高速铁路列车开行方案与列车运行图协调优化理论与方法研究
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摘要
随着我国高速铁路不断发展,“四纵四横”高速铁路网络初具规模,高速铁路的发展为提升旅客出行服务水平提供了可能。然而,现有的高速铁路运营管理理论与方法仍遵循既有线管理模式,没有根据高速铁路实际运营情况和特点进行调整与改进,制约着高速铁路服务水平的提升。其中,高速铁路列车开行方案与列车运行图编制阶段之间的不协调问题最为突出。针对该问题,论文从列车开行方案与列车运行图协调优化的必要性和可行性出发,构建高速铁路列车开行方案与列车运行图协调优化体系,并对其中一系列关键的理论与方法展开研究。主要研究内容包括以下几个方面：
(1)构建高速铁路列车开行方案与列车运行图协调优化体系。以列车开行方案和列车运行图的优化目标和约束对比为基础,分析两者之间冲突的表现形式。针对综合优化问题难于求解的特点,在现有分层优化的基础上,提出运用协调信息的列车开行方案与列车运行图协调优化方法。从协调基本理论出发,设计区间通过能力修正系数、分时段给定列车开行线路信息、分等级开行线路、可调整的停站方案、开行线路换乘关系等协调信息。结合现有列车开行方案和列车运行图编制理论与方法,构建协调优化体系,并给出具体流程。
(2)研究了考虑列车运行图协调信息的系统最优条件下列车开行方案优化设计模型与算法。首先,以现有的列车开行方案研究方法中旅客需求与运输服务之间的互动关系为基础,鉴于高速铁路运输服务需要适应旅客出行需求波动的特点,提出基于时段的旅客出行服务网络构造方法以及在该网络下的系统最优客流分配模型。针对该问题的大规模特性,设计列生成算法进行求解。其次,构建基于时段的系统最优条件下开行方案优化设计模型,并设计改进的Benders分解算法获取开行方案优化结果。该算法整合列生成、Benders分解算法和免疫克隆算法,以提升算法求解效率和精度。算例结果表明列生成算法在基于时段系统最优客流分配中的高效性,改进的Benders分解算法对开行方案问题的求解效率和精度方面都优于其它对比算法。
(3)研究了考虑列车运行图协调信息的用户平衡条件下列车开行方案优化设计模型与算法。先分析现有高速铁路用户平衡客流分配方法存在的问题,设计引入失败概率的基于超级路径的用户平衡分配方法。构建基于超级路径的用户平衡分配数学模型,并证明该模型与旅客出行平衡状态之间等价性。在基于系统最优的列车开行方案优化体系基础上,提出用户平衡条件下的列车开行方案优化设计数学模型。结合该模型的特点,提出基于拉格朗日松弛算子的割平面生成方法,并构建新的Benders分解算法。算例结果表明基于超级路径客流分配方法获取结果在各时段内取得平衡状态,改进Benders分解算法能在有效时间内获取开行方案优化结果。
(4)研究了考虑列车开行方案协调信息的列车运行图优化编制模型与算法。分析列车运行图概念与特点,提出高速铁路时空网络构建方法,网络中采用车站通过时空弧、车站停车时空弧和车站附加等待弧描述列车在车站内部的运行,以此得到可调整停站方案的时空网络。进一步以协调信息为基础,提出列车运行时间区域的概念,设计列车开行方案协调信息影响下的列车运行图优化编制数学模型。针对时空网络规模较大的特点,提出改进分支定价求解列车运行图。为加速算法的求解进程,提出启发式的列车时空路径生成方法。在列车运行图编制结果的基础上,提出协调收敛机制和协调反馈信息设置方法,构建完整的协调优化流程。算例结果表明基于时空网络的列车运行图优化编制模型能获取符合运营要求的列车运行图,改进分支定价算法的改进措施能提升算法效率,保证算法在有效时间内获取优化解。同时,算例结果还表明所设置协调收敛条件与反馈协调信息有效性。
(5)进行基于实际高速铁路网络的实例验证研究。以我国实际高速铁路路网为研究对象,结合实际客运需求数据和路网实际情况,运用基于超级路径的用户平衡列车开行方案优化方法设计开行方案,并运用改进分支定价算法求解列车运行图优化模型。通过协调优化迭代求解获取最终的列车开行方案与列车运行图优化设计结果。实例结果表明协调优化方法对于提升旅客服务水平和列车运行图效率、降低企业运营成本的有效性,能将协调优化方法应用于实际高速铁路运营管理问题中。进一步通过数学实验,得出旅客广义出行费用系数和列车时空网络构建中合理行车时间区域设置方法,提升论文研究方法应用于实际案例的可行性。
With the development of China's high-speed rail system, an initial "four vertical and four horizontal" high-speed rail network has constructed. However, the current high-speed rail transportation planning method, which is evolved from the method of conventional lines, may be the bottleneck to improve the service of level of passengers' traveling. In the planning process, the conflicts of train line planning problem and train timetabling problem are the most prominent problem. Aiming to solve that problem, a coordination optimization method is proposed by italicizing the feasibility and necessity of the coordination method to train line planning problem and train timetabling problem. A series relevant procedure has been studied in the theory and method. And the main research contents include the following:
(1) The mechanism of coordination optimization method to train line planning problem and train timetabling problem. Comparing the objective functions and constraints of train line planning problem and train timetabling problem, the conflicts of two problems are italicized. A coordination optimization is designed on the basis of current planning process with the coordination information. The coordination information including correction parameters for section passing capacity, adjustment stopping plans, service line information with different periods, different train priority and transfer connection between service lines are proposed. Then, by adjusting the current method for train line planning problem and train timetabling problem, the coordination optimization method is designed with its flowchart.
(2) The model and algorithm for train line planning optimization problem based on system optimization and train timetable coordination information. It is certainly that train line planning problem should consider the relationship between the passenger demand and transportation service. Moreover, it should meet the requirement for the fluctuation of passenger demand. Therefore, an improved dynamic service network with different periods is adopted for designing train line planning optimization model. Due to the large scale of system optimization traffic assignment, a column generation is implemented. Furthermore, an improved Benders decomposition algorithm, which combines the column generation, general Benders decomposition and immune clonal methods, is designed to promote the efficiency and accuracy of solving process.
(3) The model and algorithm for train line planning optimization problem based on user equilibrium and train timetable coordination information. Aiming to improve the current user equilibrium traffic assignment, the failure probability and strategy measure are adopted in the user equilibrium assignment method. The mathematical model of user equilibrium traffic assignment is presented, and the equivalence of the optimal solution and the equilibrium state is also proved. Train line planning coordination optimization model based on user equilibrium is designed. An improved Benders decomposition algorithm is proposed, and the cuts are generated by Lagrangian operator.
(4) The model and algorithm for train timetabling optimization problem with train line planning coordination information. An improved time-space network is designed to adjust the solution of train line planning problem. The station passing time-space arc, station dwell time-space arc and additional waiting time-space arc are implemented to describe the train movement in sections more precisely. The train running area in the time-space network is proposed to meet the need of coordination information. Then, the train timetabling optimization model is addressed. The coordination convergence rule is proposed based on the train timetabling optimization model, and the correction parameters for section passing capacity are adopted as the feedback information to re-optimization train line planning problem. A branch-and-price algorithm is designed to cope with large scale of the problem. Moreover, the algorithm can speed up the solving process with the heuristic time-space path generation.
(5) The case studies for high-speed rail network. A China's high-speed rail network is selected for the case study. Then, the model and algorithm for train line planning optimization problem based on user equilibrium are adopted to solve train line planning problem. The branch-and-price is implemented to get the train timetables. The final coordination solutions are acquired iteratively. The results show that the coordination information can promote the efficiency of the train timetable and service level of passenger. The methods for setting parameters in the solving process are tested by a series mathematical experiment on the case study to make the method easier to apply in the real-life problems.
(1)构建高速铁路列车开行方案与列车运行图协调优化体系。以列车开行方案和列车运行图的优化目标和约束对比为基础,分析两者之间冲突的表现形式。针对综合优化问题难于求解的特点,在现有分层优化的基础上,提出运用协调信息的列车开行方案与列车运行图协调优化方法。从协调基本理论出发,设计区间通过能力修正系数、分时段给定列车开行线路信息、分等级开行线路、可调整的停站方案、开行线路换乘关系等协调信息。结合现有列车开行方案和列车运行图编制理论与方法,构建协调优化体系,并给出具体流程。
(2)研究了考虑列车运行图协调信息的系统最优条件下列车开行方案优化设计模型与算法。首先,以现有的列车开行方案研究方法中旅客需求与运输服务之间的互动关系为基础,鉴于高速铁路运输服务需要适应旅客出行需求波动的特点,提出基于时段的旅客出行服务网络构造方法以及在该网络下的系统最优客流分配模型。针对该问题的大规模特性,设计列生成算法进行求解。其次,构建基于时段的系统最优条件下开行方案优化设计模型,并设计改进的Benders分解算法获取开行方案优化结果。该算法整合列生成、Benders分解算法和免疫克隆算法,以提升算法求解效率和精度。算例结果表明列生成算法在基于时段系统最优客流分配中的高效性,改进的Benders分解算法对开行方案问题的求解效率和精度方面都优于其它对比算法。
(3)研究了考虑列车运行图协调信息的用户平衡条件下列车开行方案优化设计模型与算法。先分析现有高速铁路用户平衡客流分配方法存在的问题,设计引入失败概率的基于超级路径的用户平衡分配方法。构建基于超级路径的用户平衡分配数学模型,并证明该模型与旅客出行平衡状态之间等价性。在基于系统最优的列车开行方案优化体系基础上,提出用户平衡条件下的列车开行方案优化设计数学模型。结合该模型的特点,提出基于拉格朗日松弛算子的割平面生成方法,并构建新的Benders分解算法。算例结果表明基于超级路径客流分配方法获取结果在各时段内取得平衡状态,改进Benders分解算法能在有效时间内获取开行方案优化结果。
(4)研究了考虑列车开行方案协调信息的列车运行图优化编制模型与算法。分析列车运行图概念与特点,提出高速铁路时空网络构建方法,网络中采用车站通过时空弧、车站停车时空弧和车站附加等待弧描述列车在车站内部的运行,以此得到可调整停站方案的时空网络。进一步以协调信息为基础,提出列车运行时间区域的概念,设计列车开行方案协调信息影响下的列车运行图优化编制数学模型。针对时空网络规模较大的特点,提出改进分支定价求解列车运行图。为加速算法的求解进程,提出启发式的列车时空路径生成方法。在列车运行图编制结果的基础上,提出协调收敛机制和协调反馈信息设置方法,构建完整的协调优化流程。算例结果表明基于时空网络的列车运行图优化编制模型能获取符合运营要求的列车运行图,改进分支定价算法的改进措施能提升算法效率,保证算法在有效时间内获取优化解。同时,算例结果还表明所设置协调收敛条件与反馈协调信息有效性。
(5)进行基于实际高速铁路网络的实例验证研究。以我国实际高速铁路路网为研究对象,结合实际客运需求数据和路网实际情况,运用基于超级路径的用户平衡列车开行方案优化方法设计开行方案,并运用改进分支定价算法求解列车运行图优化模型。通过协调优化迭代求解获取最终的列车开行方案与列车运行图优化设计结果。实例结果表明协调优化方法对于提升旅客服务水平和列车运行图效率、降低企业运营成本的有效性,能将协调优化方法应用于实际高速铁路运营管理问题中。进一步通过数学实验,得出旅客广义出行费用系数和列车时空网络构建中合理行车时间区域设置方法,提升论文研究方法应用于实际案例的可行性。
With the development of China's high-speed rail system, an initial "four vertical and four horizontal" high-speed rail network has constructed. However, the current high-speed rail transportation planning method, which is evolved from the method of conventional lines, may be the bottleneck to improve the service of level of passengers' traveling. In the planning process, the conflicts of train line planning problem and train timetabling problem are the most prominent problem. Aiming to solve that problem, a coordination optimization method is proposed by italicizing the feasibility and necessity of the coordination method to train line planning problem and train timetabling problem. A series relevant procedure has been studied in the theory and method. And the main research contents include the following:
(1) The mechanism of coordination optimization method to train line planning problem and train timetabling problem. Comparing the objective functions and constraints of train line planning problem and train timetabling problem, the conflicts of two problems are italicized. A coordination optimization is designed on the basis of current planning process with the coordination information. The coordination information including correction parameters for section passing capacity, adjustment stopping plans, service line information with different periods, different train priority and transfer connection between service lines are proposed. Then, by adjusting the current method for train line planning problem and train timetabling problem, the coordination optimization method is designed with its flowchart.
(2) The model and algorithm for train line planning optimization problem based on system optimization and train timetable coordination information. It is certainly that train line planning problem should consider the relationship between the passenger demand and transportation service. Moreover, it should meet the requirement for the fluctuation of passenger demand. Therefore, an improved dynamic service network with different periods is adopted for designing train line planning optimization model. Due to the large scale of system optimization traffic assignment, a column generation is implemented. Furthermore, an improved Benders decomposition algorithm, which combines the column generation, general Benders decomposition and immune clonal methods, is designed to promote the efficiency and accuracy of solving process.
(3) The model and algorithm for train line planning optimization problem based on user equilibrium and train timetable coordination information. Aiming to improve the current user equilibrium traffic assignment, the failure probability and strategy measure are adopted in the user equilibrium assignment method. The mathematical model of user equilibrium traffic assignment is presented, and the equivalence of the optimal solution and the equilibrium state is also proved. Train line planning coordination optimization model based on user equilibrium is designed. An improved Benders decomposition algorithm is proposed, and the cuts are generated by Lagrangian operator.
(4) The model and algorithm for train timetabling optimization problem with train line planning coordination information. An improved time-space network is designed to adjust the solution of train line planning problem. The station passing time-space arc, station dwell time-space arc and additional waiting time-space arc are implemented to describe the train movement in sections more precisely. The train running area in the time-space network is proposed to meet the need of coordination information. Then, the train timetabling optimization model is addressed. The coordination convergence rule is proposed based on the train timetabling optimization model, and the correction parameters for section passing capacity are adopted as the feedback information to re-optimization train line planning problem. A branch-and-price algorithm is designed to cope with large scale of the problem. Moreover, the algorithm can speed up the solving process with the heuristic time-space path generation.
(5) The case studies for high-speed rail network. A China's high-speed rail network is selected for the case study. Then, the model and algorithm for train line planning optimization problem based on user equilibrium are adopted to solve train line planning problem. The branch-and-price is implemented to get the train timetables. The final coordination solutions are acquired iteratively. The results show that the coordination information can promote the efficiency of the train timetable and service level of passenger. The methods for setting parameters in the solving process are tested by a series mathematical experiment on the case study to make the method easier to apply in the real-life problems.
引文
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