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Adaptive importance sampling for optimization under uncertainty problems

机译：不确定性问题下优化的自适应重要性抽样

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摘要

Design-under-uncertainty problems where a probabilistic performance is adopted as objective function and its estimation is obtained through stochastic simulation are discussed. The focus is on reducing the computational burden associated with the stochastic simulation through adaptive implementation of importance sampling (IS) across the iterations of the optimization algorithm. The proposed formulation relies only on available information (i.e., function evaluations) from the current iteration of the optimization process to improve estimation accuracy in subsequent iterations, and therefore corresponds to a IS selection with a small additional computational burden. Kernel density estimation (KDE) is employed to construct the IS densities based on samples distributed proportional to the integrand of the probabilistic performance. The characteristics of the proposal density are optimally selected to minimize the anticipated coefficient of variation for the objective function if such a proposal density is used as IS distribution. To avoid numerical problems that can occur when trying to develop IS for all uncertain model parameters, a prioritization is first performed using a recently proposed global sensitivity analysis to quantify the relative importance of each model parameter. Therefore, the IS density is only constructed for the most important parameters, with the exact number also a variable that is optimally selected based on the anticipated accuracy. To facilitate the overall adaptive scheme efficient guidelines for the sharing of information across iterations of the optimization algorithm are developed. The numerical example considered verifies the efficiency of the proposed adaptive IS framework.
机译：讨论了采用概率性能作为目标函数并通过随机仿真获得估计的不确定性下设计问题。重点是通过在优化算法的迭代过程中通过自适应实现重要性抽样（IS）来减少与随机模拟相关的计算负担。所提出的公式仅依赖于来自优化过程的当前迭代的可用信息（即，功能评估）以提高后续迭代中的估计精度，因此对应于具有较小附加计算负担的IS选择。内核密度估计（KDE）用于根据与概率性能的整数成正比分布的样本构造IS密度。如果将这种建议密度用作IS分布，则最佳选择建议密度的特性以最小化目标函数的预期变化系数。为了避免在尝试为所有不确定的模型参数开发IS时可能出现的数值问题，首先使用最近提出的全局敏感性分析对每个模型参数的相对重要性进行优先级划分。因此，仅针对最重要的参数构建IS密度，确切的数字也是根据预期的精度最佳选择的变量。为了促进总体自适应方案，开发了用于优化算法迭代之间信息共享的有效准则。所考虑的数值示例验证了所提出的自适应IS框架的效率。

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