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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.