铁路技术站作业计划优化编制的模型与算法研究
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摘要
技术站是铁路货物运输网络中的1类关键的节点,它的作业效率直接影响着整个铁路货物运输的可靠性和服务水平。技术站的日常运输工作由编制各种类型的作业计划来组织和调度,本文利用现代数学规划理论与方法探讨优化编制铁路技术站作业计划理论体系中的几个关键的科学问题,包括配流问题、进路调度问题和编组调车问题,主要的研究工作如下：
第2章探讨了配备有1台解体调机和1台编组调机的区段站的配流问题,该问题在于确定各列出发列车的编组内容及其车流来源,并调度各台解体和编组调机的任务,以使得各列出发列车满足满轴、正点和不违编的编组要求,且衡量配流效率的车辆在站总停留时间最小。本章首先借助于单机器调度问题的基于时刻索引变量的经典模型将该问题构建为1个囊括所有决策任务的混合整数线性规划模型,然后利用构建的模型的结构和探讨问题的特点提出了3个有效的求解算法,包括1个拉格朗日松弛算法、1个启发式算法和1个基于整数编码的遗传算法。以1个来源于实际的数值算例来测试了所提出方法的效果和效率,测试结果显示了所设计的求解方法都能快速地将实际问题求解到最优或近似最优,且它们的计算结果明显地优于由调度员在现场的实时决策环境中使用的基于先到先服务规则的经验方法找到的结果。
第3章探讨了分别为到达列车的解体作业和出发列车的编组作业配备多台解体调机和多台编组调机的单向编组站的配流问题,该问题研究的是确定各列出发列车的编组内容及其车流来源,指派并调度各台解体和编组调机的任务,以使得各列出发列车满足满轴、正点和不违编的要求,各台调机任务不冲突。利用并行机调度问题的基于时刻索引变量的模型来建模调机的指派和调度,本章首先构建了该问题的1个以车辆在站总停留时间最小为目标的混合整数线性规划模型,该模型使用1个连接约束将列车组成问题和解编排序问题纳入同一个优化体系,然后根据问题的结构和特点设计了1个精确算法和2个启发式算法,其中,精确算法为CPLEX精确求解所构建的优化模型的求解方法,启发式算法包括1个拉格朗日松弛算法和1个有偏随机键遗传算法。1个切实且大型的数值案例被用来测试了所提出的求解方法的效果和效率,测试结果显示了所提出的精确算法和有偏随机键遗传算法都能在限制的时间内获得实际问题的最优误差不高于1%的近似最优解,且由所提出的求解方法找到的解都不差于由现场的经验方法找到的解。
第4章探讨了具有两个改编系统且系统间存在车辆交换的双向编组站的配流问题,该问题在于确定各列出发列车和交换列车的编组内容及其车流来源,指派并调度各台解体和编组调机的任务,以使得各列出发列车符合开行规定,各列交换列车满足编组要求,且各台调机的任务不冲突。本章将该问题构建为1个以车辆在站总停留时间最小为目标且包含所有决策的混合整数线性规划模型,其中,有关调机运用的子问题采用并行机调度问题的基于时刻索引的经典模型进行建模。利用问题易被分解的特性,本章开发了2个有效的近似算法,包括1个使用所构建的优化模型的拉格朗日松弛算法和1个不使用所构建的优化模型的有偏随机键遗传算法。为了验证所提出方法对于实际问题的效果和效率,计算测试采用了1个切实且大型的数值案例。计算结果显示了所提出的有偏随机键遗传算法能够在不到100s内的时间内获得实际问题的接近最优的解,其最优误差接近1%,拉格朗日松弛算法也能在规定的计算时间末找到最优误差不高于3%的满意解,更为重要的是,它们的解明显地优于调度员采用的人工方法确定的解。
第5章探讨了具有多类型的作业且作业问存在复杂约束的技术站进路调度问题,该问题在于为各项行车和调车作业同时指派并调度进路,以使得所有作业在时间和空间上都无冲突,且定义的作业间的一致性约束能得到满足。本章引入车间调度问题中的工作和活动的概念来描述调度作业,并定义可囊括所有的路径选项和有限的时刻选项的进路模式的概念来表示决策变量,进而将原本包含多项决策任务的进路调度问题转换为1个只需指派提前生成的进路模式给活动的约束指派问题。本章将所定义的约束指派问题构建为1个最小化总晚点和走行时间,且满足唯一性约束、一致性约束和相容性约束的0-1线性规划模型,在建模时间-致性约束和道岔相容性约束时,基于图论的极大关联技术被用来代替传统的两两关联技术,以加强生成约束的定界质量。本章还讨论了如何拓展标准约束指派模型,以使得它能满足更多的运营要求,且从1个单一的路径模型转换为1个复合的路径和调度模型,对于标准模型的不可行问题,提出了1个迭代算法通过求解有限个辅助模型来构造可获得可行解的候选进路模式集。最后,1个真实案例的计算结果显示了相比于两两关联技术,极大关联技术可极大地减少生成的约束数,且所提出的标准模型使用的动态列车-站线-指派策略在求解质量上优于车站调度员的经验方法使用的静态列车-站线-指派策略。
第6章探讨了产生于技术站实时调度中的调车线受限的编组调车问题。给定待编车列和可使用调车线集合,该问题在于确定调车作业次数以及待编车列中的各个车辆在各次调车作业中的调动路径,以使得在不违背调车线的数量和能力约束的情况下,各列编成车列都能被实现为站顺的顺序,并需要最少的连挂钩数、调动车数、占用调车线数和溜放钩数。本章首先考虑了将1列待编车列编顺为1列编成车列的简单编组调车问题,开发了1类新的使用0-1矩阵编码编组调车方案的位串法,通过定义不同的调车线连挂原则,分别提出了1个连挂全部调车线的全线位串法和1个单独预留1条调车线给编成车列的留线位串法,1个包含迭代优化和局部搜索进程的两阶段迭代搜索算法被开发来实施这两个位串法,其中,第-阶段通过求解一系列的0-1线性规划模型来寻找需要的0-1矩阵,该矩阵再由第二阶段定义的搜索规则进行局部优化,最终获得的编组调车方案可按字典序优化拟定的连挂钩数、调动车数、占用调车线数和溜放钩数。本章还将拓展的全线和留线位串法运用于解决更具有挑战性的将多列待编车列同时组合为多列编成车列的批量编组调车问题。最后,切实的随机案例被用来体现了所提出的两个位串法都能有效地求解调车线受限的简单和批量编组调车问题,它们快速的计算时间准许将它们同时运用于解决大规模的问题实例。
Technical station is a critical node in the railroad freight transportation network, and its operation efficiency directly influences the robustness and service level of the total railroad freight transportation. Nowadays, the ordinary transportation work of technical station is organized and scheduled by various types of operation plans. This thesis focuses on several important theoretical problems including the railcar allocation problem, the route scheduling problem and the assembly shunting problems for optimally establishing the operation plan of railroad technical station, our main research works are as follows:
Chapter2investigates the railcar allocation problem at railroad district stations with single switch engine and single yard engine. The problem is to determine the composition of each outbound train, and schedule the task for each switch engine and yard engine, such that each outbound train satisfies the assembly requirements while the total dwell time of railcars staying at the station is minimized. We formulate the problem as a mixed integer linear programming model incorporating all decisions by utilizing the time-indexed conventional formulation for the single machine scheduling problems, and present three efficient solution approaches including a Lagrangian relaxation algorithm, a heuristic and an integer-based encoding genetic algorithm by exploiting the structure of the presented formulation and the characteristic of the problem. A numerical example coming from the practical situation is used to test the effectiveness and efficiency of the proposed approaches. Computational results show that our approaches can quickly solve the practical problem to optimality or approximate optimality, and their results are obviously better than that found by the first-come-first-served based empirical method adopted by the station dispatcher in the real-time decision environment.
Chapter3investigates the railcar allocation problem at railroad single-directional marshalling station with multiple switch engines and multiple yard engines. The problem lies on determining the composition of each outbound train, and assigning and scheduling the task of each switch engine and each yard engine, such that each outbound train satisfies the assembly rules and each engine is conflict-free. Utilizing the time-indexed based formulation of the parallel machine scheduling problems to model the assignment and schedule of engines, we firstly present the problem a mixed integer linear programming model to minimize the total dwell time of railcars staying at the station, which incorporates the train composition sub-problem and the engine scheduling sub-problem into the same optimization framework by using a linking constraints, and then design an exact algorithm and two heuristics according to the structure and characteristic of the problem, in which the exact algorithm is to use CPLEX to exactly solve the proposed optimization model, and the heuristics includes a Lagrangian relaxation algorithm and a biased random-key genetic algorithm. A realistic and large-scale numerical example is used to test the effectiveness and efficiency of the proposed approaches. Computational results show that our exact algorithm and biased random-key genetic algorithm can obtain approximately optimal solution with optimality gap less than1%for practical problems within the restricted computation time, and the solutions found by our approaches are not worse than that found by the empirical method used in practice.
Chapter4investigates the railcar allocation problem at railroad double-directional marshalling station with two operation systems and railcar transfer between systems. The problem consists of determining the composition of each outbound train and each transfer train, and assigning and scheduling the task of each switch engine and each yard engine, such that each outbound train meets the departure rules, each transfer train satisfies the assembly requirements, and each engine receives conflict-free tasks. We formulate the problem as a mixed integer linear programming model to minimize the total dwell time of railcars staying at the station with all decisions, in this model, the engine scheduling sub-problem is modeled by using the time-indexed classical formulation for the parallel machine scheduling problems. By utilizing the easy to be decomposed structure of the problem, we design two effective heuristics including a Lagrangian relaxation algorithm with using the proposed optimization model and a biased random-key genetic algorithm without using the proposed optimization model. To validate the effectiveness and efficiency of our proposed approaches for practical problems, computational test is conducted on a realistic and large-scale numerical example. Computational results show that our biased random-key genetic algorithm can obtain near-optimal solution with optimality gap approaching1%within the computation time less than100s, and our Lagrangian relaxation algorithm can find good solution with optimality gap not greater than3%at the end of the restricted time. More importantly, their solutions are obviously better than those determined by the manual method used by the station dispatcher.
Chapter5investigates the route scheduling problem with multiple types of operations and complicated constraints among operations at railroad technical station. This problem is to simultaneously assign and schedule route for each train and engine operation, such that all operations are conflict-free in time and space, and the defined consistency constraints are satisfied. We introduce the concept of task and activity in the job shop scheduling problem to describe the scheduling operations, and define the concept of route pattern which can incorporate all routing alternatives and partial timing alternatives to represent the decision variables, based on which we transform the original route scheduling problem with multiple decision tasks to a constrained assignment problem which only has to assign pre-computed route patterns to activities. We formulate the defined constrained assignment problem as a0-1linear programming model which minimizes the total delay and travel time and satisfies the uniqueness, consistency and compatible constraints. In modeling the time consistency and switch compatible constraints, graph based maximal correspondence technique is used to replace the traditional pair-wise correspondence technique to strength the bounding efficiency of the generated constraints. We also discuss how to extend the standard constrained assignment problem, so as to enable it to satisfy more operational requirements and transform from a single routing model to an integrated routing and scheduling model. For the infeasible issue of the standard problem, an iteration algorithm is proposed to generate candidate route patterns which can obtain feasible solutions by solving a sequence of auxiliary models. At last, computational results of a realistic example show that the maximal technique can significantly decrease the number of generated constraints compared with the pair-wise technique, and the dynamic train-to-track-assignment strategy used in our approach is better than the static train-to-track-assignment strategy used in dispatchers'empirical method in terms of solution quality.
Chapter6investigates the track capacitated train assembly shunting problem (TASP) in the real-time scheduling of railroad technical station. Given the inbound trains and shunting tracks, this problem lies on determining the number of shunting operations and the routes of each railcar of the inbound trains in each shunting operation, such that each outbound train can be realized in the correct station-based order without violating the tracks'number and capacity, while requiring minimal number of pulled-outs, shunted railcars, occupied tracks and rolled-ins. We first consider a simple TASP which assembles single inbound train into single outbound train. Using0-1matrixes to encode the assembly shunting plan, a novel bitstring method is developed for the problem. By defining different track pulled-out principles, we propose a total bitstring method and a partial bitstring method which pulls-out all tracks and especially reserves a track for the outbound train, respectively. A two-stage iteration search algorithm incorporating an iteration optimization procedure and a local search procedure is developed to implement these two methods. The first stage is to find the required0-1matrixes by solving a sequence of0-1linear programming model, which is further improved by several local rules defined in the second stage. The obtained plan can minimize the number of pulled-outs, shunted railcars, occupied tracks and rolled-ins in the lexicographical order. We also apply our extended total and partial bitstring methods to solve the more challenging batch TASP which has to simultaneously assembly multiple inbound trains into multiple outbound trains. At last, several realistic instances are used to show that our bitstring method can effectively solve the simple and batch TASP, and their fast computation time allows us to simultaneously apply them to tackle large-scale problem instances.
第2章探讨了配备有1台解体调机和1台编组调机的区段站的配流问题,该问题在于确定各列出发列车的编组内容及其车流来源,并调度各台解体和编组调机的任务,以使得各列出发列车满足满轴、正点和不违编的编组要求,且衡量配流效率的车辆在站总停留时间最小。本章首先借助于单机器调度问题的基于时刻索引变量的经典模型将该问题构建为1个囊括所有决策任务的混合整数线性规划模型,然后利用构建的模型的结构和探讨问题的特点提出了3个有效的求解算法,包括1个拉格朗日松弛算法、1个启发式算法和1个基于整数编码的遗传算法。以1个来源于实际的数值算例来测试了所提出方法的效果和效率,测试结果显示了所设计的求解方法都能快速地将实际问题求解到最优或近似最优,且它们的计算结果明显地优于由调度员在现场的实时决策环境中使用的基于先到先服务规则的经验方法找到的结果。
第3章探讨了分别为到达列车的解体作业和出发列车的编组作业配备多台解体调机和多台编组调机的单向编组站的配流问题,该问题研究的是确定各列出发列车的编组内容及其车流来源,指派并调度各台解体和编组调机的任务,以使得各列出发列车满足满轴、正点和不违编的要求,各台调机任务不冲突。利用并行机调度问题的基于时刻索引变量的模型来建模调机的指派和调度,本章首先构建了该问题的1个以车辆在站总停留时间最小为目标的混合整数线性规划模型,该模型使用1个连接约束将列车组成问题和解编排序问题纳入同一个优化体系,然后根据问题的结构和特点设计了1个精确算法和2个启发式算法,其中,精确算法为CPLEX精确求解所构建的优化模型的求解方法,启发式算法包括1个拉格朗日松弛算法和1个有偏随机键遗传算法。1个切实且大型的数值案例被用来测试了所提出的求解方法的效果和效率,测试结果显示了所提出的精确算法和有偏随机键遗传算法都能在限制的时间内获得实际问题的最优误差不高于1%的近似最优解,且由所提出的求解方法找到的解都不差于由现场的经验方法找到的解。
第4章探讨了具有两个改编系统且系统间存在车辆交换的双向编组站的配流问题,该问题在于确定各列出发列车和交换列车的编组内容及其车流来源,指派并调度各台解体和编组调机的任务,以使得各列出发列车符合开行规定,各列交换列车满足编组要求,且各台调机的任务不冲突。本章将该问题构建为1个以车辆在站总停留时间最小为目标且包含所有决策的混合整数线性规划模型,其中,有关调机运用的子问题采用并行机调度问题的基于时刻索引的经典模型进行建模。利用问题易被分解的特性,本章开发了2个有效的近似算法,包括1个使用所构建的优化模型的拉格朗日松弛算法和1个不使用所构建的优化模型的有偏随机键遗传算法。为了验证所提出方法对于实际问题的效果和效率,计算测试采用了1个切实且大型的数值案例。计算结果显示了所提出的有偏随机键遗传算法能够在不到100s内的时间内获得实际问题的接近最优的解,其最优误差接近1%,拉格朗日松弛算法也能在规定的计算时间末找到最优误差不高于3%的满意解,更为重要的是,它们的解明显地优于调度员采用的人工方法确定的解。
第5章探讨了具有多类型的作业且作业问存在复杂约束的技术站进路调度问题,该问题在于为各项行车和调车作业同时指派并调度进路,以使得所有作业在时间和空间上都无冲突,且定义的作业间的一致性约束能得到满足。本章引入车间调度问题中的工作和活动的概念来描述调度作业,并定义可囊括所有的路径选项和有限的时刻选项的进路模式的概念来表示决策变量,进而将原本包含多项决策任务的进路调度问题转换为1个只需指派提前生成的进路模式给活动的约束指派问题。本章将所定义的约束指派问题构建为1个最小化总晚点和走行时间,且满足唯一性约束、一致性约束和相容性约束的0-1线性规划模型,在建模时间-致性约束和道岔相容性约束时,基于图论的极大关联技术被用来代替传统的两两关联技术,以加强生成约束的定界质量。本章还讨论了如何拓展标准约束指派模型,以使得它能满足更多的运营要求,且从1个单一的路径模型转换为1个复合的路径和调度模型,对于标准模型的不可行问题,提出了1个迭代算法通过求解有限个辅助模型来构造可获得可行解的候选进路模式集。最后,1个真实案例的计算结果显示了相比于两两关联技术,极大关联技术可极大地减少生成的约束数,且所提出的标准模型使用的动态列车-站线-指派策略在求解质量上优于车站调度员的经验方法使用的静态列车-站线-指派策略。
第6章探讨了产生于技术站实时调度中的调车线受限的编组调车问题。给定待编车列和可使用调车线集合,该问题在于确定调车作业次数以及待编车列中的各个车辆在各次调车作业中的调动路径,以使得在不违背调车线的数量和能力约束的情况下,各列编成车列都能被实现为站顺的顺序,并需要最少的连挂钩数、调动车数、占用调车线数和溜放钩数。本章首先考虑了将1列待编车列编顺为1列编成车列的简单编组调车问题,开发了1类新的使用0-1矩阵编码编组调车方案的位串法,通过定义不同的调车线连挂原则,分别提出了1个连挂全部调车线的全线位串法和1个单独预留1条调车线给编成车列的留线位串法,1个包含迭代优化和局部搜索进程的两阶段迭代搜索算法被开发来实施这两个位串法,其中,第-阶段通过求解一系列的0-1线性规划模型来寻找需要的0-1矩阵,该矩阵再由第二阶段定义的搜索规则进行局部优化,最终获得的编组调车方案可按字典序优化拟定的连挂钩数、调动车数、占用调车线数和溜放钩数。本章还将拓展的全线和留线位串法运用于解决更具有挑战性的将多列待编车列同时组合为多列编成车列的批量编组调车问题。最后,切实的随机案例被用来体现了所提出的两个位串法都能有效地求解调车线受限的简单和批量编组调车问题,它们快速的计算时间准许将它们同时运用于解决大规模的问题实例。
Technical station is a critical node in the railroad freight transportation network, and its operation efficiency directly influences the robustness and service level of the total railroad freight transportation. Nowadays, the ordinary transportation work of technical station is organized and scheduled by various types of operation plans. This thesis focuses on several important theoretical problems including the railcar allocation problem, the route scheduling problem and the assembly shunting problems for optimally establishing the operation plan of railroad technical station, our main research works are as follows:
Chapter2investigates the railcar allocation problem at railroad district stations with single switch engine and single yard engine. The problem is to determine the composition of each outbound train, and schedule the task for each switch engine and yard engine, such that each outbound train satisfies the assembly requirements while the total dwell time of railcars staying at the station is minimized. We formulate the problem as a mixed integer linear programming model incorporating all decisions by utilizing the time-indexed conventional formulation for the single machine scheduling problems, and present three efficient solution approaches including a Lagrangian relaxation algorithm, a heuristic and an integer-based encoding genetic algorithm by exploiting the structure of the presented formulation and the characteristic of the problem. A numerical example coming from the practical situation is used to test the effectiveness and efficiency of the proposed approaches. Computational results show that our approaches can quickly solve the practical problem to optimality or approximate optimality, and their results are obviously better than that found by the first-come-first-served based empirical method adopted by the station dispatcher in the real-time decision environment.
Chapter3investigates the railcar allocation problem at railroad single-directional marshalling station with multiple switch engines and multiple yard engines. The problem lies on determining the composition of each outbound train, and assigning and scheduling the task of each switch engine and each yard engine, such that each outbound train satisfies the assembly rules and each engine is conflict-free. Utilizing the time-indexed based formulation of the parallel machine scheduling problems to model the assignment and schedule of engines, we firstly present the problem a mixed integer linear programming model to minimize the total dwell time of railcars staying at the station, which incorporates the train composition sub-problem and the engine scheduling sub-problem into the same optimization framework by using a linking constraints, and then design an exact algorithm and two heuristics according to the structure and characteristic of the problem, in which the exact algorithm is to use CPLEX to exactly solve the proposed optimization model, and the heuristics includes a Lagrangian relaxation algorithm and a biased random-key genetic algorithm. A realistic and large-scale numerical example is used to test the effectiveness and efficiency of the proposed approaches. Computational results show that our exact algorithm and biased random-key genetic algorithm can obtain approximately optimal solution with optimality gap less than1%for practical problems within the restricted computation time, and the solutions found by our approaches are not worse than that found by the empirical method used in practice.
Chapter4investigates the railcar allocation problem at railroad double-directional marshalling station with two operation systems and railcar transfer between systems. The problem consists of determining the composition of each outbound train and each transfer train, and assigning and scheduling the task of each switch engine and each yard engine, such that each outbound train meets the departure rules, each transfer train satisfies the assembly requirements, and each engine receives conflict-free tasks. We formulate the problem as a mixed integer linear programming model to minimize the total dwell time of railcars staying at the station with all decisions, in this model, the engine scheduling sub-problem is modeled by using the time-indexed classical formulation for the parallel machine scheduling problems. By utilizing the easy to be decomposed structure of the problem, we design two effective heuristics including a Lagrangian relaxation algorithm with using the proposed optimization model and a biased random-key genetic algorithm without using the proposed optimization model. To validate the effectiveness and efficiency of our proposed approaches for practical problems, computational test is conducted on a realistic and large-scale numerical example. Computational results show that our biased random-key genetic algorithm can obtain near-optimal solution with optimality gap approaching1%within the computation time less than100s, and our Lagrangian relaxation algorithm can find good solution with optimality gap not greater than3%at the end of the restricted time. More importantly, their solutions are obviously better than those determined by the manual method used by the station dispatcher.
Chapter5investigates the route scheduling problem with multiple types of operations and complicated constraints among operations at railroad technical station. This problem is to simultaneously assign and schedule route for each train and engine operation, such that all operations are conflict-free in time and space, and the defined consistency constraints are satisfied. We introduce the concept of task and activity in the job shop scheduling problem to describe the scheduling operations, and define the concept of route pattern which can incorporate all routing alternatives and partial timing alternatives to represent the decision variables, based on which we transform the original route scheduling problem with multiple decision tasks to a constrained assignment problem which only has to assign pre-computed route patterns to activities. We formulate the defined constrained assignment problem as a0-1linear programming model which minimizes the total delay and travel time and satisfies the uniqueness, consistency and compatible constraints. In modeling the time consistency and switch compatible constraints, graph based maximal correspondence technique is used to replace the traditional pair-wise correspondence technique to strength the bounding efficiency of the generated constraints. We also discuss how to extend the standard constrained assignment problem, so as to enable it to satisfy more operational requirements and transform from a single routing model to an integrated routing and scheduling model. For the infeasible issue of the standard problem, an iteration algorithm is proposed to generate candidate route patterns which can obtain feasible solutions by solving a sequence of auxiliary models. At last, computational results of a realistic example show that the maximal technique can significantly decrease the number of generated constraints compared with the pair-wise technique, and the dynamic train-to-track-assignment strategy used in our approach is better than the static train-to-track-assignment strategy used in dispatchers'empirical method in terms of solution quality.
Chapter6investigates the track capacitated train assembly shunting problem (TASP) in the real-time scheduling of railroad technical station. Given the inbound trains and shunting tracks, this problem lies on determining the number of shunting operations and the routes of each railcar of the inbound trains in each shunting operation, such that each outbound train can be realized in the correct station-based order without violating the tracks'number and capacity, while requiring minimal number of pulled-outs, shunted railcars, occupied tracks and rolled-ins. We first consider a simple TASP which assembles single inbound train into single outbound train. Using0-1matrixes to encode the assembly shunting plan, a novel bitstring method is developed for the problem. By defining different track pulled-out principles, we propose a total bitstring method and a partial bitstring method which pulls-out all tracks and especially reserves a track for the outbound train, respectively. A two-stage iteration search algorithm incorporating an iteration optimization procedure and a local search procedure is developed to implement these two methods. The first stage is to find the required0-1matrixes by solving a sequence of0-1linear programming model, which is further improved by several local rules defined in the second stage. The obtained plan can minimize the number of pulled-outs, shunted railcars, occupied tracks and rolled-ins in the lexicographical order. We also apply our extended total and partial bitstring methods to solve the more challenging batch TASP which has to simultaneously assembly multiple inbound trains into multiple outbound trains. At last, several realistic instances are used to show that our bitstring method can effectively solve the simple and batch TASP, and their fast computation time allows us to simultaneously apply them to tackle large-scale problem instances.
引文
[1]Boysen N., Fliedner M., Jaehn F. et al. Shunting yard operations:Theoretical aspects and applications[J]. European Journal of Operational Research,2012,220(1):1-14.
[2]Boysen N., Fliedner M., Jaehn F. et al. A survey on container processing in railway yards[J]. Transportation Science, http://dx.doi.org/10.1287/trsc.1120.0415.
[3]黎浩东,何世伟,王保华,等.铁路编组站阶段计划编制研究综述[J].铁道学报,2011,33(8)：13-22.
[4]Petersen E.R.. Railyard modeling:part Ⅰ. Prediction of put-through time[J]. Transportation Science,1977,11(1):37-49.
[5]Petersen E.R.. Railyard modeling:part Ⅱ. The effect of yard facilities on congestion[J]. Transportation Science,1977,11(1):50-59.
[6]Turnquist M.A., Daskin M.S.. Queuing models of classification and delay in railyards[J]. Transportation Science,1982,16(2):207-230.
[7]黄家厚.铁路编组站的系统分析及负荷的研究[J].西南交通大学学报,1986,21(4)：51-59.
[8]吴家豪.铁路编组站系统设计优化[M].北京：中国铁道出版社,1994.
[9]朱晓立,李夏苗.提速干线上编组站到解系统匹配与协调关系的研究[J].中国铁道科学,2004,25(4)：112-115.
[10]朱晓立,李夏苗.提速干线编组站出发子系统内部匹配与协调关系[J].中国铁道科学,2006,27(5)：118-121.
[11]Martland CD.. PMAKE analysis:Predicting rail yard time distributions using probabilistic train connection standards[J]. Transportation Science,1982,16(4): 476-506.
[12]Duffy M.A.. Statistical process control applied to rail freight terminal performance a case study of CSX's Radnor yard[D]. Cambridge:Massachusetts Institute of Technology, 1994.
[13]Dirnberger J.R., Barkan C.P. L. Lean railroading for improving railroad classification terminal performance:Bottleneck management methods[J]. Transportation Research Record:Journal of the Transportation Research Board,2007,1995:52-61.
[14]Dirnberger J.R. Development and application of lean railroading to improve classification terminal performance [D]. Urbana:University of Illinois Urbana-Champaign,2006.
[15]冒小栋.统计过程控制在编组站生产管理中的应用[J].铁道运输与经济,2006,28(11)：65-68.
[16]Shughart L., Ahuja R., Kumar A. et al, A comprehensive decision support system for hump yard management using simulation and optimization[R]. Technical Report, Innovation Scheduling,2009.
[17]Lin E., Cheng C.. YARDSIM:A rail yard simulation framework and its implementation in a major railroad in the U.S.[C]. Rossetti M.D., et al. Proceedings of the 2009 Winter Simulation Conference, Austin,2009. New Jersey:IEEE,2009:2532-2541.
[18]易文平.编组站到达解体系统计算机仿真[J].长沙铁道学院学报,1985,3(3)：55-61.
[19]文旭光.铁路编组站到达区间-到达场-驼峰子系统运营模拟[J].西南交通大学学报,1986,21(4)：106-112.
[20]邓西平,藤传琳.计算机模拟在编组站“到达场-驼峰”系统的应用[J].系统工程理论与实践,1988,8(4)：36-41.
[21]陶德高,方文愈.编组站双溜放驼峰到达解体系统模拟分析法的研究[J].中国铁道科学,1991,12(1)：93-102.
[22]王德,谢文炳,胡思继,等.编组站到达-解体系统与区间通过能力的协调条件[J].北方交通大学学报,1993,17(3)：265-269.
[23]张宁,张全寿.利用随机Petri网对编组站作业系统建模及分析的研究[J].铁道学报,2001,23(1)：13-18.
[24]陈刚,张殿业,张成,等.编组站解体能力影响因素的仿真技术研究[J].中国铁道科学,2006,27(2)：126-131.
[25]陈刚,张殿业.编组站运营仿真中的前向环馈仿真方法[J].中国铁道科学,2007,28(2)：94-99.
[26]陈刚.铁路编组站运营系统动态仿真[D].成都：西南交通大学,2007.
[27]孙琦,周磊山,乐逸祥,等.编组站到解系统匹配与协调关系动态仿真分析[J].系统仿真学报,2007,19(15)：3595-3598+3608.
[28]刘风先,郑时德.编组站调车场股道数计算方法的探讨[J].北方交通大学学报,1988,12(1)：37-46.
[29]孙晚华.确定编组站调车场线路数的模拟方法[J].铁道学报,1996,18(S1)：105-108.
[30]孙琦,周磊山,夏明,等.铁路编组站出发系统与区间动态能力协调仿真模型的研究[J].物流技术,2007,26(11)：132-135.
[31]易文平.编组站的最优控制、模型及应用[J].长沙铁道学院学报,1988,6(3)：80-86.
[32]易文平,秦作睿.铁路编组站作业过程实时模拟系统设计研究[J].铁道学报,1989,11(3)：67-77.
[33]刘军.基于知识的编组站作业整体仿真策略的研究[J].北方交通大学学报,1992,16(3)：40-45.
[34]刘军.用AI方法编制铁路编组站日班计划的研究[J].北方交通大学学报,1993,17(3)：270-276.
[35]刘军.一类复杂规划问题的分层规划方法[J].北方交通大学学报,1995,19(3)：401-406.
[36]钟雁,张全寿.铁路编组站调车作业计划决策支持系统的研究[J].铁道学报,1994, 1 6(4)：76-82.
[37]钟雁.一个基于动态模型的计划决策支持系统[J].北方交通大学学报,1994,18(4)：477-483.
[38]孙晚华,郑时德.编组站到达流生成方法的研究[J].北方交通大学学报,1994,18(4)：499-505.
[39]谭立刚,杨肇夏.编组站模拟系统中到达流生成的方法[J].北方交通大学学报,1998,22(6)：43-47.
[40]严霄蕙,张春迎.编组站调车作业模拟研究[J].中国矿业大学学报,2000,29(1)：97-101.
[41]刘旭,谭立刚,杨浩,等.编组站通过能力和改编能力模拟计算系统的研究[J].铁道学报,2002,24(5)：11-15.
[42]李海鹰,张超.提速干线上编组站列车到达规律[J].中国铁道科学,2007,28(6)：96-101.
[43]杨肇夏,李菊,孙晚华,等.铁路编组站技术作业模拟系统的研究[J].铁道学报,1996,18(S1)：25-32.
[44]郑时德,杨肇夏.编组站作业仿真及系统优化[M].北京：中国铁道出版社,1996.
[45]苗建瑞,蒋熙,于勇,等.铁路车站(场)列车到发与调车作业过程仿真的研究[J].北方交通大学学报,2000,24(3)：50-54.
[46]蒋熙,于勇,苗建瑞,等.编组站技术作业过程实时模拟培训系统的研究[J].铁道学报,2001,23(5)：7-11.
[47]蒋熙,苗建瑞,于勇,等.基于高层体系结构的铁路编组站综合仿真系统研究[J].系统仿真学报,2002,14(4)：481-484.
[48]贺振欢,杨肇夏.铁路编组站驼峰技术作业过程模拟实验系统的研究[J].北方交通大学学报,1998,22(3)：68-72.
[49]何世伟,宋瑞,杨浩,等.列车提速对编组站运营工作的影响研究[J].铁道学报,2000,22(5)：6-12.
[50]何世伟,宋瑞,谭立刚,等.枢纽编组站智能调度系统的设计与实现[J].北方交通大学学报,2002,26(5)：19-23.
[51]李文权.铁路区段站日工作计划优化模型及其算法的研究[D].成都：西南交通大学,1997.
[52]徐杰.区段站阶段计划自动编制模型和算法研究[D].成都：西南交通大学,2003.
[53]王正彬.区段站阶段计划调整模型与算法研究[D].成都：西南交通大学,2007.
[54]何世伟.铁路枢纽作业计划的优化编制—编组站作业计划与枢纽日班计划的模型及算法研究[D].成都：西南交通大学,1996.
[55]王明慧.编组站智能调度系统YIDS体系框架与关键技术优化理论研究[D].成都：西南交通大学,2007.
[56]薛锋.编组站调度系统配流协同优化理论与方法研究[D].成都：西南交通大学, 2009.
[57]景云.不确定条件下编组站调度系统配流模型及算法研究[D].成都：西南交通大学,2010.
[58]黎浩东.铁路编组站鲁棒阶段计划编制及调整研究[D].北京：北京交通大学,2012.
[59]牛惠民.铁路枢纽编组站作业分工整体优化的研究[D].北京：北方交通大学,1998.
[60]崔炳谋.编组站综合自动化若干问题的研究[D].北京：铁道科学研究院,2007.
[61]Burkolter D.. Capacity of railways in station areas using petri nets[D]. Zurich:ETH Zurich,2005.
[62]Herrmann T.. Stability of timetables and train routings through station regions[D]. Zurich:ETH Zurich,2006.
[63]Caimi G.. Algorithmic decision support for train scheduling in a large and highly utilised railway network[D]. Zurich:ETH Zurich,2009.
[64]Fuchsberger M.. Algorithms for railway traffic management in complex central station areas[D]. Zurich:ETH Zurich,2012.
[65]Lusby R. Optimization methods for routing trains through railway junctions[D]. Auckland:The University of Auckland,2008.
[66]Galli L.. Combinatorial and robust optimisation models and algorithms for railway applications[D]. Bologna:University of Bologna,2009.
[67]吕红霞.铁路大型客运站作业计划智能编制的优化技术和方法研究[D].成都：硒南交通大学,2008.
[68]谢楚农.客运站旅客列车运行组织优化[D].长沙：中南大学,2010.
[69]张英贵.铁路客运站股道运用优化方法与应用研究[D].长沙：中南大学,2012.
[70]贾文峥.大型铁路客运站的进路分配问题及缓冲时间研究[D].北京：北京交通大学,2010.
[71]陈彦.铁路客运站列车过站径路与调机运用优化[D].长沙：中南大学,2010.
[72]Hansmann R.. Optimal sorting of rolling stock[D]. Braunschweig:Braunschweig University of Technology,2010.
[73]Maue J.. On the problem of sorting railway freight cars[D]. Zurich:ETH Zurich,2011.
[74]Winter T.. Online and real-time dispatching problems[D]. Braunschweig:Braunschweig University of Technology,1999.
[75]Lentink R.M.. Algorithmic decision support for shunt planning[D]. Rotterdam:Erasmus University Rotterdam,2006.
[76]Van den Broek J.J.J.. MIP-based approaches for complex planning problems [D]. Eindhoven:Eindhoven University of Technology,2009.
[77]Yagar S., Saccomano F. F., Shi Q.. An efficient sequencing model for humping in a rail yard[J]. Transportation Research Part A,1983,17(4):251-262.
[78]Shi Q., Yagar S.. Case studies measuring the benefits of the HSS hump sequencing model[J]. Canadian Journal of Civil Engineering,1983,10(1):36-47.
[79]Kraft E.R., Guignard M.. A mixed integer optimization model to improve freight car classification in railroad yards[R]. Report 93-06-06, University of Pennsylvania, The Wharton School, Department of Operations and Information Management,1993.
[80]Kraft E.R.. Priority-based classification for improving connection reliability in railroad yards part I of II:integration with car scheduling[J]. Transportation Quarterly,2002, 56(1):93-105.
[81]Kraft E.R.. Priority-based classification for improving connection reliability in railroad yards part II of II:dynamic block to track assignment[J]. Transportation Quarterly,2002, 56(1):107-119.
[82]Wang X.. Improving planning for railroad yard, forestry and distribution[D]. Philadelphia:University of Pennsylvania,1997.
[83]Ferguson R.T.. Mathematical modeling of the railroad switching process[D]. Charlottesville:University of Virginia,1993.
[84]Armacost A.P.. Modeling railroad terminal operations supporting real-time network planning and control[D]. Cambridge:Massachusetts Institute of Technology,1995.
[85]Timian D.H. Current methods for optimizing rail marshalling yard operation[D]. Manhattan:Kansas State University,1994.
[86]Bektas T., Crainic T.G., Morency V.. Improving performance of rail yards through dynamic reassignments of empty cars[J]. Transportation Research Part C,2009,17(3): 259-273.
[87]Sahin G., Ahuja R.K.. Single-machine scheduling with stepwise tardiness costs and release times[J]. Journal of Industrial and Management Optimization,2011,7(4): 825-848.
[88]袁庆达,杜文,黎青松.区段站阶段计划的优化模型和算法[J].西南交通大学学报,2000,35(3)：250-254.
[89]徐杰,杜文,刘春煌.铁路技术站车流推算模型和算法[J].中国铁道科学,2005,26(4)：120-123.
[90]王正彬,杜文,吴柏青,等.基于解编顺序的阶段计划车流推算模型及算法[J].西南交通大学学报,2008,43(1)：91-95.
[91]中永生,何世伟,王保华,等.免疫算法求解编组站阶段计划配流问题研究[J].铁道学报,2009,31(4)：1-6.
[92]申永生,何世伟,黎浩东,等.自适应粒子群算法求解编组站车流推算问题的研究[J].铁道货运,2010,12(5)：5-10.
[93]黎浩东,何世伟,景云,等.考虑不同满轴约束的编组站阶段计划配流优化[J].铁道学报,2012,34(7)：1-8.
[94]何世伟,宋瑞,胡安洲.编组站阶段计划刚性与柔性优化的协调研究[J].铁道学报,1999,21(4)：1-8.
[95]He S., Song R., Hu A.. Uncertain dispatching decision and genetic algorithm for railway operations[J]. Journal of Systems Science and Systems Engineering,2000,9(2): 149-158.
[96]He S., Song R., Chaudhry S.S.. Fuzzy dispatching model and genetic algorithms for railyards operations[J]. European Journal of Operational Research,2000,124(2): 307-331.
[97]刘霆,何世伟,王保华,等.编组站调度计划随机机会约束规划模型及算法研究[J].铁道学报,2007,29(4)：12-17.
[98]黎浩东,何世伟,麻克君.编组站调度信息对阶段计划的影响及计划调整研究[J].物流技术,2010,29(1)：45-48.
[99]黎浩东,何世伟,宋瑞等.编组站阶段计划随机相关机会规划模型及算法[J].交通运输系统工程与信息,2010,10(1)：128-133.
[100]Liu B.. Study on the stochastic chance-constrained fuzzy programming model and algorithm for wagon flow scheduling in railway bureau[J]. Mathematical Problems in Engineering, doi:10.1155/2012/602153.
[101]李文权,王炜,杜文,等.铁路技术站调机运用模型及算法[J].系统工程学报,2000,15(1)：38-43.
[102]徐杰,杜文,李宗平,等.基于模拟退火算法和图着色的调机安排研究[J].铁道学报,2003,25(3)：24-30.
[103]徐杰,杜文,黎青松,等.铁路区段站决策支持系统的研究——调机的合理安排[J].四川工业学院学报,2003,22(2)：11-14.
[104]王世东,郑力,张智海,等.蚁群算法在调机运用计划中的应用[J].中国铁道科学,2007,28(3)：104-109.
[105]王烁,何世伟,黎浩东,等.禁忌搜索算法在编组站调机运用计划中的应用[J].铁道运输与经济,2011,33(2)：83-87.
[106]Keha A.B., Khowala K., Fowler J.W.. Mixed integer programming formulations for single machine scheduling problems[J]. Computers & Industrial Engineering,2009, 56(1):357-367.
[107]Zhu X., Yuan Q., Garcia-Diaz A., et al. Minimal-cost network flow problems with variable lower bounds on arc flows[J]. Computers & Operations Research,2011,38(8): 1210-1218.
[108]Koulamas C.. The single-machine total tardiness scheduling problem:Review and extensions[J], European Journal of Operational Research,2010,202(1):1-7.
[109]Garey M.R., Johnson D. S., Sethi R.. The complexity of flowshop and jobshop scheduling[J]. Mathematics of Operations Research,1976,1(2):117-129.
[110]Graham R.L., Lawler E.L., Lenstra J.K., et al. Optimization and approximation in deterministic sequencing and scheduling:A survey[J]. Annals of Discrete Mathematics, 1979,5:287-326.
[111]Fisher M.L.. The lagrangian relaxation method for solving integer programming problems[J]. Management Science,1981,27(1):1-18.
[112]Fisher M.L.. Comments on "The lagrangian relaxation method for solving integer programming problems"[J]. Management Science,2004,50(12S):1872-1874.
[113]Savelsbergh M.W.P., Uma R.N., Wein J.M.. An experimental study of LP-based approximation algorithms for scheduling problems[J]. INFORMS Journal on Computing, 2005,17(1):123-136.
[114]Gen M., Altiparmak F., Lin L.. A genetic algorithm for two-stage transportation problem using priority-based encoding[J]. OR Spectrum,2006,28(3):337-354.
[115]Ruiz R., Maroto C., Alcaraz J. Two new robust genetic algorithms for the flowshop scheduling problem[JJ. Omega,2006,34(5):461-476.
[116]Reeves C.R.. A genetic algorithm for flowshop sequencing[J]. Computers & Operations Research,1995,22(1):5-13.
[117]Murata T., Ishibuchi H., Tanaka H.. Genetic algorithms for flowshop scheduling problems[J]. Computers and Industrial Engineering,1996,30(4):1061-1071.
[118]何世伟,宋瑞,朱松年.铁路编组站阶段计划编制的模型及其算法研究[J].系统工程理论与实践,1997,17(2)：88-94.
[119]何世伟,宋瑞,朱松年.编组站阶段计划解编作业优化模型及算法[J].铁道学报,1997,19(3)：1-8.
[120]He S., Song R., Chaudhry S.S.. An integrated dispatching model for rail yards operations[J]. Computers & Operations Research,2003,30(7):939-966.
[121]何世伟,宋瑞,鲁放,等.铁路运输管理中的多机模糊排序问题及遗传算法研究[J].北京航空航天大学学报(社会科学版),2000,13(4)：4-10.
[122]王慈光.编组站列车解体方案的计数方法[J].铁道学报,2000,22(6)：1-7.
[123]王慈光.用表上作业法求解编组站配流问题的研究[J].铁道学报,2002,24(4)：1-5.
[124]王慈光.编组站静态配流网络模型[J].交通运输工程与信息学报,2003,1(2)：67-71.
[125]王慈光.编组站动态配流模型与算法研究[J].铁道学报,2004,26(1)：1-6.
[126]景云,王慈光.不确定条件下编组站动态配流模型及算法研究[J].铁道学报,2010,32(4)：8-12.
[127]郭寒英,石红国.求解编组站静态配流问题的一种改进算法[J].铁道运输与经济,2004,26(5)：74-76.
[128]景云,王慈光,王如义等.运用学习规则求解编组站静态配流问题的研究[J].铁道运输与经济,2010,32(1)：22-26.
[129]薛锋,王慈光,张展杰.编组站配流的协调优化算法[J].西南交通大学学报,2010,45(6)：932-937.
[130]薛锋,王慈光.编组站列车编组顺序的调整方法[J].铁道学报,2007,29(4)：1-5.
[131]薛锋,王慈光,罗建,等.编组站列车解体方案与编组方案的协调优化研究[J].铁道学报,2008,30(2)：1-6.
[132]曹家明,范征,毛节铭.编组站作业优化决策支持系统——解体子系统[J].铁道学 报,1993,15(4)：66-73.
[133]王明慧,赵强.编组站智能调度系统阶段计划优化模型及算法研究[J].铁道学报,2005,27(6)：1-9.
[134]王世东,郑力,张智海,等.编组站阶段计划自动编制的数学模型及算法[J].中国铁道科学,2008,29(2)：120-125.
[135]Unlu Y., Mason S.J.. Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems[J]. Computer & Industrial Engineering,2010,58(4):785-800.
[136]Krumke S.O., Thielen C.. Minimum cost flows with minimum quantities [J]. Information Processing Letters,2011,111(11):533-537.
[137]Li K., Yang S.. Non-identical parallel-machine scheduling research with minimizing total weighted completion times:Models, relaxations and algorithms[J]. Applied Mathematical Modelling,2009,33(4):2145-2158.
[138]Ruiz R., Vazquez-Rodriguez J.A.. The hybrid flow shop scheduling problem[J]. European Journal of Operational Research,2010,205(1):1-18.
[139]Ribas I., Leisten R., M.Framinan J.. Review and classification of hybrid flow shop scheduling problems from a production system and a solutions procedure perspective[J]. Computers & Operations Research,2010,37(8):1439-1454.
[140]Held M., Karp R.M.. Traveling-salesman problem and minimum spanning trees[J]. Operations Research,1970,18(6):1138-1162.
[141]Geoffrion A.M.. Lagrangean relaxation for integer programming[J]. Mathematical Programming Study.1974,2(1):82-114.
[142]Bean, J.C.. Genetic algorithms and random keys for sequencing and optimization [J]. ORSA Journal on Computing.1994,6(2):154-160.
[143]Goncalves J.F., Resende M.G.C.. Biased random-key genetic algorithms for combinatorial optimization[J]. Journal on Heuristics,2011,11(5):487-525.
[144]Resende M.G.C.. Biased random-key genetic algorithms with applications in telecommunications[J]. Top,2012,20(1):130-153.
[145]Kurz M.E., Askin R.G.. Scheduling flexible flow lines with sequence-dependent setup times[J]. European Journal of Operational Research,2004,159(1):66-82.
[146]Zandieh M., Ghomi S.M.T.F., Husseini S.M.M.. An immune algorithm approach to hybrid flow shops scheduling with sequence-dependent setup times[J]. Applied Mathematics and Computation,2006,180(1):111-127.
[147]Spears W.M., De Jong K.A.. On the virtues of parameterized uniform crossover[C]. Belew R. K., et, al. Proceedings of the Fourth International Conference on Genetic Algorithms, San Diego:1991. San Fransisco:Morgan Kaufmann,1991:230-236.
[148]杨旭东.编组站车场分工方案优选[J].长沙铁道学院学报,1986,4(3)：39-46.
[149]牛惠民,胡安洲.双向编组站车流接续的综合优化[J].铁道学报,1998,20(6)：16-21.
[150]牛惠民,胡安洲.双向编组站系统作业分工的优化模型及算法[J].中国科学(E辑),1998,28(4)：378-384.
[151]Niu H., Hu A.. Optimization model and algorithm for system operation division of labor at two-way marshaling station[J]. Science in China(series E),1998,41(5): 511-518.
[152]牛惠民.一类带有随机参数的交通优化模型及遗传算法[J].系统工程学报,2002,17(2)：103-108.
[153]牛惠民,郝克智.转场交换车流的综合优化[J].兰州铁道学院学报,1995,14(1)：73-78.
[154]牛惠民,胡安洲.双向编组站折角车流优化的模型和算法[J].北方交通大学学报,1998,22(6)：38-42.
[155]张全寿.编组站站调决策支持系统的研究[J].北方交通大学学报,1989,13(4)：64-72.
[156]牛惠民.双向编组站列车调度调整的优化模型及算法[J].中国铁道科学,2007,28(6)：102-108.
[157]薛锋,王慈光,罗建.双向编组站静态配流的优化[J].西南交通大学学报,2008,43(2)：159-164.
[158]Guignard M.. Lagrangean relaxation[J]. TOP,2003,11(2):151-228.
[159]Norman B.A., Bean J.C.. A genetic algorithm methodology for complex scheduling problems[J]. Naval Research Logistics,1999,46(2):199-211.
[160]Lusby R., Larsen J., Ehrgott M., et al. Railway track allocation:models and methods[J]. OR Spectrum,2011,33(4):843-883.
[161]Zwaneveld P.J., Kroon L.G., Romeijn H.E, et al. Routing trains through railway stations:model formulation and algorithms[J]. Transportation Science,1996,30(3): 181-194.
[162]Zwaneveld P.J. Kroon L.G.,van Hoesel S.P.M.. Routing trains through a railway station based on a node packing model [J]. European Journal of Operational Research, 2001,128(1):14-33.
[163]Kroon L.G., Romeijn H.E, Zwaneveld P.J.. Routing trains through railway stations: complexity issues[J]. European Journal of Operational Research,1997,98(3):485-498.
[164]Caimi G., Burkolter D., Herrmann T.. Finding delay-tolerant train routings through stations[C]. Fleuren H., et, al. Operations Research Proceedings 2004, Tilburg,2004. Berlin:Springer,2005:136-143.
[165]Caimi G, Burkolter D., Herrmann T., et al. Design of a railway scheduling model for dense services[J]. Networks and Spatial Economics,2009,9(1):25-46.
[166]Caprara A., Galli L., Toth P.. Solution of the train platforming problem[J]. Transportation Science,2011,45(2):246-257.
[167]Delorme X., Rodriguez J., Gandibleux X.. Heuristics for railway infrastructure saturation[J]. Electronic Notes in Theoretical Computer Science,2001,50(1):39-53.
[168]Delorme X., Gandibleux X., Rodriguez J.. GRASP for set packing problems[J]. European Journal of Operational Research,2004,153(3):564-580.
[169]Gandibleux X., Delorme X., T'Kindt V.. An ant colony optimisation algorithm for the set packing problem[C]. Dorigo M., et, al. Lecture Notes in Computer Science:Ant Colony Optimization and Swarm Intelligence, Brussels,2004. Berlin:Springer,2004, 3172:478-481.
[170]Gandibleux X., Jorge J., Angibaud S., et al. An ant colony optimization inspired algorithm for the set packing problem with application to railway infrastructure[C]. The Sixth Metaheuristics International Conference, Vienna,2005:390-396.
[171]De Luca Cardillo D., Mione N.. k L-list λ. colouring of graphs[J]. European Journal of Operational Research,1998,106(1):160-164.
[172]Billionne A.. Using integer programming to solve the train-platforming problem[J]. Transportation Science,2003,37(2):213-222.
[173]Velasquez R., Ehrgott M., Ryan D., et al. A set-packing approach to routing trains through railway station[C]. Proceedings of the 40th Annual Conference of the Operational Research Society of New Zealand, Wellington,2005:305-314.
[174]Lusby R., Larsen J., Ryan D., et al. Routing trains through railway junctions:a new set packing approach[J]. Transportation Science,2010,45(2):228-245.
[175]Lusby R., Larsen J., Ehrgott M., et al. A set packing inspired method for real-time junction train routing[J]. Computers and Operations Research,2013,40(3):713-724.
[176]Merel A., Gandibleux X., Demassey S.. Assessing railway infrastructure capacity by solving the saturation problem with an improved column generation algorithm[C].4th International Seminar on Railway Operations Modelling and Analysis, Rome,2011.
[177]Caimi G., Chudak F., Fuchsberger M. et al. A new resource-constrained multicommodity flow model for conflict-free train routing and scheduling[J]. Transportation Science,2010,45(2):212-227.
[178]Caimi G., Fuchsberger M., Laumanns M., et al. A model predictive control approach for discrete-time rescheduling in complex central railway station areas [J]. Computers and Operations Research,2012,39(11):2578-2593.
[179]Rodriguez J., Delorme X., Gandibleux X.. Railway infrastructure saturation using constraint programming approach[C]. Allan J., et, al. Computers in Railways VIII, Lemmos,2002, Southampton:WIT Press,2002:807-816.
[180]Rodriguez J.. A constraint programming model for real-time train scheduling at junctions[J]. Transportation Research Part B,2007,41(2):231-245.
[181]Rodriguez J.. Enhancement of train routing and scheduling at a terminal station with constraints programming and temporal decomposition[R], INRETS/RR-07-731-FR, France:INRETS,2007.
[182]Pellegrini P., Marliere G., Rodriguez J.. Real time railway traffic management modeling track-circuits[C]. Delling D., et, al. Proceedings of the 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems(ATMOS'12), Ljubljana:2012. Dagstuhl:Schloss Dagstuhl,2012:23-34.
[183]Corman F., Goverde R.M., D'Ariano A.. Rescheduling dense train traffic over complex station interlocking areas.//Ahuja R.K., et al. Lecture Notes in Computer Science:Robust and Online Large-Scale Optimization Models and Techniques for Transportation Systems [M], Berlin:Springer,2009,5868:369-386.
[184]Corman F., D'Ariano A., Pranzo M., et al. Effectiveness of dynamic reordering and rerouting of trains in a complicated and densely occupied station area[J]. Transportation Planning and Technology,2011,34(4):341-362.
[185]Mascis A., Pacciarelli D.. Job shop scheduling with blocking and no-wait constraints[J]. European Journal of Operational Research,2002,143(3):498-517.
[186]D'Ariano A., Pacciarelli D., Pranzo M.. A branch and bound algorithm for scheduling trains in a railway network[J]. European Journal of Operational Research,2007,183(2): 643-657.
[187]D'Ariano A., Corman F., Pacciarelli D., et al. Reordering and local rerouting strategies to manage train traffic in real-time[J]. Transportation Science,2008,42(4):405-419.
[188]Corman F., D'Ariano A., Pacciarelli D., et al. A tabu search algorithm for rerouting trains during rail operations [J]. Transportation Research Part B,2010,44(1):175-192.
[189]D'Ariano A., Pranzo M., Hansen I.A.. Conflict resolution and train speed coordination for solving real-time timetable perturbations[J]. IEEE Transactions on Intelligent Transportation Systems,2007,8(2):208-222.
[190]Flamini M., Pacciarelli D.. Real time management of a metro rail terminus[J]. European Journal of Operational Research,2008,189(3):746-761.
[191]Mannino C., Mascis A.. Optimal real-time traffic control in metro stations[J]. Operations Research,2009,57(4):1026-1039.
[192]Carey M., Carville S.. Scheduling and platforming trains at busy complex stations[J]. Transportation Research Part A,2003,37(3):195-224.
[193]Carey M., Crawford I.. Scheduling trains on a network of busy complex stations[J]. Transportation Research Part B,2007,41(2):159-178.
[194]Chakroborty P., Vikram D.. Optimum assignment of trains to platforms under partial schedule compliance [J]. Transportation Research Part B,2008,42(2):169-184.
[195]青学江,马国忠.遗传算法在区段站到发线的应用研究[J].西南交通大学学报,1998,33(4)：387-393.
[196]吕红霞,倪少权,纪洪业.技术站调度决策支持系统的研究——到发线的合理使用[J].西南交通大学学报,2000,35(3)：255-258.
[197]李文权,王炜,程世辉.铁路编组站到发线运用的排序模型和算法[J].系统工程理论与实践,2000,20(6)：75-78.
[198]徐杰,杜文,常军乾,等.基于遗传算法的区段站到发线运用优化安排[J].中国铁道科学,2003,24(2)：109-114.
[199]徐杰,杜文,李冰.铁路区段站到发线运用计划安排的优化算法[J].系统工程理论 方法应用,2003,12(3)：253-256.
[200]王正彬,杜文.铁路技术站到发线运用调整模型及算法[J].西南交通大学学报,2006,41(2)：202-205.
[201]谢楚农,黎新华.铁路客运站到发线运用优化研究[J].中国铁道科学,2004,25(5)：130-133.
[202]雷定猷,王栋,刘明翔.客运站股道运用优化模型及算法[J].交通运输工程学报,2007,7(5)：84-87.
[203]吕红霞,何大可,陈韬.基于蚁群算法的客运站到发线运用计划编制方法[J].西南交通大学学报,2008,43(2)：153-158.
[204]张英贵,雷定猷,刘明翔.铁路车站股道运用排序模型与算法[J].中国铁道科学,2010,31(2)：96-100.
[205]张英贵,雷定猷,汤波,等.铁路客运站股道运用窗时排序模型与算法[J].铁道学报,2011,33(1)：1-7.
[206]王保山,侯立新,刘海东.客运专线车站到发线运用优化方法[J].交通运输系统工程与信息,2012,12(2)：105-110.
[207]乔瑞军,朱晓宁,张天伟,等.客运专线车站到发线运用多目标优化模型[J].北京交通大学学报,2012,36(3)：57-64.
[208]苗建瑞,于勇,孟令云,等.面向稳定性的高速铁路车站作业计划优化方法[J].交通运输系统工程与信息,2012,12(3)：115-121+153.
[209]刘澜,王南,杜文.车站咽喉通过能力网络优化模型及算法研究[J].铁道学报,2002,24(6)：1-5.
[210]史峰,谢楚农,于桂芳.铁路车站咽喉区进路排列优化方法[J].铁道学报,2004,26(4)：5-9.
[211]崔炳谋,马钧培,张朴.编组站进路调度优化算法[J].中国铁道科学,2007,28(2)：100-104.
[212]龙建成,高自友,马建军,等.铁路车站进路选择优化模型及求解算法的研究[J].铁道学报,2007,29(5)：7-14.
[213]史峰,陈彦,秦进,等.铁路客运站到发线运用和接发车进路排列方案综合优化[J].中国铁道科学,2009,30(6)：108-113.
[214]陈彦,史峰,秦进,等.旅客列车过站径路优化模型与算法[J].中国铁道科学,2010,31(2)：101-107.
[215]贾文峥,毛保华,何天健,等.大型客运站股道分配问题的模型与算法[J].铁道学报,2010,32(2)：8-13.
[216]Hansen K.M.. Validation of a railway interlocking model[C]. Naftalin, M. et al. Lecture Notes in Computer Science:FME'94 Industrial Benefit of Formal Methods, Barcelona,1994. Berlin:Springer,1994,873:582-601.
[217]Montigel M.. Formal representation of track topologies by double vertex graphs[C]. Murthy T.K.S., et, al. Computers in Railways Ⅲ, Washington DC,1992. Southampton: Computational Mechanics Publications,1992:359-370.
[218]Glover F.. Maximum matching in a convex bipartite graph[J]. Naval Research Logistics Quarterly.1967,14(3):313-316.
[219]Alexe G., Alexe S., Crama Y., et al.. Consensus algorithms for the generation of all maximal bicliques[J]. Discrete Applied Mathematics.2004,145(1):11-21.
[220]Prisner E.. Bicliques in graphs Ⅰ bounds on their number[J]. Combinatorica,2000, 20(1):109-117.
[221]Faigle U., Frahlin G.. A combinatorial algorithm for weighted stable sets in bipartite graphs[J]. Discrete Applied Mathematics.2006,154(9),1380-1391.
[222]Fulkerson D. R., Gross O. A.. Incidence matrices and interval graphs[J]. Pacific Journal of Mathematics 1965,15(3):835-855.
[223]Di Stefano G., Maue J., Modelski M., et al. Models for rearranging train cars[R]. Technical Report ARRIVAL-TR-0089, ARRIVAL,2007.
[224]Gatto M., Maue J., Mihalak M., et,al. Shunting for dummies:an introductory algorithmic survey.//Ahuja R.K., et al. Lecture Notes in Computer Science:Robust and Online Large-Scale Optimization Models and Techniques for Transportation Systems[M], Berlin:Springer,2009,5868:310-337.
[225]Dahlhaus E., Horak P., Miller M., et al. The train marshalling problem[J]. Discrete Applied Mathematics,2000,103(1-3):41-54.
[226]Beygang K., Florian Dahms F., Krumke S.O.. Train marshalling problem algorithms and bounds[R]. Report in Wirtschaftsmathematik(WIMA Report) 132, University of Kaiserslautern, Department of Mathematics,2010.
[227]Brueggeman L., Fellows M., Fleischer R., et al. Train marshalling is fixed parameter tractable[C]. Kranakis E., et al. Lecture Notes in Computer Science:Proceedings of the 6th International Conference on Fun with Algorithms(FUN 2012), Venice:2012. Berlin: Springer,2012,7288:51-56.
[228]Siddiqee M.W.. Investigation of sorting and train formation schemes for a railroad hump yar[C]. Newell G.F.. Proceedings of the 5th International Symposium on the Theory of Traffic Flow and Transportation, Berkeley:1971. New York:American Elsevier Publishing Company,1972:377-387.
[229]Daganzo C.F., Dowling R.G. and Hall R.W.. Railroad classification yard throughput: the case of multistage triangular sorting[J]. Transportation Research Part A,1983,17(2): 95-106.
[230]Daganzo C.F.. Static blocking at railyards:sorting implications and track requirements [J], Transportation Science,1986,20(3):189-199.
[231]Daganzo C.F.. Dynamic blocking for railyards:part Ⅰ. homogeneous traffic[J]. Transportation Research Part B,1987,21(1):1-27.
[232]Daganzo C.F.. Dynamic blocking for railyards:part Ⅱ. heterogeneous traffic[J]. Transportation Research Part B,1987,21(1):29-40.
[233]Hansmann R.S., Zimmermann U.T. Optimal sorting of rolling stock at hump yards.// Krebs H.-J., et al. Mathematics-Key Technology for the Future:Joint Projects Between Universities and Industry[M], Berlin:Springer,2008:189-203.
[234]Jacob R., Marton P., Maue J., et al. Multistage methods for freight train classification[J]. Networks,2010,57(1):87-105.
[235]Marton P., Maue J., Nunkesser M.. An improved classification procedure for the hump yard Lausanne Triage[C]. Clausen J. et al. Proceeding of 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems(ATMOS'09), Copenhagen:2009. Dagstuhl:Schloss Dagstuhl,2009.
[236]Maue J., Nunkesser M.. Evaluation of computational methods for freight train classification schedules[R]. Technical Report ARRIVAL-TR-0184, ARRIVAL,2009.
[237]Hauser A., Maue J.. Experimental evaluation of approximation and heuristic algorithms for sorting railway cars[C]. Festa, P.. Lecture Notes in Computer Science: Proceeding of the 9th International Symposium on Experimental Algorithms, Naples: 2010. Berlin:Springer,2010,6049:154-165.
[238]Dahlhaus, E., Manne, F., Miller, M., et al. Algorithms for combinatorial problems related to train marshalling[C]. Proceeding of the Australasian Workshop on Combinatorial Algorithms, Hunter Valley,2000:7-16.
[239]Cicerone S., D'Angelo G., Di Stefano G., et al. Recoverable robustness for train shunting problems[J]. Algorithmic Operations Research,2009,4(2):102-116.
[240]Busing C., Maue J.. Robust algorithms for sorting railway cars[C]. de Berg M., et al. Lecture Notes in Computer Science:Proceedings of the 18th annual European symposium on algorithms, Part I, Liverpool:2010. Berlin:Springer,2010,6346: 350-361.
[241]李国风.表格移动调车钩计划方法[J].铁道科学技术,1965,(1)：4-9.
[242]黄世玲.按站顺编组的摘挂列车在调车中的合并线路问题.//铁道运输与经济论文集[M].北京：中国铁道出版社,1980：46-58.
[243]韩绍祖.钩计划排序原理的探讨.//铁道运输与经济论文集[M].北京：中国铁道出版社,1980：84-100.
[244]孙焰,牟世斌,张俊杰,等.求选编钩计划最优下落方案的一种最短路算法[J].铁道运输与经济,2011,33(10)：64-69.
[245]中料院数学所运筹室二组.铁道调车问题中数学方法的初步研究[J].应用数学学报,1978,1(2)：91-105.
[246]丁克诠,王志立.对随机排列落表剖分算法的一个改进[J].大连工学院学报,1987,27(4)：84+92.
[247]蔡茂诚.顺序子序列的计数问题[J].应用数学学报,1981,4(2)：141-150.
[248]朱永津,朱若鹏.任意序列重新组合为某种有序序列的研究[J].中国科学(A辑),1983,16(2)：119-127.
[249]Zhu Y., Zhu R.. Sequence reconstruction under some order-type constraints[J]. Scientia Sinica(Series A),1983,26(7):702-713.
[250]丁克诠.随机排列的伪顺序最小剖分[J].运筹学杂志,1985,4(1)：63-64.
[251]丁克诠.广义落表算法与对偶落表算法[J].数值计算与计算机应用,1987,8(2)：115-121.
[252]刘继勇.数列最优成组剖分的一个动态算法[J].国防科技大学学报,1986,8(4)：125-130.
[253]许国志,陈庆华,刘继勇.数列最优成组剖分的一个近似算法[J].科学通报,1986,31(15)：1128-1131.
[254]Xu G., Chen Q., Liu J.. An approximate algorithm of optimal digit-grouped partition of sequences[J]. Kexue Tongbao,1987,32(14):942-946.
[255]Ding K.. An algorithm for the problem of minimal number-grouped partitions of random permutations[J]. Advances In Mathematics,1986,15(1):105-106.
[256]Ding K.. An algorithm for minimal number-grouped partitions of random permutations[J]. Journal of Mathematical Research and Exposition,1990,10(4): 501-508.
[257]山东大学数学系运筹教研室表格调车法小组.表格调车法的数学理论初探[J].山东大学学报,1979,14(4)：1-15.
[258]刘德周.看图调车法[M].北京：中国铁道出版社,1979：1-214.
[259]胡安洲.统筹对口调车法及其原理.//铁道运输与经济论文集[M],北京：中国铁道出版社,1980：59-83.
[260]宋建业.摘挂列车编组调车方案优化方法的探讨[J].兰州铁道学院学报,1996,15(2)：54-63.
[261]宋建业.优化筛选摘挂列车编组调车方案的分析计算法[J].铁道学报,1999,21(3)：11-17.
[262]宋建业.车辆下落算法[J].兰州铁道学院学报,1995,14(1)：66-72.
[263]宋建业,待编车列分批解体时开口位置的确定[J].兰州铁道学院学报,1998,17(4)：102-110.
[264]宋建业.成组、混合选编方法及其计算机实现[J].兰州铁道学院学报,1999,18(2)：128-135.
[265]李夏苗,李清法.摘挂列车编组调车作业计划的优化数学模型及实现[J].长沙铁道学院学报,1996,14(2)：66-70.
[266]刘彦虎,周磊山,刘桐飞.编制摘挂列车调车作业计划的优化计算方法[J].铁道运输与经济,2008,30(3)：78-81.
[267]赵源,王巍巍,孙焰.调车钩计划编制方法研究与算法设计[J].铁道运输与经济,2004,26(9)：64-67.
[268]王雅琳,肖媛,雷友诚,等.基于排序二叉树的摘挂列车编组钩计划自动编制方法[J].中国铁道科学,2012,33(3)：116-122.
[269]高四维,高雅.调车作业智能化指挥系统的核心功能及其开发[J].铁道运输与经济,2005,27(3)：70-73.
[270]高四维,张殿业.提高调车作业指挥模型系统适应性的研究[J].交通运输系统工程与信息,2003,3(1)：84-88.
[271]高四维,张殿业.一种新的调车作业原理——“消逆法”[J].铁道学报,2003,25(5)：1-7.
[272]高四维,高雅.调车作业量发生规律研究及选编模型优化[J].中国铁道科学,2005,26(4)：107-112.
[273]高四维,高雅.集中化调车作业研究[J].铁道学报,2004,26(4)：8-13.
[274]高四维,高雅.下落方案与入线结构的“契合性”及其优化效应[J].铁道学报,2005,27(4)：10-15.
[275]高四维,高雅.对口法的“减牵”优化研究[J].铁道学报,2006,28(2)：11-16.
[2]Boysen N., Fliedner M., Jaehn F. et al. A survey on container processing in railway yards[J]. Transportation Science, http://dx.doi.org/10.1287/trsc.1120.0415.
[3]黎浩东,何世伟,王保华,等.铁路编组站阶段计划编制研究综述[J].铁道学报,2011,33(8)：13-22.
[4]Petersen E.R.. Railyard modeling:part Ⅰ. Prediction of put-through time[J]. Transportation Science,1977,11(1):37-49.
[5]Petersen E.R.. Railyard modeling:part Ⅱ. The effect of yard facilities on congestion[J]. Transportation Science,1977,11(1):50-59.
[6]Turnquist M.A., Daskin M.S.. Queuing models of classification and delay in railyards[J]. Transportation Science,1982,16(2):207-230.
[7]黄家厚.铁路编组站的系统分析及负荷的研究[J].西南交通大学学报,1986,21(4)：51-59.
[8]吴家豪.铁路编组站系统设计优化[M].北京：中国铁道出版社,1994.
[9]朱晓立,李夏苗.提速干线上编组站到解系统匹配与协调关系的研究[J].中国铁道科学,2004,25(4)：112-115.
[10]朱晓立,李夏苗.提速干线编组站出发子系统内部匹配与协调关系[J].中国铁道科学,2006,27(5)：118-121.
[11]Martland CD.. PMAKE analysis:Predicting rail yard time distributions using probabilistic train connection standards[J]. Transportation Science,1982,16(4): 476-506.
[12]Duffy M.A.. Statistical process control applied to rail freight terminal performance a case study of CSX's Radnor yard[D]. Cambridge:Massachusetts Institute of Technology, 1994.
[13]Dirnberger J.R., Barkan C.P. L. Lean railroading for improving railroad classification terminal performance:Bottleneck management methods[J]. Transportation Research Record:Journal of the Transportation Research Board,2007,1995:52-61.
[14]Dirnberger J.R. Development and application of lean railroading to improve classification terminal performance [D]. Urbana:University of Illinois Urbana-Champaign,2006.
[15]冒小栋.统计过程控制在编组站生产管理中的应用[J].铁道运输与经济,2006,28(11)：65-68.
[16]Shughart L., Ahuja R., Kumar A. et al, A comprehensive decision support system for hump yard management using simulation and optimization[R]. Technical Report, Innovation Scheduling,2009.
[17]Lin E., Cheng C.. YARDSIM:A rail yard simulation framework and its implementation in a major railroad in the U.S.[C]. Rossetti M.D., et al. Proceedings of the 2009 Winter Simulation Conference, Austin,2009. New Jersey:IEEE,2009:2532-2541.
[18]易文平.编组站到达解体系统计算机仿真[J].长沙铁道学院学报,1985,3(3)：55-61.
[19]文旭光.铁路编组站到达区间-到达场-驼峰子系统运营模拟[J].西南交通大学学报,1986,21(4)：106-112.
[20]邓西平,藤传琳.计算机模拟在编组站“到达场-驼峰”系统的应用[J].系统工程理论与实践,1988,8(4)：36-41.
[21]陶德高,方文愈.编组站双溜放驼峰到达解体系统模拟分析法的研究[J].中国铁道科学,1991,12(1)：93-102.
[22]王德,谢文炳,胡思继,等.编组站到达-解体系统与区间通过能力的协调条件[J].北方交通大学学报,1993,17(3)：265-269.
[23]张宁,张全寿.利用随机Petri网对编组站作业系统建模及分析的研究[J].铁道学报,2001,23(1)：13-18.
[24]陈刚,张殿业,张成,等.编组站解体能力影响因素的仿真技术研究[J].中国铁道科学,2006,27(2)：126-131.
[25]陈刚,张殿业.编组站运营仿真中的前向环馈仿真方法[J].中国铁道科学,2007,28(2)：94-99.
[26]陈刚.铁路编组站运营系统动态仿真[D].成都：西南交通大学,2007.
[27]孙琦,周磊山,乐逸祥,等.编组站到解系统匹配与协调关系动态仿真分析[J].系统仿真学报,2007,19(15)：3595-3598+3608.
[28]刘风先,郑时德.编组站调车场股道数计算方法的探讨[J].北方交通大学学报,1988,12(1)：37-46.
[29]孙晚华.确定编组站调车场线路数的模拟方法[J].铁道学报,1996,18(S1)：105-108.
[30]孙琦,周磊山,夏明,等.铁路编组站出发系统与区间动态能力协调仿真模型的研究[J].物流技术,2007,26(11)：132-135.
[31]易文平.编组站的最优控制、模型及应用[J].长沙铁道学院学报,1988,6(3)：80-86.
[32]易文平,秦作睿.铁路编组站作业过程实时模拟系统设计研究[J].铁道学报,1989,11(3)：67-77.
[33]刘军.基于知识的编组站作业整体仿真策略的研究[J].北方交通大学学报,1992,16(3)：40-45.
[34]刘军.用AI方法编制铁路编组站日班计划的研究[J].北方交通大学学报,1993,17(3)：270-276.
[35]刘军.一类复杂规划问题的分层规划方法[J].北方交通大学学报,1995,19(3)：401-406.
[36]钟雁,张全寿.铁路编组站调车作业计划决策支持系统的研究[J].铁道学报,1994, 1 6(4)：76-82.
[37]钟雁.一个基于动态模型的计划决策支持系统[J].北方交通大学学报,1994,18(4)：477-483.
[38]孙晚华,郑时德.编组站到达流生成方法的研究[J].北方交通大学学报,1994,18(4)：499-505.
[39]谭立刚,杨肇夏.编组站模拟系统中到达流生成的方法[J].北方交通大学学报,1998,22(6)：43-47.
[40]严霄蕙,张春迎.编组站调车作业模拟研究[J].中国矿业大学学报,2000,29(1)：97-101.
[41]刘旭,谭立刚,杨浩,等.编组站通过能力和改编能力模拟计算系统的研究[J].铁道学报,2002,24(5)：11-15.
[42]李海鹰,张超.提速干线上编组站列车到达规律[J].中国铁道科学,2007,28(6)：96-101.
[43]杨肇夏,李菊,孙晚华,等.铁路编组站技术作业模拟系统的研究[J].铁道学报,1996,18(S1)：25-32.
[44]郑时德,杨肇夏.编组站作业仿真及系统优化[M].北京：中国铁道出版社,1996.
[45]苗建瑞,蒋熙,于勇,等.铁路车站(场)列车到发与调车作业过程仿真的研究[J].北方交通大学学报,2000,24(3)：50-54.
[46]蒋熙,于勇,苗建瑞,等.编组站技术作业过程实时模拟培训系统的研究[J].铁道学报,2001,23(5)：7-11.
[47]蒋熙,苗建瑞,于勇,等.基于高层体系结构的铁路编组站综合仿真系统研究[J].系统仿真学报,2002,14(4)：481-484.
[48]贺振欢,杨肇夏.铁路编组站驼峰技术作业过程模拟实验系统的研究[J].北方交通大学学报,1998,22(3)：68-72.
[49]何世伟,宋瑞,杨浩,等.列车提速对编组站运营工作的影响研究[J].铁道学报,2000,22(5)：6-12.
[50]何世伟,宋瑞,谭立刚,等.枢纽编组站智能调度系统的设计与实现[J].北方交通大学学报,2002,26(5)：19-23.
[51]李文权.铁路区段站日工作计划优化模型及其算法的研究[D].成都：西南交通大学,1997.
[52]徐杰.区段站阶段计划自动编制模型和算法研究[D].成都：西南交通大学,2003.
[53]王正彬.区段站阶段计划调整模型与算法研究[D].成都：西南交通大学,2007.
[54]何世伟.铁路枢纽作业计划的优化编制—编组站作业计划与枢纽日班计划的模型及算法研究[D].成都：西南交通大学,1996.
[55]王明慧.编组站智能调度系统YIDS体系框架与关键技术优化理论研究[D].成都：西南交通大学,2007.
[56]薛锋.编组站调度系统配流协同优化理论与方法研究[D].成都：西南交通大学, 2009.
[57]景云.不确定条件下编组站调度系统配流模型及算法研究[D].成都：西南交通大学,2010.
[58]黎浩东.铁路编组站鲁棒阶段计划编制及调整研究[D].北京：北京交通大学,2012.
[59]牛惠民.铁路枢纽编组站作业分工整体优化的研究[D].北京：北方交通大学,1998.
[60]崔炳谋.编组站综合自动化若干问题的研究[D].北京：铁道科学研究院,2007.
[61]Burkolter D.. Capacity of railways in station areas using petri nets[D]. Zurich:ETH Zurich,2005.
[62]Herrmann T.. Stability of timetables and train routings through station regions[D]. Zurich:ETH Zurich,2006.
[63]Caimi G.. Algorithmic decision support for train scheduling in a large and highly utilised railway network[D]. Zurich:ETH Zurich,2009.
[64]Fuchsberger M.. Algorithms for railway traffic management in complex central station areas[D]. Zurich:ETH Zurich,2012.
[65]Lusby R. Optimization methods for routing trains through railway junctions[D]. Auckland:The University of Auckland,2008.
[66]Galli L.. Combinatorial and robust optimisation models and algorithms for railway applications[D]. Bologna:University of Bologna,2009.
[67]吕红霞.铁路大型客运站作业计划智能编制的优化技术和方法研究[D].成都：硒南交通大学,2008.
[68]谢楚农.客运站旅客列车运行组织优化[D].长沙：中南大学,2010.
[69]张英贵.铁路客运站股道运用优化方法与应用研究[D].长沙：中南大学,2012.
[70]贾文峥.大型铁路客运站的进路分配问题及缓冲时间研究[D].北京：北京交通大学,2010.
[71]陈彦.铁路客运站列车过站径路与调机运用优化[D].长沙：中南大学,2010.
[72]Hansmann R.. Optimal sorting of rolling stock[D]. Braunschweig:Braunschweig University of Technology,2010.
[73]Maue J.. On the problem of sorting railway freight cars[D]. Zurich:ETH Zurich,2011.
[74]Winter T.. Online and real-time dispatching problems[D]. Braunschweig:Braunschweig University of Technology,1999.
[75]Lentink R.M.. Algorithmic decision support for shunt planning[D]. Rotterdam:Erasmus University Rotterdam,2006.
[76]Van den Broek J.J.J.. MIP-based approaches for complex planning problems [D]. Eindhoven:Eindhoven University of Technology,2009.
[77]Yagar S., Saccomano F. F., Shi Q.. An efficient sequencing model for humping in a rail yard[J]. Transportation Research Part A,1983,17(4):251-262.
[78]Shi Q., Yagar S.. Case studies measuring the benefits of the HSS hump sequencing model[J]. Canadian Journal of Civil Engineering,1983,10(1):36-47.
[79]Kraft E.R., Guignard M.. A mixed integer optimization model to improve freight car classification in railroad yards[R]. Report 93-06-06, University of Pennsylvania, The Wharton School, Department of Operations and Information Management,1993.
[80]Kraft E.R.. Priority-based classification for improving connection reliability in railroad yards part I of II:integration with car scheduling[J]. Transportation Quarterly,2002, 56(1):93-105.
[81]Kraft E.R.. Priority-based classification for improving connection reliability in railroad yards part II of II:dynamic block to track assignment[J]. Transportation Quarterly,2002, 56(1):107-119.
[82]Wang X.. Improving planning for railroad yard, forestry and distribution[D]. Philadelphia:University of Pennsylvania,1997.
[83]Ferguson R.T.. Mathematical modeling of the railroad switching process[D]. Charlottesville:University of Virginia,1993.
[84]Armacost A.P.. Modeling railroad terminal operations supporting real-time network planning and control[D]. Cambridge:Massachusetts Institute of Technology,1995.
[85]Timian D.H. Current methods for optimizing rail marshalling yard operation[D]. Manhattan:Kansas State University,1994.
[86]Bektas T., Crainic T.G., Morency V.. Improving performance of rail yards through dynamic reassignments of empty cars[J]. Transportation Research Part C,2009,17(3): 259-273.
[87]Sahin G., Ahuja R.K.. Single-machine scheduling with stepwise tardiness costs and release times[J]. Journal of Industrial and Management Optimization,2011,7(4): 825-848.
[88]袁庆达,杜文,黎青松.区段站阶段计划的优化模型和算法[J].西南交通大学学报,2000,35(3)：250-254.
[89]徐杰,杜文,刘春煌.铁路技术站车流推算模型和算法[J].中国铁道科学,2005,26(4)：120-123.
[90]王正彬,杜文,吴柏青,等.基于解编顺序的阶段计划车流推算模型及算法[J].西南交通大学学报,2008,43(1)：91-95.
[91]中永生,何世伟,王保华,等.免疫算法求解编组站阶段计划配流问题研究[J].铁道学报,2009,31(4)：1-6.
[92]申永生,何世伟,黎浩东,等.自适应粒子群算法求解编组站车流推算问题的研究[J].铁道货运,2010,12(5)：5-10.
[93]黎浩东,何世伟,景云,等.考虑不同满轴约束的编组站阶段计划配流优化[J].铁道学报,2012,34(7)：1-8.
[94]何世伟,宋瑞,胡安洲.编组站阶段计划刚性与柔性优化的协调研究[J].铁道学报,1999,21(4)：1-8.
[95]He S., Song R., Hu A.. Uncertain dispatching decision and genetic algorithm for railway operations[J]. Journal of Systems Science and Systems Engineering,2000,9(2): 149-158.
[96]He S., Song R., Chaudhry S.S.. Fuzzy dispatching model and genetic algorithms for railyards operations[J]. European Journal of Operational Research,2000,124(2): 307-331.
[97]刘霆,何世伟,王保华,等.编组站调度计划随机机会约束规划模型及算法研究[J].铁道学报,2007,29(4)：12-17.
[98]黎浩东,何世伟,麻克君.编组站调度信息对阶段计划的影响及计划调整研究[J].物流技术,2010,29(1)：45-48.
[99]黎浩东,何世伟,宋瑞等.编组站阶段计划随机相关机会规划模型及算法[J].交通运输系统工程与信息,2010,10(1)：128-133.
[100]Liu B.. Study on the stochastic chance-constrained fuzzy programming model and algorithm for wagon flow scheduling in railway bureau[J]. Mathematical Problems in Engineering, doi:10.1155/2012/602153.
[101]李文权,王炜,杜文,等.铁路技术站调机运用模型及算法[J].系统工程学报,2000,15(1)：38-43.
[102]徐杰,杜文,李宗平,等.基于模拟退火算法和图着色的调机安排研究[J].铁道学报,2003,25(3)：24-30.
[103]徐杰,杜文,黎青松,等.铁路区段站决策支持系统的研究——调机的合理安排[J].四川工业学院学报,2003,22(2)：11-14.
[104]王世东,郑力,张智海,等.蚁群算法在调机运用计划中的应用[J].中国铁道科学,2007,28(3)：104-109.
[105]王烁,何世伟,黎浩东,等.禁忌搜索算法在编组站调机运用计划中的应用[J].铁道运输与经济,2011,33(2)：83-87.
[106]Keha A.B., Khowala K., Fowler J.W.. Mixed integer programming formulations for single machine scheduling problems[J]. Computers & Industrial Engineering,2009, 56(1):357-367.
[107]Zhu X., Yuan Q., Garcia-Diaz A., et al. Minimal-cost network flow problems with variable lower bounds on arc flows[J]. Computers & Operations Research,2011,38(8): 1210-1218.
[108]Koulamas C.. The single-machine total tardiness scheduling problem:Review and extensions[J], European Journal of Operational Research,2010,202(1):1-7.
[109]Garey M.R., Johnson D. S., Sethi R.. The complexity of flowshop and jobshop scheduling[J]. Mathematics of Operations Research,1976,1(2):117-129.
[110]Graham R.L., Lawler E.L., Lenstra J.K., et al. Optimization and approximation in deterministic sequencing and scheduling:A survey[J]. Annals of Discrete Mathematics, 1979,5:287-326.
[111]Fisher M.L.. The lagrangian relaxation method for solving integer programming problems[J]. Management Science,1981,27(1):1-18.
[112]Fisher M.L.. Comments on "The lagrangian relaxation method for solving integer programming problems"[J]. Management Science,2004,50(12S):1872-1874.
[113]Savelsbergh M.W.P., Uma R.N., Wein J.M.. An experimental study of LP-based approximation algorithms for scheduling problems[J]. INFORMS Journal on Computing, 2005,17(1):123-136.
[114]Gen M., Altiparmak F., Lin L.. A genetic algorithm for two-stage transportation problem using priority-based encoding[J]. OR Spectrum,2006,28(3):337-354.
[115]Ruiz R., Maroto C., Alcaraz J. Two new robust genetic algorithms for the flowshop scheduling problem[JJ. Omega,2006,34(5):461-476.
[116]Reeves C.R.. A genetic algorithm for flowshop sequencing[J]. Computers & Operations Research,1995,22(1):5-13.
[117]Murata T., Ishibuchi H., Tanaka H.. Genetic algorithms for flowshop scheduling problems[J]. Computers and Industrial Engineering,1996,30(4):1061-1071.
[118]何世伟,宋瑞,朱松年.铁路编组站阶段计划编制的模型及其算法研究[J].系统工程理论与实践,1997,17(2)：88-94.
[119]何世伟,宋瑞,朱松年.编组站阶段计划解编作业优化模型及算法[J].铁道学报,1997,19(3)：1-8.
[120]He S., Song R., Chaudhry S.S.. An integrated dispatching model for rail yards operations[J]. Computers & Operations Research,2003,30(7):939-966.
[121]何世伟,宋瑞,鲁放,等.铁路运输管理中的多机模糊排序问题及遗传算法研究[J].北京航空航天大学学报(社会科学版),2000,13(4)：4-10.
[122]王慈光.编组站列车解体方案的计数方法[J].铁道学报,2000,22(6)：1-7.
[123]王慈光.用表上作业法求解编组站配流问题的研究[J].铁道学报,2002,24(4)：1-5.
[124]王慈光.编组站静态配流网络模型[J].交通运输工程与信息学报,2003,1(2)：67-71.
[125]王慈光.编组站动态配流模型与算法研究[J].铁道学报,2004,26(1)：1-6.
[126]景云,王慈光.不确定条件下编组站动态配流模型及算法研究[J].铁道学报,2010,32(4)：8-12.
[127]郭寒英,石红国.求解编组站静态配流问题的一种改进算法[J].铁道运输与经济,2004,26(5)：74-76.
[128]景云,王慈光,王如义等.运用学习规则求解编组站静态配流问题的研究[J].铁道运输与经济,2010,32(1)：22-26.
[129]薛锋,王慈光,张展杰.编组站配流的协调优化算法[J].西南交通大学学报,2010,45(6)：932-937.
[130]薛锋,王慈光.编组站列车编组顺序的调整方法[J].铁道学报,2007,29(4)：1-5.
[131]薛锋,王慈光,罗建,等.编组站列车解体方案与编组方案的协调优化研究[J].铁道学报,2008,30(2)：1-6.
[132]曹家明,范征,毛节铭.编组站作业优化决策支持系统——解体子系统[J].铁道学 报,1993,15(4)：66-73.
[133]王明慧,赵强.编组站智能调度系统阶段计划优化模型及算法研究[J].铁道学报,2005,27(6)：1-9.
[134]王世东,郑力,张智海,等.编组站阶段计划自动编制的数学模型及算法[J].中国铁道科学,2008,29(2)：120-125.
[135]Unlu Y., Mason S.J.. Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems[J]. Computer & Industrial Engineering,2010,58(4):785-800.
[136]Krumke S.O., Thielen C.. Minimum cost flows with minimum quantities [J]. Information Processing Letters,2011,111(11):533-537.
[137]Li K., Yang S.. Non-identical parallel-machine scheduling research with minimizing total weighted completion times:Models, relaxations and algorithms[J]. Applied Mathematical Modelling,2009,33(4):2145-2158.
[138]Ruiz R., Vazquez-Rodriguez J.A.. The hybrid flow shop scheduling problem[J]. European Journal of Operational Research,2010,205(1):1-18.
[139]Ribas I., Leisten R., M.Framinan J.. Review and classification of hybrid flow shop scheduling problems from a production system and a solutions procedure perspective[J]. Computers & Operations Research,2010,37(8):1439-1454.
[140]Held M., Karp R.M.. Traveling-salesman problem and minimum spanning trees[J]. Operations Research,1970,18(6):1138-1162.
[141]Geoffrion A.M.. Lagrangean relaxation for integer programming[J]. Mathematical Programming Study.1974,2(1):82-114.
[142]Bean, J.C.. Genetic algorithms and random keys for sequencing and optimization [J]. ORSA Journal on Computing.1994,6(2):154-160.
[143]Goncalves J.F., Resende M.G.C.. Biased random-key genetic algorithms for combinatorial optimization[J]. Journal on Heuristics,2011,11(5):487-525.
[144]Resende M.G.C.. Biased random-key genetic algorithms with applications in telecommunications[J]. Top,2012,20(1):130-153.
[145]Kurz M.E., Askin R.G.. Scheduling flexible flow lines with sequence-dependent setup times[J]. European Journal of Operational Research,2004,159(1):66-82.
[146]Zandieh M., Ghomi S.M.T.F., Husseini S.M.M.. An immune algorithm approach to hybrid flow shops scheduling with sequence-dependent setup times[J]. Applied Mathematics and Computation,2006,180(1):111-127.
[147]Spears W.M., De Jong K.A.. On the virtues of parameterized uniform crossover[C]. Belew R. K., et, al. Proceedings of the Fourth International Conference on Genetic Algorithms, San Diego:1991. San Fransisco:Morgan Kaufmann,1991:230-236.
[148]杨旭东.编组站车场分工方案优选[J].长沙铁道学院学报,1986,4(3)：39-46.
[149]牛惠民,胡安洲.双向编组站车流接续的综合优化[J].铁道学报,1998,20(6)：16-21.
[150]牛惠民,胡安洲.双向编组站系统作业分工的优化模型及算法[J].中国科学(E辑),1998,28(4)：378-384.
[151]Niu H., Hu A.. Optimization model and algorithm for system operation division of labor at two-way marshaling station[J]. Science in China(series E),1998,41(5): 511-518.
[152]牛惠民.一类带有随机参数的交通优化模型及遗传算法[J].系统工程学报,2002,17(2)：103-108.
[153]牛惠民,郝克智.转场交换车流的综合优化[J].兰州铁道学院学报,1995,14(1)：73-78.
[154]牛惠民,胡安洲.双向编组站折角车流优化的模型和算法[J].北方交通大学学报,1998,22(6)：38-42.
[155]张全寿.编组站站调决策支持系统的研究[J].北方交通大学学报,1989,13(4)：64-72.
[156]牛惠民.双向编组站列车调度调整的优化模型及算法[J].中国铁道科学,2007,28(6)：102-108.
[157]薛锋,王慈光,罗建.双向编组站静态配流的优化[J].西南交通大学学报,2008,43(2)：159-164.
[158]Guignard M.. Lagrangean relaxation[J]. TOP,2003,11(2):151-228.
[159]Norman B.A., Bean J.C.. A genetic algorithm methodology for complex scheduling problems[J]. Naval Research Logistics,1999,46(2):199-211.
[160]Lusby R., Larsen J., Ehrgott M., et al. Railway track allocation:models and methods[J]. OR Spectrum,2011,33(4):843-883.
[161]Zwaneveld P.J., Kroon L.G., Romeijn H.E, et al. Routing trains through railway stations:model formulation and algorithms[J]. Transportation Science,1996,30(3): 181-194.
[162]Zwaneveld P.J. Kroon L.G.,van Hoesel S.P.M.. Routing trains through a railway station based on a node packing model [J]. European Journal of Operational Research, 2001,128(1):14-33.
[163]Kroon L.G., Romeijn H.E, Zwaneveld P.J.. Routing trains through railway stations: complexity issues[J]. European Journal of Operational Research,1997,98(3):485-498.
[164]Caimi G., Burkolter D., Herrmann T.. Finding delay-tolerant train routings through stations[C]. Fleuren H., et, al. Operations Research Proceedings 2004, Tilburg,2004. Berlin:Springer,2005:136-143.
[165]Caimi G, Burkolter D., Herrmann T., et al. Design of a railway scheduling model for dense services[J]. Networks and Spatial Economics,2009,9(1):25-46.
[166]Caprara A., Galli L., Toth P.. Solution of the train platforming problem[J]. Transportation Science,2011,45(2):246-257.
[167]Delorme X., Rodriguez J., Gandibleux X.. Heuristics for railway infrastructure saturation[J]. Electronic Notes in Theoretical Computer Science,2001,50(1):39-53.
[168]Delorme X., Gandibleux X., Rodriguez J.. GRASP for set packing problems[J]. European Journal of Operational Research,2004,153(3):564-580.
[169]Gandibleux X., Delorme X., T'Kindt V.. An ant colony optimisation algorithm for the set packing problem[C]. Dorigo M., et, al. Lecture Notes in Computer Science:Ant Colony Optimization and Swarm Intelligence, Brussels,2004. Berlin:Springer,2004, 3172:478-481.
[170]Gandibleux X., Jorge J., Angibaud S., et al. An ant colony optimization inspired algorithm for the set packing problem with application to railway infrastructure[C]. The Sixth Metaheuristics International Conference, Vienna,2005:390-396.
[171]De Luca Cardillo D., Mione N.. k L-list λ. colouring of graphs[J]. European Journal of Operational Research,1998,106(1):160-164.
[172]Billionne A.. Using integer programming to solve the train-platforming problem[J]. Transportation Science,2003,37(2):213-222.
[173]Velasquez R., Ehrgott M., Ryan D., et al. A set-packing approach to routing trains through railway station[C]. Proceedings of the 40th Annual Conference of the Operational Research Society of New Zealand, Wellington,2005:305-314.
[174]Lusby R., Larsen J., Ryan D., et al. Routing trains through railway junctions:a new set packing approach[J]. Transportation Science,2010,45(2):228-245.
[175]Lusby R., Larsen J., Ehrgott M., et al. A set packing inspired method for real-time junction train routing[J]. Computers and Operations Research,2013,40(3):713-724.
[176]Merel A., Gandibleux X., Demassey S.. Assessing railway infrastructure capacity by solving the saturation problem with an improved column generation algorithm[C].4th International Seminar on Railway Operations Modelling and Analysis, Rome,2011.
[177]Caimi G., Chudak F., Fuchsberger M. et al. A new resource-constrained multicommodity flow model for conflict-free train routing and scheduling[J]. Transportation Science,2010,45(2):212-227.
[178]Caimi G., Fuchsberger M., Laumanns M., et al. A model predictive control approach for discrete-time rescheduling in complex central railway station areas [J]. Computers and Operations Research,2012,39(11):2578-2593.
[179]Rodriguez J., Delorme X., Gandibleux X.. Railway infrastructure saturation using constraint programming approach[C]. Allan J., et, al. Computers in Railways VIII, Lemmos,2002, Southampton:WIT Press,2002:807-816.
[180]Rodriguez J.. A constraint programming model for real-time train scheduling at junctions[J]. Transportation Research Part B,2007,41(2):231-245.
[181]Rodriguez J.. Enhancement of train routing and scheduling at a terminal station with constraints programming and temporal decomposition[R], INRETS/RR-07-731-FR, France:INRETS,2007.
[182]Pellegrini P., Marliere G., Rodriguez J.. Real time railway traffic management modeling track-circuits[C]. Delling D., et, al. Proceedings of the 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems(ATMOS'12), Ljubljana:2012. Dagstuhl:Schloss Dagstuhl,2012:23-34.
[183]Corman F., Goverde R.M., D'Ariano A.. Rescheduling dense train traffic over complex station interlocking areas.//Ahuja R.K., et al. Lecture Notes in Computer Science:Robust and Online Large-Scale Optimization Models and Techniques for Transportation Systems [M], Berlin:Springer,2009,5868:369-386.
[184]Corman F., D'Ariano A., Pranzo M., et al. Effectiveness of dynamic reordering and rerouting of trains in a complicated and densely occupied station area[J]. Transportation Planning and Technology,2011,34(4):341-362.
[185]Mascis A., Pacciarelli D.. Job shop scheduling with blocking and no-wait constraints[J]. European Journal of Operational Research,2002,143(3):498-517.
[186]D'Ariano A., Pacciarelli D., Pranzo M.. A branch and bound algorithm for scheduling trains in a railway network[J]. European Journal of Operational Research,2007,183(2): 643-657.
[187]D'Ariano A., Corman F., Pacciarelli D., et al. Reordering and local rerouting strategies to manage train traffic in real-time[J]. Transportation Science,2008,42(4):405-419.
[188]Corman F., D'Ariano A., Pacciarelli D., et al. A tabu search algorithm for rerouting trains during rail operations [J]. Transportation Research Part B,2010,44(1):175-192.
[189]D'Ariano A., Pranzo M., Hansen I.A.. Conflict resolution and train speed coordination for solving real-time timetable perturbations[J]. IEEE Transactions on Intelligent Transportation Systems,2007,8(2):208-222.
[190]Flamini M., Pacciarelli D.. Real time management of a metro rail terminus[J]. European Journal of Operational Research,2008,189(3):746-761.
[191]Mannino C., Mascis A.. Optimal real-time traffic control in metro stations[J]. Operations Research,2009,57(4):1026-1039.
[192]Carey M., Carville S.. Scheduling and platforming trains at busy complex stations[J]. Transportation Research Part A,2003,37(3):195-224.
[193]Carey M., Crawford I.. Scheduling trains on a network of busy complex stations[J]. Transportation Research Part B,2007,41(2):159-178.
[194]Chakroborty P., Vikram D.. Optimum assignment of trains to platforms under partial schedule compliance [J]. Transportation Research Part B,2008,42(2):169-184.
[195]青学江,马国忠.遗传算法在区段站到发线的应用研究[J].西南交通大学学报,1998,33(4)：387-393.
[196]吕红霞,倪少权,纪洪业.技术站调度决策支持系统的研究——到发线的合理使用[J].西南交通大学学报,2000,35(3)：255-258.
[197]李文权,王炜,程世辉.铁路编组站到发线运用的排序模型和算法[J].系统工程理论与实践,2000,20(6)：75-78.
[198]徐杰,杜文,常军乾,等.基于遗传算法的区段站到发线运用优化安排[J].中国铁道科学,2003,24(2)：109-114.
[199]徐杰,杜文,李冰.铁路区段站到发线运用计划安排的优化算法[J].系统工程理论 方法应用,2003,12(3)：253-256.
[200]王正彬,杜文.铁路技术站到发线运用调整模型及算法[J].西南交通大学学报,2006,41(2)：202-205.
[201]谢楚农,黎新华.铁路客运站到发线运用优化研究[J].中国铁道科学,2004,25(5)：130-133.
[202]雷定猷,王栋,刘明翔.客运站股道运用优化模型及算法[J].交通运输工程学报,2007,7(5)：84-87.
[203]吕红霞,何大可,陈韬.基于蚁群算法的客运站到发线运用计划编制方法[J].西南交通大学学报,2008,43(2)：153-158.
[204]张英贵,雷定猷,刘明翔.铁路车站股道运用排序模型与算法[J].中国铁道科学,2010,31(2)：96-100.
[205]张英贵,雷定猷,汤波,等.铁路客运站股道运用窗时排序模型与算法[J].铁道学报,2011,33(1)：1-7.
[206]王保山,侯立新,刘海东.客运专线车站到发线运用优化方法[J].交通运输系统工程与信息,2012,12(2)：105-110.
[207]乔瑞军,朱晓宁,张天伟,等.客运专线车站到发线运用多目标优化模型[J].北京交通大学学报,2012,36(3)：57-64.
[208]苗建瑞,于勇,孟令云,等.面向稳定性的高速铁路车站作业计划优化方法[J].交通运输系统工程与信息,2012,12(3)：115-121+153.
[209]刘澜,王南,杜文.车站咽喉通过能力网络优化模型及算法研究[J].铁道学报,2002,24(6)：1-5.
[210]史峰,谢楚农,于桂芳.铁路车站咽喉区进路排列优化方法[J].铁道学报,2004,26(4)：5-9.
[211]崔炳谋,马钧培,张朴.编组站进路调度优化算法[J].中国铁道科学,2007,28(2)：100-104.
[212]龙建成,高自友,马建军,等.铁路车站进路选择优化模型及求解算法的研究[J].铁道学报,2007,29(5)：7-14.
[213]史峰,陈彦,秦进,等.铁路客运站到发线运用和接发车进路排列方案综合优化[J].中国铁道科学,2009,30(6)：108-113.
[214]陈彦,史峰,秦进,等.旅客列车过站径路优化模型与算法[J].中国铁道科学,2010,31(2)：101-107.
[215]贾文峥,毛保华,何天健,等.大型客运站股道分配问题的模型与算法[J].铁道学报,2010,32(2)：8-13.
[216]Hansen K.M.. Validation of a railway interlocking model[C]. Naftalin, M. et al. Lecture Notes in Computer Science:FME'94 Industrial Benefit of Formal Methods, Barcelona,1994. Berlin:Springer,1994,873:582-601.
[217]Montigel M.. Formal representation of track topologies by double vertex graphs[C]. Murthy T.K.S., et, al. Computers in Railways Ⅲ, Washington DC,1992. Southampton: Computational Mechanics Publications,1992:359-370.
[218]Glover F.. Maximum matching in a convex bipartite graph[J]. Naval Research Logistics Quarterly.1967,14(3):313-316.
[219]Alexe G., Alexe S., Crama Y., et al.. Consensus algorithms for the generation of all maximal bicliques[J]. Discrete Applied Mathematics.2004,145(1):11-21.
[220]Prisner E.. Bicliques in graphs Ⅰ bounds on their number[J]. Combinatorica,2000, 20(1):109-117.
[221]Faigle U., Frahlin G.. A combinatorial algorithm for weighted stable sets in bipartite graphs[J]. Discrete Applied Mathematics.2006,154(9),1380-1391.
[222]Fulkerson D. R., Gross O. A.. Incidence matrices and interval graphs[J]. Pacific Journal of Mathematics 1965,15(3):835-855.
[223]Di Stefano G., Maue J., Modelski M., et al. Models for rearranging train cars[R]. Technical Report ARRIVAL-TR-0089, ARRIVAL,2007.
[224]Gatto M., Maue J., Mihalak M., et,al. Shunting for dummies:an introductory algorithmic survey.//Ahuja R.K., et al. Lecture Notes in Computer Science:Robust and Online Large-Scale Optimization Models and Techniques for Transportation Systems[M], Berlin:Springer,2009,5868:310-337.
[225]Dahlhaus E., Horak P., Miller M., et al. The train marshalling problem[J]. Discrete Applied Mathematics,2000,103(1-3):41-54.
[226]Beygang K., Florian Dahms F., Krumke S.O.. Train marshalling problem algorithms and bounds[R]. Report in Wirtschaftsmathematik(WIMA Report) 132, University of Kaiserslautern, Department of Mathematics,2010.
[227]Brueggeman L., Fellows M., Fleischer R., et al. Train marshalling is fixed parameter tractable[C]. Kranakis E., et al. Lecture Notes in Computer Science:Proceedings of the 6th International Conference on Fun with Algorithms(FUN 2012), Venice:2012. Berlin: Springer,2012,7288:51-56.
[228]Siddiqee M.W.. Investigation of sorting and train formation schemes for a railroad hump yar[C]. Newell G.F.. Proceedings of the 5th International Symposium on the Theory of Traffic Flow and Transportation, Berkeley:1971. New York:American Elsevier Publishing Company,1972:377-387.
[229]Daganzo C.F., Dowling R.G. and Hall R.W.. Railroad classification yard throughput: the case of multistage triangular sorting[J]. Transportation Research Part A,1983,17(2): 95-106.
[230]Daganzo C.F.. Static blocking at railyards:sorting implications and track requirements [J], Transportation Science,1986,20(3):189-199.
[231]Daganzo C.F.. Dynamic blocking for railyards:part Ⅰ. homogeneous traffic[J]. Transportation Research Part B,1987,21(1):1-27.
[232]Daganzo C.F.. Dynamic blocking for railyards:part Ⅱ. heterogeneous traffic[J]. Transportation Research Part B,1987,21(1):29-40.
[233]Hansmann R.S., Zimmermann U.T. Optimal sorting of rolling stock at hump yards.// Krebs H.-J., et al. Mathematics-Key Technology for the Future:Joint Projects Between Universities and Industry[M], Berlin:Springer,2008:189-203.
[234]Jacob R., Marton P., Maue J., et al. Multistage methods for freight train classification[J]. Networks,2010,57(1):87-105.
[235]Marton P., Maue J., Nunkesser M.. An improved classification procedure for the hump yard Lausanne Triage[C]. Clausen J. et al. Proceeding of 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems(ATMOS'09), Copenhagen:2009. Dagstuhl:Schloss Dagstuhl,2009.
[236]Maue J., Nunkesser M.. Evaluation of computational methods for freight train classification schedules[R]. Technical Report ARRIVAL-TR-0184, ARRIVAL,2009.
[237]Hauser A., Maue J.. Experimental evaluation of approximation and heuristic algorithms for sorting railway cars[C]. Festa, P.. Lecture Notes in Computer Science: Proceeding of the 9th International Symposium on Experimental Algorithms, Naples: 2010. Berlin:Springer,2010,6049:154-165.
[238]Dahlhaus, E., Manne, F., Miller, M., et al. Algorithms for combinatorial problems related to train marshalling[C]. Proceeding of the Australasian Workshop on Combinatorial Algorithms, Hunter Valley,2000:7-16.
[239]Cicerone S., D'Angelo G., Di Stefano G., et al. Recoverable robustness for train shunting problems[J]. Algorithmic Operations Research,2009,4(2):102-116.
[240]Busing C., Maue J.. Robust algorithms for sorting railway cars[C]. de Berg M., et al. Lecture Notes in Computer Science:Proceedings of the 18th annual European symposium on algorithms, Part I, Liverpool:2010. Berlin:Springer,2010,6346: 350-361.
[241]李国风.表格移动调车钩计划方法[J].铁道科学技术,1965,(1)：4-9.
[242]黄世玲.按站顺编组的摘挂列车在调车中的合并线路问题.//铁道运输与经济论文集[M].北京：中国铁道出版社,1980：46-58.
[243]韩绍祖.钩计划排序原理的探讨.//铁道运输与经济论文集[M].北京：中国铁道出版社,1980：84-100.
[244]孙焰,牟世斌,张俊杰,等.求选编钩计划最优下落方案的一种最短路算法[J].铁道运输与经济,2011,33(10)：64-69.
[245]中料院数学所运筹室二组.铁道调车问题中数学方法的初步研究[J].应用数学学报,1978,1(2)：91-105.
[246]丁克诠,王志立.对随机排列落表剖分算法的一个改进[J].大连工学院学报,1987,27(4)：84+92.
[247]蔡茂诚.顺序子序列的计数问题[J].应用数学学报,1981,4(2)：141-150.
[248]朱永津,朱若鹏.任意序列重新组合为某种有序序列的研究[J].中国科学(A辑),1983,16(2)：119-127.
[249]Zhu Y., Zhu R.. Sequence reconstruction under some order-type constraints[J]. Scientia Sinica(Series A),1983,26(7):702-713.
[250]丁克诠.随机排列的伪顺序最小剖分[J].运筹学杂志,1985,4(1)：63-64.
[251]丁克诠.广义落表算法与对偶落表算法[J].数值计算与计算机应用,1987,8(2)：115-121.
[252]刘继勇.数列最优成组剖分的一个动态算法[J].国防科技大学学报,1986,8(4)：125-130.
[253]许国志,陈庆华,刘继勇.数列最优成组剖分的一个近似算法[J].科学通报,1986,31(15)：1128-1131.
[254]Xu G., Chen Q., Liu J.. An approximate algorithm of optimal digit-grouped partition of sequences[J]. Kexue Tongbao,1987,32(14):942-946.
[255]Ding K.. An algorithm for the problem of minimal number-grouped partitions of random permutations[J]. Advances In Mathematics,1986,15(1):105-106.
[256]Ding K.. An algorithm for minimal number-grouped partitions of random permutations[J]. Journal of Mathematical Research and Exposition,1990,10(4): 501-508.
[257]山东大学数学系运筹教研室表格调车法小组.表格调车法的数学理论初探[J].山东大学学报,1979,14(4)：1-15.
[258]刘德周.看图调车法[M].北京：中国铁道出版社,1979：1-214.
[259]胡安洲.统筹对口调车法及其原理.//铁道运输与经济论文集[M],北京：中国铁道出版社,1980：59-83.
[260]宋建业.摘挂列车编组调车方案优化方法的探讨[J].兰州铁道学院学报,1996,15(2)：54-63.
[261]宋建业.优化筛选摘挂列车编组调车方案的分析计算法[J].铁道学报,1999,21(3)：11-17.
[262]宋建业.车辆下落算法[J].兰州铁道学院学报,1995,14(1)：66-72.
[263]宋建业,待编车列分批解体时开口位置的确定[J].兰州铁道学院学报,1998,17(4)：102-110.
[264]宋建业.成组、混合选编方法及其计算机实现[J].兰州铁道学院学报,1999,18(2)：128-135.
[265]李夏苗,李清法.摘挂列车编组调车作业计划的优化数学模型及实现[J].长沙铁道学院学报,1996,14(2)：66-70.
[266]刘彦虎,周磊山,刘桐飞.编制摘挂列车调车作业计划的优化计算方法[J].铁道运输与经济,2008,30(3)：78-81.
[267]赵源,王巍巍,孙焰.调车钩计划编制方法研究与算法设计[J].铁道运输与经济,2004,26(9)：64-67.
[268]王雅琳,肖媛,雷友诚,等.基于排序二叉树的摘挂列车编组钩计划自动编制方法[J].中国铁道科学,2012,33(3)：116-122.
[269]高四维,高雅.调车作业智能化指挥系统的核心功能及其开发[J].铁道运输与经济,2005,27(3)：70-73.
[270]高四维,张殿业.提高调车作业指挥模型系统适应性的研究[J].交通运输系统工程与信息,2003,3(1)：84-88.
[271]高四维,张殿业.一种新的调车作业原理——“消逆法”[J].铁道学报,2003,25(5)：1-7.
[272]高四维,高雅.调车作业量发生规律研究及选编模型优化[J].中国铁道科学,2005,26(4)：107-112.
[273]高四维,高雅.集中化调车作业研究[J].铁道学报,2004,26(4)：8-13.
[274]高四维,高雅.下落方案与入线结构的“契合性”及其优化效应[J].铁道学报,2005,27(4)：10-15.
[275]高四维,高雅.对口法的“减牵”优化研究[J].铁道学报,2006,28(2)：11-16.