A novel scalable test problem suite for multimodal multiobjective optimization

This paper proposes a novel scalable multimodal multiobjective test problem suite. The proposed test problems have various properties, such as presence of local Pareto optimal set (PS), scalable number of PSs, nonuniformly distributed PSs, discrete Pareto front (PF), and scalable number of variables and objectives. All of the test problems proposed in this paper are continuous optimization problems. Therefore, they can be used to measure different capacities of multimodal multiobjective continuous optimization algorithms. Moreover, a landscape visualization method for multiobjective problems is proposed to show the properties of the multimodal multiobjective test problems. Based on the landscapes, the characteristics of these problems are analyzed and characterized. Furthermore, the existing multimodal multiobjective optimization algorithms and several popular multiobjective algorithms are tested and compared with the novel test problem suite. Then, a discussion on the desired properties of multimodal multiobjective optimization algorithms and future works on multimodal multiobjective optimization are presented.