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In optimization problems, the expensive black-box function implies severely restricted budgets in terms of evaluation. Some Bayesian optimization methods have been proposed to solve this problem, such as expected improvement (EI) and hierarchical expected improvement (HEI). Neither EI nor HEI is parallel, which depends on a one-point-at-a-time strategy. In this work, a new parallel Bayesian framework based on the minimum energy criterion is proposed to improve these popular one-point methods. The new proposed framework can save time and costs by reducing the number of iterations and avoid the local optimization trap by encouraging the exploration of the optimization space. Additionally, a shrink-augment strategy is also introduced to correct the local surrogate model for the black-box function adaptively, which could also benefit the optimization. Some numerical and illustrative experiments are presented to demonstrate the superiority of our proposed method over some other Bayesian methods. The results show that the novel framework can balance exploitation and exploration well and has great performance in global optimization.

Parallel efficient global optimization by using the minimum energy criterion