Decomposition Approaches To Mixed Integer Dynamic Optimization

混合整数动态优化的分解方法

• 批准号: 9703623
• 负责人: Paul Barton
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703623&HistoricalAwards=false
• 关键词: Decomposition; Approaches; Mixed; Integer; Dynamic

Abstract - Barton - 9703623 This research will investigate a rigorous and practical approach to the optimization of nonlinear dynamic systems coupled with integer decisions variables, termed mixed integer dynamic optimization problems. An iteration strategy will be developed and tested that has the potential to avoid total enumeration of the discrete decision space, and on termination yields information on the distance to the global solution. The work is motivated by the need to achieve better solutions to two important problems in the chemical industries: the development of an optimal batch process for a new product, and the synthesis of cost effective operating procedures (for example, start-up and shut-down) subject to safety and operational constraints. The approach will involve decomposition to a primal and a master problem. The primal problem is one in which the binary decision variables are fixed to yield a classical variational problem. This primal is highly nonconvex and will be difficult to solve to guaranteed global optimality. To take care of that problem, the PI plans to use a master problem based on the solution to a screening model: a simplified model of the problem at hand, derived via an unrelated modeling effort, that provides a rigorous lower bound on the solution to the overall problem. A decomposition iteration based on these two subproblems will be used to explore the discrete decision space, and on termination, yield information on the distance to the global solution.

摘要-巴顿- 9703623 本研究将探讨一个严格而实用的方法来优化非线性动态系统与整数决策变量，称为混合整数动态优化问题。 将开发和测试一种迭代策略，该策略有可能避免离散决策空间的全部枚举，并在终止时产生关于到全局解的距离的信息。 这项工作的动机是需要更好地解决化学工业中的两个重要问题：为新产品开发最佳批处理工艺，以及在安全和操作约束条件下合成具有成本效益的操作程序（例如，启动和关闭）。 该方法将涉及分解为一个原始问题和一个主问题。 原始问题是一个二元决策变量是固定的，产生一个经典的变分问题。 这个原始是高度非凸的，并且很难保证全局最优性。 为了解决这个问题，PI计划使用基于筛选模型解决方案的主问题：手头问题的简化模型，通过不相关的建模工作导出，为整体问题的解决方案提供严格的下限。 基于这两个子问题的分解迭代将用于探索离散决策空间，并在终止时，产生关于到全局解的距离的信息。