Differential Evolution with Adaptive Grid-Based Mutation Strategy for Multi-Objective Optimization

Abstract

Differential Evolution (DE) has been extensively adopted for multi-objective optimization due to its efficient and straightforward framework. In DE, the mutation operator influences the evolution of the population. In this paper, an adaptive Grid-based Multi-Objective Differential Evolution is proposed to address multi-objective optimization (ad-GrMODE). In ad-GrMODE, an adaptive grid environment is employed to perform a mutation strategy in conjunction with performance indicators. The grid reflects the convergence and diversity performance together but is associated with the user-specified parameter “div”. To solve this problem, we adaptively tune the parameter “div”. Among the DE mutation strategies, “DE/current-to-best/1” is applied extensively in single-objective optimization. This paper extends the application of “DE/current-to-best/1” to multi-objective optimization. In addition, a two-stage environmental selection is adopted in ad-GrMODE, where in the first stage, one-to-one selection between the parent and its corresponding offspring solution is performed. In addition, to preserve elitism, a stochastic selection is adopted with respect to performance metrics. We conducted experiments on 16 benchmark problems, including the DTLZ and WFG, to validate the performance of the proposed ad-GrMODE algorithm. Besides the benchmark problem, we evaluated the performance of the proposed method on real-world problems. Results of the experiments show that the proposed algorithm outperforms the eight state-of-the-art algorithms.