Towards Effective Mutation for Knowledge Transfer in Multifactorial Differential Evolution

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for the solving of continuous optimization problems. In the last decades, a plethora of DE variants have been proposed in the literature for enhanced optimization performance. However, most of these DE variants are designed to solve a single problem in a single run. Recently, a multifactorial DE (MFDE) has been proposed to conduct evolutionary search on multiple tasks simultaneously. Benefitting from the implicit knowledge transfer among different tasks, MFDE has demonstrated a superior performance against the single-task DE in terms of convergence speed and solution quality. In MFDE, the knowledge transfer is realized via the mutation operation conducted on solutions with different skill factors. However, despite a lot of mutation strategies suggested in the literature, the current MFDE takes DE/rand/1 as the only strategy for knowledge transfer. The impacts of different mutation strategies on the performance of MFDE is still unexplored. Taking this cue, in this paper, we embark a study to investigate how different mutation strategies for knowledge transfer affect the performance of MFDE. In particular, besides DE/rand/1, another four commonly-used mutation strategies are adapted for the purpose of multitask optimization. Further, towards effective mutation for knowledge transfer in MFDE, a new mutation strategy called DE/best/1+ρ, which is able to adjust its behavior along the search process is proposed. Lastly, comprehensive empirical studies are conducted to investigate the performance of existing and the new proposed mutation strategies on the 9 single-objective multitasking benchmarks.