Iterative scenario based reduction technique for stochastic optimization using conditional value-at-risk
Iterative scenario based reduction technique for stochastic optimization using conditional value-at-risk
复制标题
使用条件风险值进行随机优化的基于迭代场景的缩减技术
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Mínguez
中科院分区：
文献类型：
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作者：
R. García;R. Mínguez
在过去的几十年中，已经开发了一些在竞争市场中管理风险的工具，例如条件风险价值。这些技术主要应用于基于场景和/或有限采样的随机规划模型，在大规模模型的情况下，根据场景的数量大大增加了它们的大小，有时会导致棘手的问题。该缺点在文献中使用（i）场景缩减方法和/或（ii）加速优化技术来解决。然而，当减少场景的数量时，部分随机信息丢失。在本文中，提出了一种迭代方案，以获得一个随机问题的解决方案表示的随机过程，通过一组场景和/或有限采样，并通过条件风险值建模风险。这种迭代方法依赖于这样一个事实，即优化条件风险价值的随机规划问题的解决方案仅取决于损失分布上尾的情景。因此，随机问题的解是通过在迭代方案内求解具有减少的场景数量的问题（子问题）来获得的。这种策略的结果在一个重要的减少计算负担的大规模问题，同时保持所有的随机信息嵌入在原来的一组场景。此外，每个子问题可以使用加速优化技术来解决。所提出的方法是非常容易实现的，数值结果表明，计算时间的减少可以是戏剧性的，并且随着初始场景或样本数量的增加而更加明显。
In the last decades, several tools for managing risks in competitive markets, such as the conditional value-at-risk, have been developed. These techniques are applied in stochastic programming models primarily based on scenarios and/or finite sampling, which in case of large-scale models increase considerably their size according to the number of scenarios, sometimes resulting in intractable problems. This shortcoming is solved in the literature using (i) scenario reduction methods, and/or (ii) speeding up optimization techniques. However, when reducing the number of scenarios, part of the stochastic information is lost. In this paper, an iterative scheme is proposed to get the solution of a stochastic problem representing the stochastic processes via a set of scenarios and/or finite sampling, and modeling risk via conditional value-at-risk. This iterative approach relies on the fact that the solution of a stochastic programming problem optimizing the conditional value-at risk only depends on the scenarios on the upper tail of the loss distribution. Thus, the solution of the stochastic problem is obtained by solving, within an iterative scheme, problems with a reduced number of scenarios (subproblems). This strategy results in an important reduction in the computational burden for large-scale problems, while keeping all the stochastic information embedded in the original set of scenarios. In addition, each subproblem can be solved using speeding-up optimization techniques. The proposed method is very easy to implement and, as numerical results show, the reduction in computing time can be dramatic, and more pronounced as the number of initial scenarios or samples increases.