Research on Value of Information to Combinatorial Optimization

信息对组合优化的价值研究

基本信息

批准号：
10680428
负责人：
ISHII Hiroaki
金额：
$ 1.86万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680428/
关键词：
Fuzzy random variable Variational inequality problem Mollifier Fuzzy duedate Fuzzy processing time Fuzzy random facility location problem Fuzzy random knapsack problem Fuzzy random spanning problem ファジィ関数ファジィ微分配置問題スケジューリング情報の価値

项目摘要

This research is to investigate value of information to combinatorial optimization. The aim of this research is to clarify the effects of random and fuzzy factors in the combinatorial optimization models. Especially the solutions are changed according to the existence of uncertainty and/or ambiguity. First we considered linear programming problems under both random and fuzzy factors. Based on the results on so called these fuzzy random linear programming problems, we considered scheduling problems with fuzzy data and fuzzy constraint, spanning tree problems with fuzzy random edge costs, knapsack problem with fuzzy and random coefficients and facility location problem with fuzzy distance and fuzzy goal. In order to find the difference between the solution of ordinary problem and that of fuzzy random version, we introduced fuzzy random variables to above problems of combinatorial optimization and proposed efficient algorithms for solving their deterministic equivalent problems. We obtained some results on solutions of these problems. Further we investigated also basic mathematical analysis of value of information by considering functional analysis, especially variational inequality and introduced a new concept of fuzzy derivatives to apply optimization under ambiguity.

本研究旨在调查信息对组合优化的价值。本研究的目的是阐明组合优化模型中随机和模糊因素的影响。特别是，解决方案根据不确定性和/或模糊性的存在而改变。首先，我们考虑随机因素和模糊因素下的线性规划问题。基于这些模糊随机线性规划问题的结果，我们考虑了具有模糊数据和模糊约束的调度问题、具有模糊随机边成本的生成树问题、具有模糊和随机系数的背包问题以及具有模糊距离和模糊的设施选址问题。目标。为了找到普通问题的解决方案与模糊随机版本的解决方案之间的差异，我们将模糊随机变量引入到上述组合优化问题中，并提出了解决其确定性等价问题的有效算法。我们在解决这些问题方面取得了一些成果。此外，我们还通过考虑泛函分析，特别是变分不等式，研究了信息价值的基本数学分析，并引入了模糊导数的新概念，以在模糊性下应用优化。