Research In Mixed-Integer Programming

研究将集中在理论和技术需要开发一个鲁棒和有效的算法为一般混合整数规划问题。将研究的主题包括有效的公式、预处理、分解、逻辑测试、线性规划、约束生成、分支和并行处理。该项目还将涉及开发模块化实验代码，以测试和评估基础研究产生的想法和方法。由于各种各样的实际问题都可以用这种方法来表述，因此对一种高效、鲁棒的混合整数规划算法有着巨大的需求。但是，许多更大、更困难的问题无法通过现有的方法在合理的时间内解决到（接近）最优。这些大型混合整数模型中的一些来自物流和制造业领域的优化问题。因此，发展有效的方法将对改进生产和分配过程的规划和操作产生重大影响。

The research will focus on the theory and techniques needed to develop a robust and efficient algorithm for the general mixed integer programming problem. Topics that will be studied include efficient formulation, preprocessing, decomposition, logical testing, linear programming, constraint generation, branching and parallel processing. The project will also involve the development of a modular experimental code to test and evaluate the ideas and methodology that result from the basic research. There is tremendous demand for an efficient and robust mixed integer programming algorithm because a great variety of practical problems can be formulated in this way. But many of the larger and more difficult ones cannot be solved to (near) optimality in a reasonable amount of time by the existing methodology. Some of these large mixed integer models arise from optimization problems in the areas of logistics and manufacturing. Thus, the development of efficient methods would have a significant impact on improving the planning and operation of production and distribution processes.