区间参数型不确定优化问题的进化算法研究

项目名称： 区间参数型不确定优化问题的进化算法研究

项目编号： No.61463045

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 李和成

作者单位： 青海师范大学

项目金额： 42万元

中文摘要： 不确定性广泛存在于信息科学、计算机科学、运筹学和工程管理领域. 不确定参数的出现产生了大量的不确定优化问题，主要有随机规划、模糊规划和区间规划. 对这些不确定问题，传统方法往往很难求解. 在这三类问题中，随机规划和模糊规划分别需要概率分布和模糊隶属度函数，而区间规划利用区间描述变量的不确定性，只需要少量信息即可获得参数的上下界，因此在不确定性建模方面体现了很好的方便性和经济性. .本项目主要研究区间参数型不确定优化问题的进化算法，主要包括具有区间参数的单目标优化问题、带区间参数的双层规划和带区间参数的多目标优化问题. 通过充分考虑问题的结构特点和最优性特征，设计求解对应问题的进化算法并分析收敛性. 项目的研究成果将有效弥补不确定性优化方法的理论成果，并能有效解决涉及不确定性参数的工程优化问题.

中文关键词： 区间参数优化问题；进化算法；双层规划；多目标优化；最优解

英文摘要： Uncertainty widely exists in information science, computer science, operational research and engineering management, etc. Lots of uncertain optimization problems are generated when uncertain parameters are involved, such as stochastic programming, fuzzy programming as well as interval programming. Traditional approaches always show poor performance in dealing with these uncertain problems. In three classes of problems, both stochastic programming and fuzzy programming need probability distributions and fuzzy membership functions, respectively, whereas interval programming use intervals to describe the uncertainty of variables, which only requires a small amount of information for obtaining the lower and upper bounds of parameters. Hence, interval programming is conveninent and economical in dealing with uncertain problems. The project is focused on evolutionary algorithms for solving uncertain optimization problems with interval parameters, including single-objective optimization problems with interval parameters, bilevel programming problems with interval parameters and multi-objective optimization involving interval parameters. Making full use of problem-specific features and optimality conditions, we develop evolutionary algorithms for each class of problems and analyze the convergence of algorithms. The research will enrich the theoretical results of uncertain optimization and can promote practical engineering problem with uncertainty to be solved.

英文关键词： Optimization problems with interval parameters;Evolutionary algorithm;Bilevel programming;Multi-objective optimization;Optimal solutions