Parallel multi-objective Bayesian optimization approaches based on multi-fidelity surrogate modeling

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Aerospace product design optimizations, such as micro-aerial vehicle fuselage design, often involve multiple objectives. Multi-objective Bayesian optimization (MOBO) is an efficient approach in solving problems concerning multiple conflicting objectives. Conventional MOBO approaches are often limited by sequential optimizations, which can only add one sample in each iteration. The parallel computing strategy is a desirable way to accelerate the optimization process by adding a batch of samples in one iteration. Unfortunately, existing parallel MOBO approaches are constrained to handling single-fidelity data, thereby missing out on the potential benefits of utilizing auxiliary low-fidelity data. To further improve the optimization efficiency of the parallel MOBO approach, this paper proposes two parallel MOBO approaches based on multi-fidelity surrogate modeling. Specially, the cheap auxiliary low-fidelity data can be utilized to improve the performance of the parallel MOBO approach by multi-fidelity surrogate modeling. The updating points and fidelity levels are determined by a modified hypervolume excepted improvement function, and two parallel computing strategies are developed for multi-point sampling. Additionally, a constraint handling strategy is developed for problems with constraints by adopting the probability of feasibility functions. The proposed approaches are demonstrated through numerical benchmark examples and two real-world applications involving the multi-objective optimizations of a micro-aerial vehicle fuselage and a metamaterial vibration isolator. Results in the real-world applications show that the proposed approaches significantly improve the optimization efficiency with faster convergence speed and exhibit superior overall performance compared with the state-of-the-art MOBO methods.