An Adaptive Parallel EI Infilling Strategy Extended by Non-Parametric PMC Sampling Scheme for Efficient Global Optimization

Abstract

This paper presents a novel adaptive parallel Expected Improvement (EI) infilling strategy for Efficient Global Optimization (EGO) by introducing a two-staged Non-parametric Population Monte Carlo Sampling (NPMS) scheme. The samples are uniformly generated from EI function in the first stage and converge to sub-domains of high EI values thresholded by a non-parametric sampling selection method in Population Monte Carlo (PMC) iterative succession. In the second stage, learning from potential information, Density-Based Spatial Clustering (DBSCAN) method is used to cluster samples and converge to candidate points. Compared to the original EI strategy, NPMS improves the minimum result by 14.6% and reduces the number of candidate points by 15.8% on our benchmark cases of EGO. Furthermore, 13 test functions involving different input space sizes, difficulties, and dimensions are conducted on six strategies including NPMS, and the results showed that NPMS achieves the highest ranking in terms of result finding and cost savings but slightly decreases optimization efficiency. Benefiting from broad sampling and dynamic clustering, especially in large input space size cases, NPMS not only guarantees high result accuracy but also reduces optimization costs by up to 34.9% compared to other parallel methods. Finally, our proposed NPMS-extended EI strategy has successfully reduced the number of candidate points, which is expected to provide a cost-practical approach to more complex problems.

Keywords

• Expected improvement
• multi-peak characteristics
• parallel infilling strategy
• population Monte Carlo
• sampling method