SAMPLING UNCERTAIN CONSTRAINTS UNDER PARAMETRIC DISTRIBUTIONS
SAMPLING UNCERTAIN CONSTRAINTS UNDER PARAMETRIC DISTRIBUTIONS
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DOI：
10.1109/wsc.2018.8632432
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
H. Lam;Fengpei Li
中科院分区：
文献类型：
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作者：
H. Lam;Fengpei Li
我们考虑优化问题的不确定性约束，需要满足概率。当数据可用时，获得此类问题的可行解的常见方法是施加采样约束，遵循所谓的场景生成（SG）方法。然而，当数据大小是小的，采样约束可能不支持所获得的解决方案的可行性的保证。本文研究了如何利用参数信息和蒙特卡罗模拟的力量，以获得可行的解决方案，即使数据不足以支持使用SG。我们的方法利用了一个分布鲁棒的优化配方，通知蒙特卡洛样本量需要实现我们的保证。
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following the so-called scenario generation (SG) approach. However, when the data size is small, the sampled constraints may not support a guarantee on the feasibility of the obtained solution. This paper studies how to leverage parametric information and the power of Monte Carlo simulation to obtain feasible solutions even when the data are not sufficient to support the use of SG. Our approach makes use of a distributionally robust optimization formulation that informs the Monte Carlo sample size needed to achieve our guarantee.