Multiple Populations for Multiple Objectives Framework with Bias Sorting for Many-objective Optimization

The convergence and diversity enhancement of multiobjective evolutionary algorithms (MOEAs) to efficiently solve many-objective optimization problems (MaOPs) is an active topic in evolutionary computation. By considering the advantages of the multiple populations for multiple objectives (MPMO) framework in solving multiobjective optimization problems and even MaOPs, this article proposes an MPMO-based algorithm with a bias sorting (BS) method (termed MPMO-BS) for solving MaOPs to achieve both good convergence and diversity performance. For convergence, the BS method is applied to each population of the MPMO framework to enhance the role of nondominated sorting by biasedly paying more attention to the objective optimized by the corresponding population. This way, all the populations in the MPMO framework evolve together to promote the convergence performance on all objectives of the MaOP. For diversity, an elite learning strategy is adopted to generate locally mutated solutions, and a reference vector-based maintenance method is adopted to preserve diverse solutions. The performance of the proposed MPMO-BS algorithm is assessed on 29 widely used MaOP test problems and two real-world application problems. The experimental results show its high effectiveness and competitiveness when compared with seven state-of-the-art MOEAs for many-objective optimization.