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This paper proposes a method to use reference points as preferences to guide a particle swarm algorithm to search towards preferred regions of the Pareto front. A decision maker can provide several reference points, specify the extent of the spread of solutions on the Pareto front as desired, or include any bias between the objectives as preferences within a single execution. We incorporate the reference point method into two multi-objective particle swarm algorithms, the non-dominated sorting PSO, and the maximinPSO. This paper first demonstrates the usefulness of the proposed reference point based particle swarm algorithms, then compare the two algorithms using a hyper-volume metric. Both particle swarm algorithms are able to converge to the preferred regions of the Pareto front using several feasible or infeasible reference points.

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In this paper we propose to use a distance metric based on user-preferences to efficiently find solutions for manyobjective problems. We use a particle swarm optimization (PSO) algorithm as a baseline to demonstrate the usefulness of this distance metric, though the metric can be used in conjunction with any evolutionary multi-objective (EMO) algorithm. Existing user-preference based EMO algorithms rely on the use of dominance comparisons to explore the searchspace. Unfortunately, this is ineffective and computationally expensive for many-objective problems. In the proposed distance metric based PSO, particles update their positions and velocities according to their closeness to preferred regions in the objective-space, as specified by the decision maker. The proposed distance metric allows an EMO algorithm's search to be more effective especially for many-objective problems, and to be more focused on the preferred regions, saving substantial computational cost. We demonstrate how to use a distance metric with two user-preference based PSO algorithms, which implement the reference point and light beam search methods. These algorithms are compared to a userpreference based PSO algorithm relying on the conventional dominance comparisons. Experimental results suggest that the distance metric based algorithms are more effective and efficient especially for difficult many-objective problems.

Abstract. In this paper we propose to use a distance metric based on user-preferences to efficiently find solutions for many-objective problems. In a user-preference based algorithm a decision maker indicates regions of the objective-space of interest, the algorithm then concentrates only on those regions to find solutions. Existing user-preference based evolutionary many-objective algorithms rely on the use of dominance comparisons to explore the search-space. Unfortunately, this is ineffective and computationally expensive for many-objective problems. The proposed distance metric allows an evolutionary many-objective algorithm's search to be focused on the preferred regions, saving substantial computational cost. We demonstrate how to incorporate the proposed distance metric with a user-preference based genetic algorithm, which implements the reference point and light beam search methods. Experimental results suggest that the distance metric based algorithm is effective and efficient, especially for difficult many-objective problems.