Mathematical Sciences: Theoretical and Algorithmic Studies in Combinatorial Problem-Solving

数学科学：组合问题解决的理论和算法研究

• 批准号: 8508955
• 负责人: Manfred Padberg
• 金额: $ 9.46万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1985
• 资助国家: 美国
• 起止时间: 1985-07-01 至 1988-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8508955&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theoretical; Algorithmic; Studies

Mathematical programming is concerned with the optimization of functions in many variables subject to side constraints. Combinatorial optimization addresses the same problem with an additional complication brought about by the inclusion of indivisible activities, i.e., by variables that must assume integer values. In purely combinatorial problems, all variables must be integer. Since its inception shortly after World War II, mathematical programming ideas have been successfully utilized to formulate and to solve many complex planning problems, with applications covering the entire range from the quantitative social sciences to engineering science. The increased ability to numerically solve mathematical programming problems has brought about a greater demand to incorporate indivisible activities into the planning models. This research aims to extend the computational frontiers of combinatorial problem-solving as well as to achieve a better mathematical understanding of combinatorial optimization problems.

数学规划涉及受侧面约束的许多变量的函数优化。 组合优化解决了同样的问题，但由于包含不可分割的活动（即必须采用整数值的变量）而带来了额外的复杂性。 在纯组合问题中，所有变量都必须是整数。 自二战后不久诞生以来，数学规划思想已被成功地用来制定和解决许多复杂的规划问题，其应用涵盖了从定量社会科学到工程科学的整个范围。 数值解决数学规划问题的能力的增强带来了将不可分割的活动纳入规划模型的更大需求。 这项研究旨在扩展组合问题解决的计算前沿，并更好地数学理解组合优化问题。