Sets evolution-based particle swarm optimization for many-objective problems

Optimization problems with more than three objectives, i.e., many-objective problems (MaOPs), have gained more and more attentions in the field of evolutionary multi-objective optimization (EMO) in that the powerful Pareto comparisons and evolutionary strategies are very scarce. Particle swarm optimization (PSO) is an effective method for multi-objective problems, however, it has not been well scaled for solving those MaOPs. In this paper, a set evolution guided PSO for MaOPs (S-MOPSO for short) is presented by regarding the sets of solutions together with the solutions themselves as “particles” in different evolutionary processes. The framework of the algorithm is first presented, and then the optimization objectives of the MaOPs are converted according to the commonly used metrics of EMOs to provide the search space of sets. Accordingly, the method for evolving the sets of solutions in the PSO framework is given along with finely selecting the global and local best sets particles. The merits of the proposed algorithm are experimentally demonstrated by applying it to scalable benchmark many-objective functions.