Distribution and Moment-Robust Optimization Models and Algorithms

分布和矩鲁棒优化模型和算法

• 批准号: 1100868
• 负责人: Sanjay Mehrotra
• 金额: $ 20万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100868&HistoricalAwards=false
• 关键词: Distribution; Moment; Robust; Optimization; Models

Optimization models and methods are widely used in decision problems. Incorporating parameter uncertainty is important in constructing representative optimization models. This parameter uncertainty may be described by a probability distribution, the moments of a probability distribution, or using bounds and confidence intervals on moments. When estimating uncertain parameters, information is also available on the error distribution of the estimated parameter. The research objective of this award is to study properties and develop algorithmic methods for solving multivariate optimization models that incorporate parameter uncertainty using limited knowledge on their distribution, and the parameter estimation errors. The optimization models will be based on using parameter distribution moment estimates. The models will incorporate moment estimation errors using a suitable penalty approach. If successful, the results of this research will lead to the development of a new class of decision optimization modeling tools with associated algorithmic techniques for solving these models. This award will contribute to better handling of parameter uncertainty in single and two-stage inventory planning models, the classical least squares model, and the models involving objectives described by quadratic functions. A better understanding of algorithmic implications of parameter uncertainty in these problems will provide foundation for handling parameter uncertainty in other application models that use the planning, the least squares and quadratic objectives as basic building blocks. The award will also contribute to the development of computational tools implementing the algorithms solution techniques. Experiments will be performed to validate the algorithms, and to compare the properties of the solutions generated from the models incorporating distributional knowledge with those that ignore this information.

优化模型和方法在决策问题中有着广泛的应用。消除参数不确定性是构造典型优化模型的重要内容。 该参数不确定性可以通过概率分布、概率分布的矩或使用矩的界限和置信区间来描述。在估计不确定参数时，也可获得关于估计参数的误差分布的信息。该奖项的研究目标是研究属性并开发用于解决多变量优化模型的算法方法，这些模型使用对其分布和参数估计误差的有限知识来解决参数不确定性。 优化模型将基于使用参数分布矩估计。 该模型将采用适当的惩罚方法纳入矩估计误差。 如果成功的话，这项研究的结果将导致一类新的决策优化建模工具的开发与相关的算法技术来解决这些模型。 该奖项将有助于更好地处理单阶段和两阶段库存计划模型、经典最小二乘模型以及涉及由二次函数描述的目标的模型中的参数不确定性。 更好地理解这些问题中参数不确定性的算法含义，将为处理其他使用规划、最小二乘和二次目标作为基本构建块的应用模型中的参数不确定性提供基础。 该奖项还将有助于实现算法解决方案技术的计算工具的开发。 将进行实验，以验证算法，并比较从模型中产生的解决方案的属性，将分布知识与那些忽略此信息。