中文摘要：

针对采用机车肩回交路的重载铁路线路，将其列车运行图中的列车运行线转化为节点，机车周转线转化为边，运用机车转化为流，从而将机车周转图的优化问题转化为网络流问题。在此基础上，以运用机车数最少、单机走行数最少、附挂机车数最少、机车在站停留时间最短和机车工作均衡性最好为优化目标，以网络流问题中的节点流量守恒和节点流量要满足节点需求为约束条件，建立肩回交路条件下的多机牵引机车周转图多目标优化模型。按照优化目标函数的优先级，采用分层序列法对模型求解，并利用C#语言编写程序，通过调用ILOGCPLEX优化软件实现了该算法。算例表明，采用所给模型和据此编制的机车周转图优化程序，可以快速优化肩回交路条件下的多机牵引机车周转图。

英文摘要：

For heavy haul railway with locomotive arm routing, the train path in train diagram is converted to a node, locomotive turnaround line to an arc and the locomotive to the flow. So the problem of optimi- zing locomotive working diagram can be transformed into the problem of network flow. On this basis, the multi-objective optimization model for locomotive working diagram under the conditions of locomotive arm routing and multi locomotive traction is built, which aims the minimum numbers of locomotives in opera- tion, the minimum number of deadheading locomotives, the minimum number of dead hauling locomotives, the minimum detention time of locomotives at station and the best equilibrium characteristics of locomotive operation. The constrained condition is that the node flow conservation and node flow should meet the node demand in network flow problem. Following the priority level of optimization object functions, the lexicographic method is employed to find the optimal solution. C~ language is used to compile program, this algorithm is realized by calling the optimization software ILOG CPLEX. Numerical example shows that the proposed model and program can fast arm routing and multi locomotive traction. optimize the locomotive working diagram with locomotive