This paper proposes a sequential design for maximizing a stochastic computer simulator output, $y\left(\mathit{x}\right)$, over an unknown optimization domain. The training data used to estimate the optimization domain are a set of (historical) inputs, often from a physical system modeled by the simulator. Two methods are provided for estimating the simulator input domain. An extension of the well-known efficient global optimization algorithm is presented to maximize $y\left(\mathit{x}\right)$. The domain estimation/maximization procedure is applied to two readily understood analytic examples. It is also used to solve a problem in nuclear safety by maximizing the k-effective “criticality coefficient” of spent fuel rods, considered as one-dimensional heterogeneous fissile media. One of the two domain estimation methods relies on expertise-type constraints. We show that these constraints, initially chosen to address the spent fuel rod example, are robust in that they also lead to good results in the second analytic optimization example. Of course, in other applications, it could be necessary to design alternative constraints that are more suitable for these applications.

本文提出了一种顺序设计，以最大化随机计算机模拟器的输出， $ÿ（\mathit{X}）$，在未知的优化域上。用于估计优化域的训练数据是一组（历史）输入，通常来自模拟器建模的物理系统。提供了两种方法来估计模拟器输入域。提出了著名的高效全局优化算法的扩展，以最大程度地提高$ÿ（\mathit{X}）$。将域估计/最大化过程应用于两个易于理解的分析示例。它还通过最大化乏燃料棒的k-有效“临界系数”（被视为一维非均质裂变介质）来解决核安全问题。两种域估计方法之一依赖于专业知识类型的约束。我们表明，最初选择用于解决乏燃料棒示例的这些约束是稳健的，因为它们在第二个分析优化示例中也能产生良好的结果。当然，在其他应用程序中，可能有必要设计更适合于这些应用程序的替代约束。