多目标线性规划的一种几何模型求解法

The Geometry Model Method(GMM) for Multi-objective Linear Programme Problcms

本文提出多目标线性规划求解的一种新方法:几何模型求解法(简称GMM)。GMM以参考文献[2]的研究为基础,在求出全部可行域顶点一次得到多目标函数值后,建立决策空间的几何模型,决策者用此模型进行决策分析,找到决策空间中使所有目标函数值都达到令决策者满意的某一点。GMM法与参考文献[3]提出的ISTM法相比,具有更直观、更明确的优点。GMM法计算量少、按参考文献[1]的数学模型在计算机上实现速度快,利于求解大规模多目标线性规划问题。

This paper develops a new method for solving multi-objective linear programme problems,called Germetry Model Method(GMM).Based on the research of Reference[2],a geometrymodel,in decision space,is developed after all the vertexes in a feasible region and the values ofa multi-objective function arc found.The model is used to carry out a decision analysis and tosearch for a point at that the ralue of the multi-objective function is rest satisfied.This method is more andio-visual and more explicit than ISTM method described inReference[3].It has less amount of calculation and a high speed of computation,which is help-ful to solve the large scale multi-objective linear programme problems.