Systematic scenario generation (SG) methods have emerged as an invaluable tool to handle uncertainty towards the efficient solution of stochastic programming (SP) problems. The quality of SG methods depends on their consistency to generate scenario sets which guarantee stability on solving SPs and lead to stochastic solutions of good quality. In this context, we delve into the optimisation-based Distribution and Moment Matching Problem (DMP) for scenario generation and propose a game-theoretic approach which is formulated as a Mixed-Integer Linear Programming (MILP) model. Nash bargaining approach is employed and the terms of the objective function regarding the statistical matching of the DMP are considered as players. Results from a capacity planning case study highlight the quality of the stochastic solutions obtained using MILP DMP models for scenario generation. Furthermore, the proposed game-theoretic extension of DMP enhances in-sample and out-of-sample stability with respect to the challenging problem of user-defined parameters variability.

中文翻译：

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通过博弈论方法稳定地生成基于优化的场景

系统场景生成（SG）方法已成为处理不确定性以有效解决随机规划（SP）问题的宝贵工具。SG 方法的质量取决于它们生成场景集的一致性，从而保证求解 SP 的稳定性并产生高质量的随机解。在这种背景下，我们深入研究了用于场景生成的基于优化的分布和矩匹配问题（DMP），并提出了一种博弈论方法，该方法被制定为混合整数线性规划（MILP）模型。采用纳什讨价还价方法，并将有关 DMP 统计匹配的目标函数项视为参与者。容量规划案例研究的结果突出了使用 MILP DMP 模型生成场景所获得的随机解决方案的质量。此外，所提出的 DMP 博弈论扩展增强了针对用户定义参数可变性这一挑战性问题的样本内和样本外稳定性。