Adaptive probabilistic branch and bound for level set approximation
Adaptive probabilistic branch and bound for level set approximation
复制标题
水平集逼近的自适应概率分支定界
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Joyce W. Yen
中科院分区：
文献类型：
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作者：
Z. Zabinsky;Wei Wang;Yanto Prasetio;A. Ghate;Joyce W. Yen
我们提出了一种概率分支和结合方法（PBNB）方法，用于定位可行区域的子集，该区域包含解决方案以实现用户指定分位数的级别集合。 PBNB设计用于优化连续或有限域上的嘈杂（和确定性）函数，并与单个现有解决方案相比提供了更多信息。它使用基于订单统计的分析来指导分支和修剪程序以平衡计算工作。统计分析还规定了在子区域内要采样的点数，也规定了在每个样本点估计真实函数值所需的复制数量。当算法终止时，它将返回溶液的集中子区域，其概率与其最佳间隙结合，并将全局最佳溶液作为副产品估算。提出了有关基准问题的数值实验。
We present a probabilistic branch-and-bound (PBnB) method for locating a subset of the feasible region that contains solutions in a level set achieving a user-specified quantile. PBnB is designed for optimizing noisy (and deterministic) functions over continuous or finite domains, and provides more information than a single incumbent solution. It uses an order statistics based analysis to guide the branching and pruning procedures for a balanced allocation of computational effort. The statistical analysis also prescribes both the number of points to be sampled within a sub-region and the number of replications needed to estimate the true function value at each sample point. When the algorithm terminates, it returns a concentrated sub-region of solutions with a probability bound on their optimality gap and an estimate of the global optimal solution as a by-product. Numerical experiments on benchmark problems are presented.