Adaptive probabilistic branch and bound with confidence intervals for level set approximation
Adaptive probabilistic branch and bound with confidence intervals for level set approximation
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DOI：
10.1109/wsc.2013.6721488
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发表时间：
2013-12
期刊：
影响因子：
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通讯作者：
Hao Huang;Z. Zabinsky
中科院分区：
文献类型：
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作者：
Hao Huang;Z. Zabinsky
我们提出了一个模拟优化算法称为概率分支和置信区间（PBnB与CI），这是设计来近似的水平集的解决方案，为用户定义的分位数。PBnB与CI开发的确定性和噪声问题的混合连续和离散变量。结果的质量进行统计分析与顺序统计技术和置信区间的推导。此外，样本和重复的数量被设计为实现一定质量的解决方案。当该算法终止时，它提供期望分位数的具有置信区间的估计，以及近似水平集，包括真实期望水平集中的统计保证集、统计修剪集和未统计指定的集。我们还提出了基准函数的数值实验，以可视化的算法和它的能力。
We present a simulation optimization algorithm called probabilistic branch and bound with confidence intervals (PBnB with CI), which is designed to approximate a level set of solutions for a user-defined quantile. PBnB with CI is developed for both deterministic and noisy problems with mixed continuous and discrete variables. The quality of the results is statistically analyzed with order statistic techniques and confidence intervals are derived. Also, the number of samples and replications are designed to achieve a certain quality of solutions. When the algorithm terminates, it provides an estimation of the desired quantile with confidence intervals, and an approximation level set, including a statistically guaranteed set in the true desirable level set, a statistically pruned set, and a set which is not statistically specified. We also present numerical experiments with benchmark functions to visualize the algorithm and its capability.