A many-objective particle swarm optimizer based on indicator and direction vectors for many-objective optimization

Balancing the convergence and diversity simultaneously is very challenging for traditional many-objective evolutionary algorithms on solving many objective optimization problems (MaOPs). A novel many-objective particle swarm optimization (PSO) algorithm based on the unary epsilon indicator and the direction vectors, termed as IDMOPSO, is proposed to robustly and effectively address MaOPs. The strategies of selecting personal best (pbest) and global best (gbest) take both the convergence and diversity into consideration. The selection of personal best is based on the unary epsilon indicator and the Pareto dominance to enhance the capability of local exploration. Apart from this, an external archive based on the unary epsilon indicator and the direction vectors is used to maintain the non-dominated solutions found during the search process. Extensive comparative experiments on DTLZ, DTLZ⁻¹, WFG, and WFG⁻¹ problems with varied number of objectives show that IDMOPSO is effective and flexible in addressing MaOPs. The effectiveness of the proposed strategies is also analyzed in detail.