CAREER: Advanced Mixed Integer Programming Formulations

职业：高级混合整数规划公式

• 批准号: 1351619
• 负责人: Juan Pablo Vielma
• 金额: $ 40万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-02-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1351619&HistoricalAwards=false
• 关键词: CAREER; Advanced; Mixed; Integer; Programming

The research objective of this Faculty Early Career Development (CAREER) Program award is to improve the effectiveness of Mixed Integer Programming (MIP) by developing and using a new paradigm for constructing linear and nonlinear MIP formulations. Such formulations are used to describe the selection among a finite number of alternatives in optimization models and their attributes can significantly affect the performance of the software employed to solve these models. Unfortunately, there is often a strong trade-off between favorable formulation attributes. The research in this award will result on methods to systematically reduce these trade-offs. The approach to develop these methods will include a mathematical analysis of the proposed paradigm, the design of algorithms to construct the associated MIP formulations and extensive computational experiments to evaluate their effectiveness. The deliverables of this work include new mathematical techniques for constructing and analyzing MIP formulations, algorithms and software for using and evaluating advanced MIP formulations, and educational material for engineering students and practitioners. If successful, the results of this research will provide tools to improve the effectiveness of optimization software for a wide range of MIP applications in business, science and engineering. Recent examples of such applications include efficient energy production and dispatch, clinical trial design and analysis, and trajectory optimization of unmanned aerial vehicles. Results from this research will be disseminated through various channels to allow their integration into commercial optimization software. In addition, all developed techniques will be implemented in open-source software tools available through a variety of modeling languages. The educational material developed in this award will help students at all levels develop crucial mathematical modeling skills. Graduate and undergraduate students will further benefit from this award through lectures and research experience.

本学院早期职业发展（Career）计划奖的研究目标是通过开发和使用构建线性和非线性混合整数规划（MIP）公式的新范式来提高混合整数规划（MIP）的有效性。这些公式用于描述在有限数量的优化模型备选方案中进行选择，它们的属性会显著影响用于求解这些模型的软件的性能。不幸的是，在有利的配方属性之间往往存在着强烈的权衡。本奖项的研究结果将是系统地减少这些权衡的方法。开发这些方法的方法将包括对所提出的范式的数学分析，构建相关MIP公式的算法设计以及评估其有效性的广泛计算实验。这项工作的可交付成果包括用于构建和分析MIP公式的新数学技术，用于使用和评估先进MIP公式的算法和软件，以及用于工程学生和从业人员的教育材料。如果成功，本研究的结果将为提高优化软件在商业、科学和工程领域的广泛应用的有效性提供工具。最近此类应用的例子包括高效能源生产和调度，临床试验设计和分析，以及无人驾驶飞行器的轨迹优化。这项研究的结果将通过各种渠道传播，以便将其集成到商业优化软件中。此外，所有开发的技术都将通过各种建模语言在开源软件工具中实现。该奖项开发的教育材料将帮助各级学生发展关键的数学建模技能。研究生和本科生将通过讲座和研究经验进一步受益于该奖项。