Development and Implementation of Algorithms for Stochastic Integer Programming

这项研究解决了随机优化问题，这些问题由于整数决策变量的存在而变得更加复杂，以模拟多周期或多阶段设置中的逻辑和其他离散决策。为了应对多阶段随机整数优化问题的计算复杂性，本研究将开发新的方法学、算法和原型软件。整数规划的值函数的基本性质将与这些优化问题的固有可分解性一起被利用，以便开发随问题大小而很好地扩展的算法。生产计划与调度、选址、交通、财务、工程设计等方面的大量问题要求在存在不确定性的情况下进行决策。例如，不确定性支配着燃料的价格、电力的供应和对化学品的需求。随机优化是应用数学的一个分支，它为不确定条件下的审慎决策提供了系统的工具。随机优化的一个关键困难是处理一个巨大的不确定空间，这导致了非常大规模的优化模型。开发的算法将在研究人员广泛分布的全局优化包Baron中实现，并提供给研究社区。如果成功，这个项目可能会对许多经济部门在不确定情况下的决策产生深远影响。

This research addresses stochastic optimization problems that are further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multistage setting. To cope with the computational complexity of multistage stochastic integer optimization problems, this research will develop new methodology, algorithms, and prototype software. Fundamental properties of the value function of integer programs will be exploited in conjunction with inherent decomposability of these optimization problems in order to develop algorithms that scale well with problem size. A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. Stochastic optimization is the branch of applied mathematics that provides systematic tools to prudent decision-making under uncertainty. A key difficulty in stochastic optimization is in dealing with an uncertainty space that is huge and which leads to very large-scale optimization models. The developed algorithms will be implemented in the investigator's widely distributed global optimization package BARON and made available to the research community. If successful, this project could have profound implications in decision-making under uncertainty in many sectors of the economy.