Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

We propose to couple the R2 performance measure and Particle Swarm Optimization in order to handle multi/many-objective problems. Our proposal shows that through a well-designed interaction process we could maintain the metaheuristic almost inalterable and through the R2 performance measure we did not use neither an external archive nor Pareto dominance to guide the search. The proposed approach is validated using several test problems and performance measures commonly adopted in the specialized literature. Results indicate that the proposed algorithm produces results that are competitive with respect to those obtained by four well-known MOEAs. Additionally, we validate our proposal in many-objective optimization problems. In these problems, our approach showed its main strength, since it could outperform another well-known indicator-based MOEA.