A parallel constrained Bayesian optimization algorithm for high-dimensional expensive problems and its application in optimization of VRB structures

Variable-thickness rolled blank (VRB) structures can offer excellent crashworthiness and weight reduction potential with its large-scale applications with satisfying manufacturing constraints, whose crashworthiness optimization is classified into the high-dimensional expensive problem including explicit and implicit constraints. Therefore, an efficient parallel constrained Bayesian optimization (PCBO) algorithm is proposed to improve the global searching accuracy and efficiency from three aspects: (1) the bilog transformation for implicit constraints is introduced to reduce the difficulty of identifying the feasibility of "expensive" sample points near constraint boundaries; (2) the trust region updating strategy is introduced to balance the exploration and exploitation of the searching process by dynamically updating the searching space; (3) the parallel high-quality points addition strategy based on multiple acquisition functions (PPA-MAF) is proposed, which not only increases the diversity of the optimal solutions but also achieves the multi-task parallel computation. Seven classical cases are adopted to validate the convergence and robustness of PCBO algorithm by comparing with several popular algorithms. Finally, the crashworthiness optimization of a VRB bumper system is performed by the proposed algorithm which can get better lightweight case under satisfying the manufacturing and performance constraints.