Multimodal Multi-objective Optimization: A Preliminary Study

In real world applications, there are many multi-objective optimization problems. Most existing multi-objective optimization algorithms focus on improving the diversity, spread and convergence of the solutions in the objective space. Few works study the distribution of solutions in the decision space. In practical applications, some multi-objective problems have different Pareto sets with the same objective values and these problems are defined as multimodal multi-objective optimization problems. It is of great significance to provide all the Pareto sets for the decision maker. This paper describes the concept of multimodal multi-objective optimization problems in detail. Novel test functions are also designed to judge the performance of different algorithms. Moreover, some existing multi-objective algorithms are tested and compared. Finally, a decision space based niching multi-objective evolutionary algorithm is proposed to solve these problems. The experimental results suggest that existing multi-objective optimization algorithms fail to find all the Pareto sets while the proposed algorithm is able to find almost all the Pareto sets without deteriorating the distribution of solutions in the objective space.