Polyhedral Combinatorics and Algorithms for Stochastic Integer Programming

随机整数规划的多面体组合和算法

• 批准号: 0942154
• 负责人: Yongpei Guan
• 金额: $ 12.45万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-05-16 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0942154&HistoricalAwards=false
• 关键词: Polyhedral; Combinatorics; Algorithms; Stochastic; Integer

This grant provides funding to study polyhedral combinatorics and algorithms for stochastic integer programming (IP). During the last decade, stochastic IP has received broad attention in the literature as an efficient tool for modeling and solving real-time decision making problems with the consideration of uncertain events. Meanwhile, stochastic IP incorporates both the complexity of integer programming and stochastic linear programming, which makes it challenging to solve large-scale problems. This research focuses on studying fundamental structures of general stochastic IP and developing fast algorithms for the solution of large-scale problems. The research work consists of 1) studying strong valid inequalities and developing efficient branch-and-cut algorithms for stochastic lot-sizing problems, 2) exploring polyhedral combinatorics for general stochastic IP, and 3) identifying properties that would lead to fast polynomial time and approximation algorithms for several special classes of stochastic IP problems. Significant efforts will also be spent developing teaching modules for integer programming and stochastic optimization. Undergraduate and graduate students, emphasizing underrepresented groups, will participate in the project.If successful, the results of this research will lead to scientific methodology innovations for stochastic IP. Polyhedral studies will contribute to the development of improved commercial software for a wide range of stochastic IP problems. The results may also be combined with decomposition algorithms and optimization-based heuristics to improve modeling and computational capabilities on large-scale practical problems. Examples include production planning, manufacturing repair overhaul workforce scheduling, and facility location problems. The research outcomes will finally provide content and methodologies that can be incorporated into graduate level courses and can serve as the bases for development of new courses.

这笔资金用于研究多面体组合学和随机整数规划(IP)算法。在过去的十年里，随机IP作为一种考虑不确定事件的实时决策问题的建模和求解的有效工具，受到了文献的广泛关注。同时，随机IP融合了整数规划和随机线性规划的复杂性，给大规模问题的求解带来了挑战。本研究致力于研究一般随机IP的基本结构，并开发解决大规模问题的快速算法。研究工作包括：1)研究强有效的不等式，提出求解随机批量问题的有效分枝割算法；2)研究一般随机IP问题的多面体组合问题；3)确定几类特殊类型的随机IP问题的多项式时间和逼近算法的性质。还将花费大量精力开发整数规划和随机优化的教学模块。本科生和研究生将参与该项目。如果成功，这项研究结果将导致随机知识产权的科学方法论创新。多面体研究将有助于为广泛的随机IP问题开发改进的商业软件。结果还可以与分解算法和基于优化的启发式算法相结合，以提高对大规模实际问题的建模和计算能力。例如，生产计划、制造维修大修、劳动力调度和设施选址问题。研究成果最终将提供可纳入研究生课程的内容和方法，并可作为开发新课程的基础。