最大化期望改进函数的分枝定界算法
Branch and Bound Algorithms for Maximizing Expected Improvement Functions
摘要：
确定性计算机模拟通常被用来代替复杂的物理实验。虽然比物理实验便宜，但计算机代码运行起来仍然很耗时。用于探索确定性模拟器的响应表面的有效策略是使用对计算机代码的近似，诸如高斯过程（GP）模型，结合用于选择可用于构建GP模型的设计点的序贯抽样策略。这些研究的最终目标通常是估计模拟器输出的特定特征，例如最大值、最小值或水平集（轮廓）。在用GP模型近似这些特征之前，必须完成计算机模拟器的充分运行。具有期望改进（EI）函数的序贯设计可以以最少的运行次数产生对特征的良好估计。面临的挑战是，预期的改善功能本身往往是多模态的，难以最大化。我们开发的分支定界算法，有效地最大限度地提高EI函数在特定的问题，包括同时估计的最小值和最大值，并在估计的轮廓。这些分支定界算法优于其他优化策略，如遗传算法，并在许多顺序的设计步骤，可以导致显着优越的准确性，在估计感兴趣的功能。
英文摘要：
Deterministic computer simulations are often used as a replacement for complex physical experiments. Although less expensive than physical experimentation, computer codes can still be time-consuming to run. An effective strategy for exploring the response surface of the deterministic simulator is the use of an approximation to the computer code, such as a Gaussian process (GP) model, coupled with a sequential sampling strategy for choosing design points that can be used to build the GP model. The ultimate goal of such studies is often the estimation of specific features of interest of the simulator output, such as the maximum, minimum, or a level set (contour). Before approximating such features with the GP model, sufficient runs of the computer simulator must be completed. Sequential designs with an expected improvement (EI) function can yield good estimates of the features with a minimal number of runs. The challenge is that the expected improvement function itself is often multimodal and difficult to maximize. We develop branch and bound algorithms for efficiently maximizing the EI function in specific problems, including the simultaneous estimation of a minimum and a maximum, and in the estimation of a contour. These branch and bound algorithms outperform other optimization strategies such as genetic algorithms, and over a number of sequential design steps can lead to dramatically superior accuracy in estimation of features of interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
