A multi-objective bayesian optimization approach based on variable-fidelity multi-output metamodeling

Practical engineering problems are often involved multiple computationally expensive objectives. A promising strategy to alleviate the computational cost is the variable-fidelity metamodel-based multi-objective Bayesian optimization approach. However, the existing approaches are under the assumption of independent correlations across the multiple objectives by constructing a variable-fidelity metamodel for each objective, which may lose some useful information in a way. To facilitate the usage of the variable-fidelity metamodel-based multi-objective Bayesian optimization approach, a multi-objective Bayesian optimization approach based on variable-fidelity multi-output (VFMO) metamodeling is proposed in this paper. A variable-fidelity multi-output metamodeling approach is developed to model the multiple objectives jointly, which can capture the latent correlations across the multiple objectives and further enhance the optimization. Furthermore, a weighted expected hypervolume improvement acquisition function based on the VFMO metamodeling approach (VFMO-WEHVI) is proposed for multi-objective optimization. The weight coefficients are adaptively determined according to the information from the current metamodel, which allows a better tradeoff between global exploration and local exploitation. Moreover, the probability of feasibility is introduced to deal with multi-objective optimization problems with constraints. The effectiveness of the proposed approach is demonstrated using five analytical benchmark examples and the multi-objective optimization of a metamaterial vibration isolator. Results indicate that the proposed VFMO-WEHVI approach has the best overall performance compared with the state-of-the-art approaches.