Mathematical modeling and optimization under uncertainty

不确定性下的数学建模与优化

• 批准号: RGPIN-2015-05063
• 负责人: Gzara, Fatma
• 金额: $ 1.46万
• 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613334
• 关键词: Mathematical; modeling; optimization; under; uncertainty

Mathematical models arising from application areas such as logistics, supply chain design, distribution, and transportation planning remain challenging despite the recent advances in software and hardware capabilities. In addition to large size, variability in design parameters leads to significant complexity both in modeling and in solution methodologies. While it is common to assume that parameters are known and constant, variability is inherent to all practical problems and often times, solutions generated by deterministic models turn out to be infeasible or far from optimal when implemented. On the other hand, optimization problems that model variability explicitly are generally more challenging due to stochasticity and nonlinearity. The appropriate approach to model randomness depends on the amount of information available. Under perfect information, parameters are assumed to be known and constant during the planning horizon and the resulting models are deterministic. Under risk, stochastic modeling assumes that parameters follow a probability distribution. Robust optimization is an emerging framework for modeling under uncertainty where no distribution information is available. The focus of this research is on modeling and optimization under uncertainty. We propose models and develop specialized optimization tools to handle uncertainty. Fortunately such complex problems tend to exhibit special structure, which makes them suitable for decomposition methodologies such as Lagrangian relaxation/column generation, Dantzig-Wolfe decomposition, and Benders decomposition. Two application areas will be investigated under this framework: disaster response network design and airline operations planning. In both application areas, stochastic and robust optimization will be explored. The goal is to come up with robust designs that optimize classical objectives like profit or cost but also remain valid or allow smooth recovery when settings change. The proposal provides rich research questions suitable for rigorous highly qualified personnel training.  In total, three Ph.D. and four MASc. students will have the opportunity to carry out both theoretical and applied research.  They will gain skills in analysis and modeling of quantitative decision making as well as in developing algorithms and using sophisticated optimization software. The students will apply their research work in decision making for disaster management and airline operations planning. Both areas are highly applicable and provide students the qualifications to work in academia, the airline industry, government,  aid agencies, etc.

从物流、供应链设计、配送和运输计划等应用领域产生的数学模型仍然具有挑战性，尽管最近在 软件和硬件功能。除了大尺寸外，设计参数还具有可变性 导致建模和解决方案方法都非常复杂。当它 通常假设参数是已知和恒定的，可变性是固有的 所有实际问题以及通常情况下，由确定性模型生成的解决方案都会产生 实施时不可行或远未达到最佳状态。另一方面，优化 由于随机性的原因，显式建模可变性的问题通常更具挑战性 和非线性。建模随机性的适当方法取决于 可用的信息。在完全信息下，假设参数是已知的，并且 在计划范围内是恒定的，所得到的模型是确定性的。在风险之下， 随机建模假设参数服从概率分布。健壮 优化是一种新兴的建模框架，用于在没有分布的不确定情况下进行建模 信息是可用的。 本文研究的重点是不确定条件下的建模与优化。我们建议 模型，并开发专门的优化工具来处理不确定性。幸运的是，这样 复杂问题往往表现出特殊的结构，这使得它们适合于分解方法，如拉格朗日松弛/列生成、Dantzig-Wolfe分解和Bders 腐烂。在这一框架下将研究两个应用领域：灾难应对网络设计和航空公司运营规划。在这两个应用领域，随机性 并将探索稳健优化。我们的目标是提出健壮的设计， 优化传统目标，如利润或成本，但也要保持有效或允许平稳恢复 当设置更改时。 提案提供了丰富的研究问题，适合严格的、高素质的人才培养。总共有三个博士和四个硕士。学生将有机会进行理论和应用研究。他们将获得定量决策的分析和建模技能，以及开发算法和使用复杂优化软件的技能。学生将把他们的研究成果应用于灾难管理和航空公司运营规划的决策中。这两个领域都非常适用，都为学生提供了在学术界、航空业、政府、医疗援助机构等工作的资格。