Multi-modal multi-objective particle swarm optimization with self-adjusting strategy

Since the exploration of multiple solution sets will lead to the deterioration of convergence in multi-objective particle swarm optimization, the motion of the particles is severely disturbed by the under-convergence solutions in multi-modal multi-objective optimization problems (MMOPs). To solve this problem, a multi-modal multi-objective particle swarm optimization with self-adjusting strategy (MMOPSOSS) is proposed to promote the complete convergence of multiple solution sets through the self-adjusting of parameters and population size. First, a multi-swarm optimization framework is designed to obtain diverse convergence directions. Second, a self-adjusting local search mechanism is introduced to improve the search performance of sub-swarms in the potential regions according to the feedback information detected by diversity entropy under this framework. Third, a sub-swarm-balancing strategy is developed to balance the degree of convergence among different regions by adjusting the size of the sub-swarms. Finally, MMOPSOSS is compared with several multi-modal multi-objective optimization algorithms in benchmark experiments and engineering simulation experiments. The results demonstrate that MMOPSOSS has a positive effect on the convergence of multiple solution sets for MMOPs.