Incorporating decision maker preference in multiobjective evolutionary algorithm

There is no existence of single best trade-off solution in multi-objective optimization frameworks with many competing objectives, as a decision maker´s (DM) opinion is concerned. In this paper, we propose a preference-based multi-objective optimization evolutionary algorithm (MOEA) to help the decision maker (DM) choosing the final best solution(s). Our algorithm is called ASA-NSGA-II. The approach is accomplished by replacing the crowding estimator technique in NSGA-II algorithm by applying an extended angle-based dominance technique. The contribution of ASA-NSGA-II can be illustrated by the geometric angle between a pair of solutions by using an arctangent function and compare the angle with a threshold angle. The specific bias intensity parameter is then introduced to the threshold angle in order to approximate the portions of desirable solutions based on the DM´s preference. We consider two and three-objective benchmark problems. In addition, we also provide an application problem to observe the usefulness of our algorithm in practical context.