Distribution and Moment-Robust Optimization Models and Algorithms

优化模型和方法在决策问题中有着广泛的应用。在构建具有代表性的优化模型时，考虑参数不确定性是很重要的。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度来描述。当估计不确定参数时，还可以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多变量优化模型的性质并开发算法方法，利用对其分布和参数估计误差的有限知识来解决包含参数不确定性的多变量优化模型。优化模型将基于使用参数分布矩估计。这些模型将使用适当的惩罚方法来考虑矩估计误差。如果成功，这项研究的结果将导致开发一类新的决策优化建模工具，以及相关的算法技术来求解这些模型。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，将为在以规划、最小二乘和二次目标为基本构件的其他应用模型中处理参数不确定性提供基础。该奖项还将有助于开发实现算法解决方案技术的计算工具。将进行实验以验证算法，并比较从包含分布知识的模型生成的解的属性与那些忽略这些信息的解的属性。

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.