Decomposition Approaches To Mixed Integer Dynamic Optimization

摘要-巴顿-9703623这项研究将探索一种严谨而实用的方法来优化具有整数决策变量的非线性动态系统，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，并且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过程，以及在安全和操作限制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要问题。原始问题是这样一个问题，其中二元决策变量是固定的，以产生一个经典的变分问题。这个原问题是高度非凸的，很难求解到保证的全局最优性。为了解决这个问题，PI计划使用基于筛选模型的解决方案的主问题：手头问题的简化模型，通过不相关的建模工作得出，它为整个问题的解决方案提供了严格的下限。基于这两个子问题的分解迭代将被用来探索离散决策空间，并在终止时产生关于到全局解的距离的信息。

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.