区间数线性规划及其区间解的研究  

Study on Interval-parameter Linear Programming and Its Interval Solutions

作　　者：牛彦涛[1] 黄国和[1] 张晓萱[1] 杨勇平[2] 

机构地区：[1]华北电力大学能源与环境研究中心,北京102206 [2]华北电力大学能源与动力工程学院,北京102206

出　　处：《运筹与管理》2010年第3期23-29,共7页Operations Research and Management Science

基　　金：国家重点基础研究发展计划(973)项目资助(2005CB724201)

摘　　要：区间数线性规划可用于处理含有离散区间数的不确定性优化问题。针对已有算法所求区间解可能包含非可行解的缺陷,基于可能度概念提出了区间数线性规划的有效解、弱有效解、最优解及其解域的定义,给出了改进解法,所得区间解为以上解域的子集。以一个数值模型为例求解,将运算结果与已有算法所得区间解作了对比,说明了改进解法的有效性。An interval-parameter linear programming method is useful for reflecting uncertainty in discrete intervals,however,unfeasible zones for generating interval solutions could exist based on the existing algorithms.In this study,innovative algorithms are proposed.Several concepts of effective solution,soft effective solution,and optimal solution as well as their sets are proposed for tackling such an issue,based on the concept of possibility degree for the comparison between two interval numbers.And the resulting interval solutions are subsets of solution sets above.A numerical example is given and the solutions are compared with those of existing algorithms,which verify new algorithms.

关 键 词：区间数线性规划 可能度 区间解 有效解 弱有效解 

分 类 号：O221.1[理学—运筹学与控制论]