Expensive Many-objective Optimization Assisted by Adaptive Modeling

Surrogate model-assisted multi-objective optimization has increasingly prevailed in solving expensive multi-/many-objective optimization problems. However, most research has advocated updating each model on each echo by the designed infill sampling approach. After the model-based search for the optimum, the approximated model of each objective may not need to be updated. Therefore, this paper proposes a GP model-assisted multi-objective optimization method with an adaptive modeling approach, with an angle and uncertainty-based infill sampling strategy assisting with updating. The estimated error change of all test samples is utilized in this adaptive modeling approach to assess if the surrogate model of each objective needs to be changed. The model, meanwhile, is improved by two infill individuals based on non-dominated sorting of estimations and uncertainties, respectively. One of the sampling criteria is to choose the potential individual for boosting the exploitation of the optimal solutions using estimation-based sorting and angles with samples. Following the uncertainty-based non-dominated sorting, the other aims to choose the infill individual for exploring the potential optimum position. Experiments on two multi-objective test suites and one real-world application indicate that the proposed method outperforms five contemporary classic optimization algorithms.