基于单源多段图方法的多目标决策算法与应用

A Multiple Objective Decision Making Arithmetic and Application Based on Single Source Multiple Chart Method

单源多段图方法是解决系统规划中单目标决策问题的有效方法,但在大量的工程应用中所要解决的往往是多目标决策问题,其数学模型较为复杂,设计算法也比较困难,是研究的难点热点之一。文中提出一种基于单源多段图方法的多目标决策算法。主要做法是:将m个目标,分别用单源多段图方法求其最小(大)代价,而后,将多目标因素化成无量纲数,再将各种目标因素所占的权重μ1,μ2,…μm,进行分配,最后再求其最小,从而得到结果。也就是mincost=min(μ1c1+μ2c2+…+μmcm),其中ci代表第i个目标因素的最小代价。还设计了相应的算法,并求其复杂度T(n)=O(cmn),其中m为目标数,n为多段图节点的个数,c是计算多段图中任意节点到终点的计算量。文中给出了计算实例。经我单位在运输实际的规划计算中应用证明,比经验算法可节省代价21.3%。

The method of single source multiple chart is an effective way to solve single objective decision making problems, but the real problems we often meet in project application are multiple objective decision making, the mathematic model of which are complex, and it is difficult to design algorithm and it is also one of hot topic researched. Provides a multiple objective decision making algorithm based on single source multiple chart method. The main steps are as follows： at first use single source multiple chart method to figure out the minimal or maximal value cost of m objectives respectively, and then, transform the multiple objectives factors to infinitude data, and assign weights belonging to every objective factors, at last,calculate the minimal cost to obtain the result. That is, mincost= min（ μ1 c1 ＋ μ2 c2 ＋ … ＋μmcm）, in which, ci stands for the lowest cost of objective factor i .The paper also provides relevant algorithm,and calculate its complexity,which is T（ n ） = O（cmn ）, inwhich, m stands for the numher of objectives, n stands for the amount of multiple chart nodes, c stands for calculational amount of counting from random node to end point. An example which demonstrates how to use this method is presented. This method can save 21.3 percent cost comparing with experience method, which proved in the application of solving the transport cost in my company.