Solving Multimodal Optimization Problems through a Multiobjective Optimization Approach

This paper proposes a novel multiobjective optimization approach for solving multimodal optimization problems (MMOPs). An MMOP at hand is first transformed into a bi-objective optimization problem. The two objectives are constructed totally conflict by using the distance information and the objective function value. In this way, multiple optima of an MMOP are converted into the nondominated solutions of the transformed bi-objective optimization problem. Then, multi-objective optimization techniques based on differential evolution are applied to solve the bi-objective problem. In addition, a modified solution comparison criterion is proposed to improve the accuracy level of the final solutions. The performance of the proposed approach is evaluated on a suite of benchmark functions. Experimental results show that the proposed approach is very competitive compared with six state-of-the-art multimodal optimization algorithms on most of the benchmark functions.