We consider Ranking and Selection (R&S) in the presence of spatial correlation among designs. The performance of each design can only be evaluated through stochastic simulation with heterogeneous noise. Our primary objective is to maximize the probability of correct selection (PCS) by optimally allocating the simulation budget considering the spatial correlation among designs. We propose using Gaussian process regression (GPR) to model the spatial correlation and develop a GPR-based optimal computing budget allocation (GPOCBA) framework to derive an asymptotically optimal allocation policy. Additionally, we analyze the impact of spatial correlation on allocation policy and quantify its benefits under specific cases. We also introduce a sequential implementation of GPOCBA and establish convergence results. Numerical experiments show that the proposed GPOCBA method significantly outperforms the widely used OCBA, demonstrating improved computational efficiency by considering spatial correlation in R&S problems.

中文翻译：

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使用高斯过程回归的最优计算预算分配


我们在设计之间存在空间相关性的情况下考虑排名和选择 （R&S）。每个设计的性能只能通过使用异构噪声的随机仿真来评估。我们的主要目标是通过考虑设计之间的空间相关性来优化分配仿真预算，从而最大限度地提高正确选择的概率 （PCS）。我们建议使用高斯过程回归 （GPR） 对空间相关性进行建模，并开发基于 GPR 的最优计算预算分配 （GPOCBA） 框架来推导出渐近最优分配策略。此外，我们分析了空间相关性对分配策略的影响，并量化了其在特定情况下的好处。我们还介绍了 GPOCBA 的顺序实施并建立了收敛结果。数值实验表明，所提出的 GPOCBA 方法明显优于广泛使用的 OCBA，表明在 R&S 问题中考虑空间相关性提高了计算效率。