Two-stage particle swarm optimization with dual-indicator fusion ranking for multi-objective problems

Elite solutions guiding population evolution are often used as one of main ideas to improve the performance of multi-objective particle swarm optimization (MOPSO). However, in most research work, sole Pareto dominance criterion is often used to evaluate solutions. This sole criterion may easily cause some problems, such as the premature convergence. In this study, we propose an MOPSO variant with dual-indicator fusion ranking (TPSO-DF), to evaluate elite solutions and to guide search without sacrificing diversity. In TPSO-DF, two indicators are introduced by using the convergence and diversity information, respectively. Both indicators are then fusioned in a ranking measure to focus on valuable information and to filter out solutions with these valuable information. Meanwhile, an adaptive global leader selection strategy is introduced to take full advantage of valuable information and to guide population evolution toward the optimal direction. As another contribution of this study, a two-stage hybrid mutation strategy is designed by utilizing the valuable information differently in different evolutionary states of the algorithm to enhance performance. Compared to eight representative multi-objective evolutionary algorithms, the performance of TPSO-DF is validated by extensive experiments on ZDT and DTLZ test suites, as well as one practical problem. Experimental results show that TPSO-DF can achieve competitive performance on most of the test functions.