Cutting Planes for Mixed-Integer Programs

整数和混合整数程序出现在从物流到超大规模集成设计的大量应用中。最近的割平面技术在整数规划的求解中已被证明是非常成功的。不幸的是，割平面技术还没有以同样的频率或成功地应用于混合整数程序。这项研究的目标是发展这项技术的理论，因为它与混合整数规划有关，并实现为混合整数规划生成割平面的算法。最终，我们的目标是使用这些算法解决大型混合整数规划。混合整数规划的应用如此广泛，其解决方法的技术进步将产生跨越许多学科的深远影响。其他目标包括建立混合整数程序的公共域库，并向研究人员提供开发的算法。

Integer and mixed-integer programs arise in a wealth of applications ranging from logistics to very large scaled integration design. Recent cutting plane techniques have proven remarkably successful in the solution of integer programs. Unfortunately, cutting plane techniques have not been applied with the same frequency or success to mixed-integer programs. The goal of this research is to develop the theory surrounding this technique as it relates to mixed-integer programming and to implement algorithms that generate cutting planes for mixed-integer programs. Ultimately, the goal is to solve large mixed-integer programs using these algorithms. Applications of mixed-integer programming are so extensive that advances in techniques for their solution will have far reaching consequences extending across many disciplines. Additional objectives include establishing a public domain library of mixed-integer programs and providing developed algorithms to researchers.