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.

尽管最近在物流、供应链设计、分销和运输规划等应用领域产生的数学模型仍然具有挑战性 软件和硬件能力。除了尺寸大之外，设计参数也存在差异 导致建模和解决方案方法的显着复杂性。虽然它 通常假设参数已知且恒定，可变性是固有的 所有实际问题通常都会由确定性模型生成解决方案 实施时不可行或远非最佳。另一方面，优化 由于随机性，显式模拟可变性的问题通常更具挑战性 和非线性。模型随机性的适当方法取决于 可用的信息。在完美信息下，假设参数已知并且 在规划范围内是恒定的，并且生成的模型是确定性的。面临风险， 随机建模假设参数遵循概率分布。强壮的 优化是一种新兴的建模框架，用于在无分布的不确定性下进行建模 信息可用。 本研究的重点是不确定性下的建模和优化。我们建议 模型并开发专门的优化工具来处理不确定性。幸好这样 复杂问题往往表现出特殊的结构，这使得它们适合分解方法，例如拉格朗日松弛/列生成、Dantzig-Wolfe 分解和 Benders 分解。该框架下将研究两个应用领域：灾害响应网络设计和航空公司运营规划。在这两个应用领域中，随机 并将探索鲁棒优化。目标是提出稳健的设计 优化利润或成本等经典目标，但仍保持有效或允许顺利恢复 当设置改变时。 该提案提供了丰富的研究问题，适合严格的高素质人才培训。  总共有三名博士学位。和四个硕士学位。学生将有机会进行理论和应用研究。  他们将获得定量决策分析和建模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工作应用于灾害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，为学生提供在学术界、航空业、政府、援助机构等工作的资格。