A two-stage adaptive multi-fidelity surrogate model-assisted multi-objective genetic algorithm for computationally expensive problems

Surrogate model-assisted multi-objective genetic algorithms (MOGA) show great potential in solving engineering design problems since they can save computational cost by reducing the calls of expensive simulations. In this paper, a two-stage adaptive multi-fidelity surrogate (MFS) model-assisted MOGA (AMFS-MOGA) is developed to further relieve their computational burden. In the warm-up stage, a preliminary Pareto frontier is obtained relying only on the data from the low-fidelity (LF) model. In the second stage, an initial MFS model is constructed based on the data from both LF and high-fidelity (HF) models at the samples, which are selected from the preliminary Pareto set according to the crowding distance in the objective space. Then the fitness values of individuals are evaluated using the MFS model, which is adaptively updated according to two developed strategies, an individual-based updating strategy and a generation-based updating strategy. The former considers the prediction uncertainty from the MFS model, while the latter takes the discrete degree of the population into consideration. The effectiveness and merits of the proposed AMFS-MOGA approach are illustrated using three benchmark tests and the design optimization of a stiffened cylindrical shell. The comparisons between the proposed AMFS-MOGA approach and some existing approaches considering the quality of the obtained Pareto frontiers and computational efficiency are made. The results show that the proposed AMFS-MOGA method can obtain Pareto frontiers comparable to that obtained by the MOGA with HF model, while significantly reducing the number of evaluations of the expensive HF model.

Automated summary

The paper introduces a two-stage adaptive multi-fidelity surrogate model-assisted multi-objective genetic algorithm (AMFS-MOGA), which involves obtaining a preliminary Pareto frontier using low-fidelity model data in the first stage and constructing an initial MFS model based on samples selected from the preliminary Pareto set in the second stage. The fitness values of individuals are evaluated using the MFS model, which is adaptively updated according to prediction uncertainty and population diversity. The effectiveness of the proposed approach is demonstrated through benchmark tests and design optimization, showing comparable results to traditional methods while significantly reducing computational costs.