Approximating robust Pareto fronts by the MEOF-based multiobjective evolutionary algorithm with two-level surrogate models

The multiobjective optimization problems (MOPs) under uncertain environments are very challenging to be solved due to the sensitivities of some robust decision variables. To find the robust Pareto fronts (PFs) of these MOPs, the mean effective objective function (MEOF) is often used for evaluating the qualities of solutions in the existing evolutionary multiobjective optimization (EMO) algorithms. In the MEOF evaluation, the objective function values of multiple solutions in the neighborhood of a certain solution should be averaged. As a result, the MEOF-based EMO algorithms consume a large number of function evaluations to find robust PFs with high qualities. To overcome this weakness, we propose a new MEOF-based EMO framework with two-level surrogate models, denoted by EMO-MEOF/TS, which utilizes radial basis function and Gaussian process model to predict high-quality robust solutions at the levels of global search and local search. Some experiments are conducted to evaluate the performance of the proposed framework on some modified MOPs with robust decision variables. Our experimental results demonstrate that EMO-MEOF/TS is advantageous against several robust MOEAs in approximating the PFs of MOPs with robust characteristics.