Hyperplane-Assisted Multi-objective Particle Swarm Optimization with Twofold Proportional Assignment Strategy

In the simultaneous optimization of multiple objectives, how to balance convergence promotion and diversity preservation in the evolutionary process is a key and challenging problem. In this research, a hyperplane-assisted multi-objective particle swarm optimization with a twofold proportional assignment strategy (tpahaMOPSO) is suggested to ameliorate the optimization performance of MOPSO. First, the external archive is maintained in combination with hyperplane-based convergence evaluation and shift-based density estimation to retain high-quality candidate solutions. Second, a twofold proportional assignment scheme is designed to search the surrounding region of candidate solutions with better potential to emphasize convergence and diversity, respectively. Third, the domination relationship and convergence difference are combined to select a more reasonable individual historical best and reduce the risk of particle aggregation. Finally, the proposed tpahaMOPSO was compared with ten representative and advanced multi-objective optimization algorithms on 22 widely used test functions with different characteristics. The simulation results present that the developed tpahaMOPSO got the best result in 11 benchmark functions for both IGD and HV criteria. Concurrently, the Friedman test was applied for ranking analysis and the proposed algorithm also obtained excellent statistical analysis results. The promising performance and strong competitiveness of the proposed tpahaMOPSO have been verified by different experimental studies.