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对于不成对机车周转图，多基于固定的机车运转区段且为单机牵引进行研究，传统机车周转图的勾划方法难以适应非固定区段机车周转图编制的需求.机车的非固定区段运用有利于缩短机车周转时间，优化机车周转方案，对提高机车运用效率意义重大.本文在充分考虑部分双机牵引不成对机车周转图中可能出现的情况:到达单机牵引列车数与出发单机牵引列车数不同,到达双机牵引列车数与出发双机牵引列车数不同.综合分析铁路运输运营效益、列车运行图均衡性等具体要求，以机车在站停留时间、机车周转图均衡性、机车周转距离、机车运用数量等4个目标函数为求解目标的基础上，建立了机车周转图的01多目标规划模型，并给出求解的方法.最后以西宁西—西宁货区段进行实例验证，得出了对应的最少机车总消耗时间，最优附挂方案和机车周转图.

Dual Traction Locomotive Turnaround Optimization Model Based on Non-Fixed Sections

Regarding the unpaired locomotive turnaround diagram,previous studies usually focused on fixed sections and single traction.The traditional method for locomotive turnaround diagram determination failed to meet the demand of non-fixed sections.Reasonable utilization of the locomotive in non-fixed sections usually reduces the locomotive turnaround time,optimizes the locomotive turnaround plan and thus improves the locomotive efficiency.This paper takes full consideration of two possible situations in dual traction unpaired locomotive turnaround diagram: the number of arrival single traction train does not equal the number of departure single traction train;the number of arrival dual traction train does not equal the number of departure dual traction train.By comprehensively analyzing the benefits of rail transport operation and the balance of train diagram,four objective functions are formulated: locomotive dwell time in station;the balance of locomotive turnaround diagram;locomotive turnaround distance,and locomotive number.Then,the 0-1 multi-objective planning model of locomotive turnaround diagram is developed and a corresponding algorithm is proposed.In the last section,the Xining East station-Xining cargo section is taken as an example.Several key results are obtained: the least corresponding locomotive elapsed time,optimal attached solution and locomotive turnaround diagram.