Bridge Connecting Multiobjetive and Multimodal: A New Approach for Multiobjetive Optimization via Multimodal Optimization

Abstract

Multimodal optimization problem (MMOP) and multiobjective optimization problem (MOP) are two kinds of widely-studied problems in the optimization and evolutionary computation (EC) community. Although the MMOP and the MOP share a common characteristic that they both require the EC algorithms to obtain a set of solutions., this interesting relationship has not arisen sufficient attentions in the EC research community. The two branches of MMOP and MOP almost develop independently in the EC community. In this paper., we make the first attempt to fill the gap by building a bridge to connect the MOP to the MMOP., with the following contributions. Firstly., a novel and innovative idea is proposed to solve MOP by connecting the MOP to the MMOP. Secondly., an example of transformation method is illustrated to show the feasibility of the bridge connecting the MOP to the MMOP. Thirdly., experiments are conducted and the results show the effectiveness of using MMOP algorithms to obtain solutions that can be well mapped back to reflect the Pareto front of the MOP. Last but not least., this new perspective on connecting MOP to MMOP will inspire more diversity and more efficient future works on the topic of deep researches into both MMOP and MOP.