DMOPSO: Dual multi-objective particle swarm optimization

Since multi-objective optimization algorithms (MOEAs) have to find exponentially increasing number of nondominated solutions with the increasing number of objectives, it is necessary to discriminate more meaningful ones from the other nondominated solutions by additionally incorporating user preference into the algorithms. This paper proposes dual multi-objective particle swarm optimization (DMOSPO) by introducing secondary objectives of maximizing both user preference and diversity to the nondominated solutions obtained for primary objectives. The proposed DMOSPO can induce the balanced exploration of the particles in terms of user preference and diversity through the dual-stage of nondominated sorting such that it can generate preferable and diverse nondominated solutions. To demonstrate the effectiveness of the proposed DMOPSO, empirical comparisons with other state-of-the-art algorithms are carried out for benchmark functions. Experimental results show that DMOPSO is competitive with the other compared algorithms and properly reflects the user´s preference in the optimization process while maintaining the diversity and solution quality.