A Three-Stage Surrogate Model Assisted Multi-Objective Genetic Algorithm for Computationally Expensive Problems

Multi-objective optimization problems (MOPs) are commonly encountered in practical engineering. Multi-objective evolutionary algorithms (MOEAs) are one of the powerful methods to solve MOPs. However, MOEAs require a large number of fitness evaluations, which limits the practical application of MOEAs. Surrogate model assisted evolutionary algorithm (SAEA) can effectively alleviate the computation burden of MOEAs by replacing time-consuming simulation with the surrogate model. In this paper, a three-stage adaptive multi-fidelity surrogate (MFS) model assisted multi-objective genetic algorithm(MOGA) are proposed. In the first stage, a cheap low-fidelity (LF) model is adopted to obtain a preliminary Pareto frontier (PF). In the second stage, some of the individuals are selected and sent to high-fidelity (HF) model to construct MFS models, which are used to evaluate the fitness functions and sequentially updated according to the model management strategy. During this stage, in order to obtain a better PF, a fidelity control strategy is developed to subjectively determine when transforming is conducted to the third stage, in which all the individuals are evaluated by the HF model. Three benchmark tests are used to test the performance of the proposed method. Results show that the proposed method performs better than online MFS model assisted MOGA( OLMFM-MOGA) and NSGA-II with HF model, especially when the correlation between the LF and HF models is very poor.