Stable optimisation-based scenario generation via game theoretic approach
Stable optimisation-based scenario generation via game theoretic approach
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DOI：
10.1016/j.compchemeng.2024.108646
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发表时间：
2023-11
期刊：
影响因子：
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通讯作者：
Georgios L. Bounitsis;L. Papageorgiou;Vassilis M. Charitopoulos
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文献类型：
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作者：
Georgios L. Bounitsis;L. Papageorgiou;Vassilis M. Charitopoulos
系统的场景生成（SG）方法已经成为一个宝贵的工具，以处理不确定性的有效解决随机规划（SP）问题。SG方法的质量取决于它们生成场景集的一致性，这些场景集保证求解SP的稳定性并导致高质量的随机解。在这种情况下，我们深入研究了基于优化的分布和矩匹配问题（Moment Matching Problem）的场景生成，并提出了一个博弈论的方法，这是制定为一个混合线性规划（MILP）模型。纳什讨价还价的方法和条款的目标函数的统计匹配的竞争对手被认为是球员。容量规划案例研究的结果突出了质量的随机解决方案，使用MILP模型的情况下生成。此外，所提出的博弈论扩展的样本内和样本外的稳定性方面的用户定义的参数变化的挑战性问题，增强。
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.