Multimodal multiobjective optimization with differential evolution

This paper proposes a multimodal multiobjective Differential Evolution optimization algorithm (MMODE). The technique is conceived for deployment on problems with a Pareto multimodality, where the Pareto set comprises multiple disjoint subsets, all of which map to the same Pareto front. A new contribution is the formulation of a decision-variable preselection scheme that promotes diversity of solutions in both the decision and objective space. A new mutation-bound process is also introduced as a supplement to a classical mutation scheme in Differential Evolution methods, where offspring that lie outside the search bounds are given a second opportunity to mutate, hence reducing the density of individuals on the boundaries of the search space. New multimodal multiobjective test functions are designed, along with analytical expressions for their Pareto sets and fronts. Some test functions introduce more complicated Pareto-front shapes and allow for decision-space dimensions greater than two. The performance of the MMODE algorithm is compared with five other state-of-the-art methods. The results show that MMODE realizes superior performance by finding more and better distributed Pareto solutions.