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）研究建议通过研究连续变量的特殊性质来开发混合积分方案的优化和e-优化的新方法。前提是连续变量是求解混合整数规划时经常被忽略的一个重要困难来源。更好地理解它们的特殊性将为混合整数规划的优化提供改进的方法。所提出的方法包括对连续变量提升的一般理论的发展。该理论将应用于增强各种标准的分支和切割特征（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）。它还将应用于混合整数程序的计算效率e-优化技术的设计。计算实验将在实际问题上验证这些方法。如果成功，该项目将导致当前混合整数规划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及经济的所有部门，包括金融、林业和制造业。它将产生具有内置功能的软件，以执行有效的基于场景的最佳解决方案分析。这些改进的特性在一个更全局地考虑决策问题和不确定性无处不在的环境中是必不可少的。通过它的教育成分，这个研究项目将为实践者提供一个可访问的参考，当通用软件失败时，如何用最先进的混合整数编程技术解决问题。

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.