Performance comparison of EMO algorithms on test problems with different search space shape

We examine the performance of evolutionary multi-objective optimization (EMO) algorithms on various shapes of the search space in the objective space (i.e., the feasible region in the objective space). To analyze the advantage and disadvantage of each EMO algorithm on the shape of the search space, we propose a meta-optimization method which can automatically create multi-objective optimization problems (MOPs) for clarifying the advantage and disadvantage of EMO algorithms. In particular, we propose a two-level model to generate such MOPs. In the upper level, MOPs are handled as solutions. Some design variables of each MOP are optimized in this level. In the lower level, each MOP is used to calculate the relative performance between two EMO algorithms. The relative performance is regarded as the fitness of the MOP in the upper level. Thus, by maximizing the relative performance, we can obtain an MOP which differentiates the search performance between two EMO algorithms. Through computational experiments, we obtained two interesting observations. One is that Pareto dominance-based EMO algorithms have a low escaping ability from local Pareto-optimal regions. The other is that it is difficult for decomposition- and indicator-based EMO algorithms to find solutions along the entire Pareto front.