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Research Initiation: Investigations in Nonlinear-Objective Combinatorial Optimization

研究启动：非线性目标组合优化研究

基本信息

批准号：
9401424
负责人：
Jonathan Lee
金额：
$ 9.27万
依托单位：
University of Kentucky Research Foundation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1994
资助国家：
美国
起止时间：
1994-09-15 至 1998-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401424&HistoricalAwards=false
关键词：
Research Initiation Investigations Nonlinear Objective

项目摘要

9401424 Lee The research is concerned with the modeling and investigation of solution techniques for nonlinear-objective combinatorial optimization problems. Three basic solution techniques are to be investigated. These techniques are (1) a combination of linearization and polyhedral methods, (2) combination of eigenvalue bounding methods with polyhedral and Lagrangian methods, and (3) model assessment through geometric methods. Three classes of problems are identified as sources of problems to be used in testing the models and their solution methods. The application areas for which the algorithms will be tested are network design problems with inter-link costs, fixed charge facility location problems, and experimental design problems. The outcome of this research are the development of (1) more general methods for tightening integer programming formulations of difficult discrete planning problems with nonlinear objective function, (2) techniques for integrating algebraic bounding methods for planning problems with nonlinear objective functions, and (3) general principles for the design of branch-and-cut procedures for integer programming based approaches for discrete planning problems with both linear and nonlinear objective function. Other outcomes of the research will be the development of understanding similar to those of planning problems in network design and experimental design problems.

9401424李本研究致力于非线性-目标组合优化问题的建模和求解技术的研究。将研究三种基本的解决方法。这些技术是(1)线性化和多面体方法相结合，(2)特征值定界法与多面体和拉格朗日方法相结合，以及(3)通过几何方法进行模型评估。三类问题被确定为要用于测试模型及其解决方法的问题的来源。算法将被测试的应用领域是具有互联链路成本的网络设计问题、固定收费设施选址问题和实验设计问题。这项研究的结果是发展了(1)更一般的方法，用于紧凑具有非线性目标函数的复杂离散规划问题的整数规划公式，(2)集成具有非线性目标函数的规划问题的代数定界方法，以及(3)基于整数规划的分枝割程序设计的一般原则，用于具有线性和非线性目标函数的离散规划问题的方法。研究的其他结果将是对网络设计中的规划问题和实验设计问题的理解的发展。