two-objective to 10-objective optimization problems, the modified NSGA-II approach shows its efficacy in finding an adequate set of Pareto-optimal points. 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.