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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.

小行星9401424 本研究系针对非线性目标组合最佳化问题之建模与求解技术之研究。要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的组合，（2）特征值边界方法与多面体和拉格朗日方法的组合，以及（3）通过几何方法的模型评估。三类问题被确定为用于测试模型及其解决方法的问题源。该算法将被测试的应用领域是网络设计问题与互连成本，固定收费设施的位置问题，和实验设计问题。本研究的成果是：（1）开发了更一般的方法，用于收紧具有非线性目标函数的困难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的技术，（3）线性和非线性目标函数离散规划问题的基于整数规划的分支切割方法设计的一般原则。研究的其他成果将是类似于网络设计中的规划问题和实验设计问题的理解的发展。