Abstract: Vehicles starting from many starting points，passing through certain transportation network to arrive at other many destinations，searching for an optimum transportation plan is a basic network optimization question.The conventional linear programming methods only consider of the supply restraint and the demand restraint，don’t consider restraints of crossroad capacity and road section capacity，don’t get the optimal solutions based on the route，and don’t adapt to the actual project request.This article gives network optimization model based on routes.Moreover，ordinary methods is complex to use for searching routes of directed loop transport network，and is not easy to understand.This article gives a searching-routes method based on relational matrices of directed loop transport network，establishs the network optimization model considering supply restraints，demand restraints，crossroad and road section capacity restraints.It is easy to program and understand for engineers and technicians.The model and the method are suitable for certain large-scale construction item.

Key words: relational matrix, transport network, network optimization, directed loop

摘要： 从多个出发点出发，经过一定的交通运输网络到达另外多个到达地点，寻求最优运输方案是网络优化的一个基本问题。常规的线性规划方法只考虑供应约束与需求约束，没有考虑交叉路口通行能力、路段通行能力等约束，没有按照路线求最优解，已不适应实际工程要求。给出按照路线寻求最优运输分配方案的网络优化模型。另外，对于稍微复杂一些的有向有环运输网络，通常路线搜索方法比较复杂且不易理解。给出了基于关系矩阵搜索有向有环网络有效路线的方法，建立了具有供应约束、路口和路段通行能力约束、需求约束的相应模型。易于编程且具有便于一般工程技术人员容易理解的优点。该模型与算法适合于某些工程量巨大的大型施工项目。

关键词: 关系矩阵, 运输网络, 网络优化, 有向有环