Large-scale many-objective particle swarm optimizer with fast convergence based on Alpha-stable mutation and Logistic function

The challenges of the most multi-objective particle swarm optimization (MOPSO) algorithms are to improve the selection pressure, equilibrate the convergence and diversity when tackling large-scale many-objective problems. To overcome these challenges, this paper proposes a novel PSO-based large-scale many-objective algorithm, named as LMPSO. In LMPSO, the Alpha-stable mutation is performed to enhance the diversity of swarm for avoiding premature convergence. And the parameters of PSO and Alpha-stable mutation are dynamically set following the Logistic function, which emphasize different convergence and diversity at different optimization stages. Moreover, LMPSO adopts a fitness to maintain the external archive, and the calculation of fitness is based on binary additive epsilon indicator. The binary indicator is also used to update the personal best of particles to avoid wrongly selecting dominance resistance solutions (DRSs). Aims for improving the selection pressure, the proposed algorithm employs a concept of dominance resistance error to identify the DRSs. To verify this idea, the DTLZ, ZDT, and LSMOP test suites with up to 1000 decision variables and 10-objective are used to qualify the performance of LMPSO. The simulations reveal the fact that the LMPSO significantly outruns the several chosen state-of-the-art algorithms when solving large-scale many-objective test instances.