Theory and Applications of Stochastic Bilevel Mixed-Integer Programming

随机双层混合整数规划理论与应用

• 批准号: 418627-2012
• 负责人: Ozaltin, Osman
• 金额: $ 0.62万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=531277
• 关键词: Theory; Applications; Stochastic; Bilevel; Mixed

Bilevel programs model the hierarchical relationship between two autonomous and possibly conflicting decision makers: the leader and the follower. Each decision maker controls a distinct set of variables, and the decisions are made sequentially. First, the upper-level decisions are made by the leader, after which the lower-level decisions are made by the follower. The follower is affected by the decisions of the leader, while the follower's decisions in return affect the leader. Conventional bilevel programming models are deterministic, although many real life problems include uncertain parameters. Stochastic programming can be used to model optimization problems under uncertainty. However, that framework does not naturally extend to bilevel programs as it involves a single decision level. The main goal of the present work is to take a new approach and study "bilevel stochastic programs" in terms of modeling, theory and methodology. Our approach thus combines and expands the research on bilevel programming and stochastic programming.

双层计划模拟了两个自治的、可能相互冲突的决策者之间的等级关系：领导者和追随者。每个决策者控制着一组不同的变量，决策是按顺序做出的。首先，上级决策由领导作出，之后下级决策由追随者做出。追随者受领导者的决定影响，而追随者的决定反过来影响领导者。传统的双层规划模型是确定性的，尽管现实生活中的许多问题都包含不确定的参数。随机规划可以用来模拟不确定条件下的优化问题。然而，该框架并不自然地扩展到双层方案，因为它涉及单一的决策层。本文的主要目的是从模型、理论和方法论三个方面对“双层随机规划”进行研究。因此，我们的方法结合并扩展了双层规划和随机规划的研究。