A Fast Multipoint Expected Improvement for Parallel Expensive Optimization

Abstract

The multipoint expected improvement (EI) criterion is a well-defined parallel infill criterion for expensive optimization. However, the exact calculation of the classical multipoint EI involves evaluating a significant amount of multivariate normal cumulative distribution functions, which makes the inner optimization of this infill criterion very time consuming when the number of infill samples is large. To tackle this problem, we propose a novel fast multipoint EI criterion in this work. The proposed infill criterion is calculated using only univariate normal cumulative distributions; thus, it is easier to implement and cheaper to compute than the classical multipoint EI criterion. It is shown that the computational time of the proposed fast multipoint EI is several orders lower than the classical multipoint EI on the benchmark problems. In addition, we propose to use cooperative coevolutionary algorithms (CCEAs) to solve the inner optimization problem of the proposed fast multipoint EI by decomposing the optimization problem into multiple subproblems with each subproblem corresponding to one infill sample and solving these subproblems cooperatively. Numerical experiments show that using CCEAs can improve the performance of the proposed algorithm significantly compared with using standard evolutionary algorithms. This work provides a fast and efficient approach for parallel expensive optimization.