D-NSGA-II: Dual-Stage Nondominated Sorting Genetic Algorithm-II

This paper proposes a novel multi-objective optimization algorithm, dual-stage nondominated sorting genetic algorithm-II (D-NSGA-II) for many-objective problems. Since the percentage of the nondominated solutions increases exponentially with the increasing number of objectives, just finding the nondominated solutions is not enough for solving many-objective problems. In other words, it is necessary to discriminate more meaningful ones from the other non-dominated solutions by additionally incorporating user preference into the algorithms. The proposed D-NSGA-II can obtain not only user preference oriented, but also diverse nondominated solutions by introducing an additional stage of multi-objective optimization. The second stage employs the corresponding secondary objectives, global evaluation and crowding distance which were proposed in the previous research for representing the user's preference to a solution and the crowdedness around a solution, respectively. To demonstrate the effectiveness of the proposed algorithm, some benchmark functions are tested and the outcomes of the proposed D-NSGA-II and the NSGA-II are empirically compared. Experimental results show that D-NSGA-II properly reflects the user's preference in the optimization process as well as the performance in terms of the diversity and solution quality is competitive with the NSGA-II.