CAREER: Improving the Optimization and Re-Optimization of Mixed Integer Programs through the Study of Continuous Variables

本学院早期职业发展（CAREER）研究提出通过研究连续变量的特殊性质，开发混合integerprograms的优化和e-优化的新方法。前提是连续变量是混合整数规划求解中的一个重要困难来源，而这一点往往被忽视。更好地了解它们的特殊性将产生优化混合整数规划的改进方法。所提出的方法包括在发展的一般理论的连续变量的提升。这个理论将被应用于增强各种标准的分支和切割功能（基于线性规划的启发式，切割平面）和不太传统的方法（原始算法）。它也将被应用到混合整数规划的计算效率的e-优化技术的设计。并通过实际问题的计算实验验证了本文方法的有效性。如果成功，该项目将导致当前混合整数编程技术的能力和性能的改进。它将产生通用软件，能够更有效地解决耗时的问题，并能够解决棘手的问题。这些改善的受益者几乎遍布所有经济部门，包括金融、林业和制造业。它将产生具有内置功能的软件，以执行基于最佳解决方案的有效分析。这些改进的功能是必不可少的，在一个环境中，决策问题被认为是更加全球化和不确定性是无所不在的。通过它的教育部分，这个研究项目将提供一个参考访问从业者如何，当通用软件失败，以解决最先进的混合整数编程技术的问题。

This Faculty Early Career Development (CAREER) research proposes to develop new methodologies for the optimization and e-optimization of mixed integerprograms through the study of the particular nature of continuous variables. The premise is that continuous variables are an important source of difficulty in the solution of mixed integer programs that is often ignored. A better understanding of their specificity will yield improved methods for the optimization of mixed integer programs. The approach proposed consists in the development of a general theory for the lifting of continuous variables. This theory will be applied to enhance various standard branch-and-cut features (linear programming-based heuristic, cutting planes) and less traditional methods (primal algorithms). It will also be applied to the design of computationally efficient e-optimization techniques for mixed integer programs. Computational experiments will be carried out to validate the approaches on practical problems. If successful, this project will result in the improvement of the capabilities and performance of the current mixed integer programming technologies. It will yield general-purpose software capable of solving time-consuming problems more efficiently and capable of solving intractable problems. The benefactors of these improvements are in virtually all sectors of the economy including finance, forestry, and manufacturing. It will yield software with built-in capabilities to perform efficient scenario-based analysis of optimal solutions. These improved features are essential in an environment where decision problems are considered more globally and where uncertainty is omni-present. Through its educational component, this research project will provide a reference accessible to practitioners about how, when general-purpose software fails, to solve problems with the most advanced mixed integer programming technologies.