Hybrid many-objective particle swarm optimization set-evolution

Many-objective optimization problems (MaOPs) are difficult to be solved by those traditional evolutionary multi-objective (EMO) algorithms due to the loss of enough selection pressure. The indicator-based EMO developed for MaOPs has been proved to be effective, however, it has not been well combined with the framework of particle swarm optimization (PSO). Therefore, we here propose a hybrid indicator-based PSO for MaOPs, in which the sets of solutions are evolved as an “individual”. First, the sets-oriented PSO is designed to perform the evolution on the sets. The global and local best particles are well explored by considering the performance of the evolution and the computational cost. Then, the solutions in some selected sets are further evolved by a modified mutation to approximate to the true Pareto set in the original MaOP space. The proposed algorithm is experimentally validated on some benchmark MaOPs and its merit is empirically demonstrated by comparing to indicator-based evolutionary genetic algorithms and NSGAII.