A Reformulation-Linearization Technique with Application to Production, Location, Distribution, and Design Problems

该项目涉及一个新的设计 再公式化-线性化技术（RLT）及其发展 它适用于各种类别的问题， 生产，位置分配，经济学和各种工程 以及系统设计和操作环境。 这件事的核心 方法是根据以前的国家 科学基金会的项目，以产生紧密的，更高的 一维线性规划表示， 多项式零一混合整数规划问题 基本 RLT程序具有相当程度的灵活性， 被用来开发有效的算法变体。 各种 转型和实施方案将在 为了提高解决离散和 连续非凸决策问题 RLT的效用 方案在生成方面和严格有效的不等式 重要的离散类问题也将探讨。 这 将有益于其他算法的混合整数0 - 1问题。 开发的方法将专门用于解决 不定凹二次规划，线性互补 问题、位置分配问题和固定费用问题 在不同的上述应用中出现。

This project is concerned with the design of a new Reformulation-Linearization Technique (RLT) and the development of its application to various classes of problems arising in production, location-allocation, economics, and various engineering and systems design and operational contexts. At the heart of this methodology is a procedure developed under a previous National Science Foundation project for generating tight, higher dimensional, linear programming representations for linear and polynomial zero-one mixed-integer programming problems. The basic RLT procedure possesses a considerable degree flexibility that can be exploited to develop effective algorithmic variants. Various transformations and implementation schemes will be investigated in order to enhance the capability in solving both discrete and continuous nonconvex decision problems. The utility of the RLT scheme in generating facets and tight valid inequalities for important discrete classes of problems will also be explored. This will benefit other algorithms for mixed-integer zero-one problems. The methodology developed will be specialized to solve indefinite and concave quadratic programs, linear complementarily problems, location-allocation problems, and fixed-charge problems that arise in the different aforementioned applications.