Behavioural-based mathematical programming: algorithmics and applications

基于行为的数学规划：算法和应用

• 批准号: RGPIN-2017-05073
• 负责人: Marcotte, Patrice
• 金额: $ 2.99万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=636748
• 关键词: Behavioural; based; mathematical; programming; algorithmics

The aim of my research is to study, from both the theoretical and computational points of view, decision problems that involve agents with conflicting objectives. To fix ideas, let us consider the problem of setting tolls on the links of a highway. In order to optimize the revenue, one must take into account the behaviour of drivers, who want to minimize their own travel cost. If tolls are low, revenue will be low. If tolls are high, revenue will also be low, due to the low number of drivers for which the highway will be attractive. One must then strike the right balance, taking into account user behaviour. Although it has been shown that, even in that simple setting, the problem is hard to solve, the situation becomes all the more complex when behaviour varies across the population or when congestion occurs. Such problems fit the framework of bilevel mathematical programs, or leader-follower games. In these games, the leader factors into its optimization problem the rational reaction of an adversary or a population impacted by his decisions. This reaction would be the drivers' path choices in our introductory example. This situation is ubiquitous. Indeed, it is the exception that all variables of a problem are controlled by the leader.

我的研究目的是从理论和计算的角度研究涉及具有冲突目标的代理的决策问题。为了解决这个问题，让我们考虑设置高速公路路段收费的问题。为了优化收入，必须考虑司机的行为，他们希望尽量减少自己的出行成本。如果通行费低，收入就会低。如果通行费高，收入也会低，因为高速公路对司机的数量少。然后，必须考虑到用户行为，取得适当的平衡。尽管已经表明，即使在这种简单的环境中，问题也很难解决，但当人群的行为发生变化或发生拥堵时，情况就会变得更加复杂。此类问题符合双层数学程序或领导者-追随者博弈的框架。在这些博弈中，领导者将对手或受其决策影响的人群的理性反应纳入其优化问题。在我们的介绍性示例中，这种反应将是驾驶员的路径选择。这种情况是普遍存在的。事实上，问题的所有变量都由领导者控制是一个例外。