Scenario generation is required for most applications of stochastic programming to evaluate the expected effect of decisions made under uncertainty. We propose a novel and effective problem-based scenario generation method for two-stage stochastic programming that is agnostic to the specific stochastic program and kind of distribution. Our contribution lies in studying how an output distribution may change across decisions and exploit this for scenario generation. From a collection of output distributions, we find a few components that largely compose these, and such components are used directly for scenario generation. Computationally, the procedure relies on evaluating the recourse function over a large discrete distribution across a set of candidate decisions, while the scenario set itself is found using standard and efficient linear algebra algorithms that scale well. The method’s effectiveness is demonstrated on four case study problems from typical applications of stochastic programming to show it is more effective than its distribution-based alternatives. Due to its generality, the method is especially well suited to address scenario generation for distributions that are particularly challenging.

中文翻译：

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通过分解输出分布生成基于问题的场景

大多数随机规划应用都需要场景生成来评估在不确定性下做出的决策的预期效果。我们提出了一种新颖且有效的基于问题的两阶段随机规划场景生成方法，该方法与特定的随机程序和分布类型无关。我们的贡献在于研究输出分布如何随着决策而变化，并利用它来生成场景。从输出分布的集合中，我们找到了一些主要组成这些的组件，这些组件直接用于场景生成。在计算上，该过程依赖于评估一组候选决策的大离散分布上的追索函数，而场景集本身是使用可扩展的标准且高效的线性代数算法找到的。该方法的有效性在随机规划典型应用的四个案例研究问题上得到了证明，表明它比基于分布的替代方案更有效。由于其通用性，该方法特别适合解决特别具有挑战性的分布的场景生成。