A Scalable Multimodal Multiobjective Test Problem

Recently, multimodal multiobjective optimization has started to attract a lot of attention. Its task is to find multiple Pareto optimal solution sets in the decision space, which are equivalent in the objective space. In some applications, it is important to find multiple global and local Pareto optimal solution sets in the decision space, which have similar quality in the objective space. In evolutionary computation, a wide variety of test problems with various characteristics are needed for fair comparison of different algorithms. However, we have only a small number of test problems for multimodal multiobjective optimization. In this paper, we propose a scalable multimodal multiobjective test problem with respect to the five parameters: (i) the number of objectives, (ii) the number of decision variables, (iii) the number of equivalent Pareto optimal solution sets in the decision space, (iv) the number of local Pareto fronts, and (v) the number of local Pareto optimal solution sets in the decision space for each local Pareto front. Our proposal is the first scalable test problem with respect to all of these five parameters.