基于周期事件系统的高速铁路列车运行图编制模型及算法研究
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摘要
列车运行图(基本图)编制问题存在着两个基本特征,一是问题规模庞大,关系复杂；二是隐含了一个周而复始的周期性条件。根据离散事件动态系统(DEDS)的建模思路,按路网单元对列车运行轨迹进行分割,通过关键事件集实现列车运行曲线离散化是研究运行图编制问题最基本的方法。另一方面,基于周期事件调度问题(PESP)的相关研究是解决周期(节拍)列车运行图的重要方法,虽然与普通列车运行图“周期”特征在含义上有所不同,但是同样为描述周期发生的事件提供了支持。运行图编制问题的本质是NP问题也就无法确定的解的解析形式,有时候针对特定的目标甚至精确解也无法得出。由列车运行图的定序优化理论与列车越行行为序关系分析可知,如果给定了列车的序,那么可以在一个确定多项式时间内找出这个列车序下的最优方案或证明该列车序不可行,因此提出了列车运行图编制中列车间的关系和特征问题新的思考。本文在综合了既有列车运行图编制以及定序列车运行图编制的研究基础上,提出了并定义了周期事件系统并以此为基础根据列车间的关系建模研究高速铁路列车运行图编制方法与计算机编制技术。本文的研究工作和创新体现在以下几点：
(1)综合既有非周期列车运行图和周期运行图的编制建模思想与理论基础,将高速铁路列车运行图归结为离散事件特征与周期特征。因此首先提出并定义了周期事件系统,该系统研究一类数量为有限集,沿有向周期环以固定周期值T循环往复发生的离散事件群体。相对于既有的研究方法,周期事件系统建模更着重对事件间位差序尤其是紧邻序关系,在问题的描述上采用定义在周期环上向量及运算进行刻画。在此基础上提出了周期事件方程和周期向量方程,这两组以向量为核心的等式关系表征了周期事件系统的可行规则和约束,同时也是建模分析的基本工具。结合这两组方程提出了周期事件系统一般模型和问题解决五阶段策略。
(2)建立了宏观路网、基本路网及微观路网三层路网拓扑结构,以适应在不同的场景下针对性的列车运行图编制问题建模策略。提出了基于PES和三层路网架构表述的高速铁路列车运行图编制模型。通过基于周期向量方程二次支撑扩展技术将原模型化简,大为降低了问题的复杂度提高了可解性和解的通用性。设计了一种遗传算法来解决扩展表示后的向量规划,通过算例证明该算法有效。
(3)针对高速铁路列车运行图的实践需求,提出了高速铁路列车运行图模板化编制思路。所谓模板表征了特定的列车轨迹特征及列车群关系特征,这些特征可能来源于列车运行的规则要求,也可能来源于人工经验的总结与表达。基于PES的列车运行图编制理论可以很好的应用于列车运行图的模板化编制问题。在此基础上研究了高速铁路列车运行图编图过程中常见的问题,如矩形施工天窗、到发线判定与安排以及定点约束问题。
(4)设计开发了基于PES的高速铁路列车运行图模板化编制系统,实现理论与实践上的相互契合。
Two basic characteristics can be found in a train scheduling (off-line) problem, the huge discrete solving scale, and the periodic cycle implied in the schedule. According to the modeling c of discrete event dynamic systems (DEDS), the running trajectories of trains are divided into discrete events series by railway network units, which is the most fundamental method to research train scheduling problem via discretization of train through a set of critical event. On the other hand, the relevant studies on periodic event scheduling problem (PESP) are important methods to makeup periodic train timetable. Although being different from regular train timetable in the meaning of "periodic", PESP theory provides methodology support for the description of periodic events. A train scheduling problem is regarded as a NP problem in nature, and the analytical form of undetermined solutions becomes rarely found. With the research on ordinal optimization theory of train scheduling and ordinal relation analysis of train overtaking behavior, it is known that the event value is not important sometimes. As the train sequence is given, the solutions can be work out in a fixed polynomial time that are optimal for the train sequence or proved to be unfeasible. As ordinal optimization problem eventually is converted to event time point value model for solution, a reflec-tion is stimulated about the relationship between the train in train diagram and the implied periodic feature, mentioned previously.
Based on a combination of DEDS and PESP Train Working Diagram methodolog-ies and ordinal train scheduling theory, Periodic Event System concept is defined and modeling of the relationship between trains is proposed. By these preliminary studies, high-speed railway train scheduling problem is discussed. Briefly, the work and innova-tion are reflected in the following aspects:
(1)With the reference of DEDS and PESP train scheduling conception and theore-tical basis, a novel methodology named Periodic Event System (PES) is proposed and defined, which concentrates on the discrete and periodic nature of a train schedule. The PES can be regarded as a finite set of discrete events, occurring constantly along the direction on a periodic ring with a fixed periodic value T. Relative to existing research, PES focuses on the ordinal shaft of the periodic events, especially for the adjoining events. With description mechanism of periodic ring and vectors defined, two analysis equations called periodic events equation and periodic vectors equation are provided as elementary tools, expressing the core feasible rules and constraints. With this under-standing, a PES generic model and a five-stage problem-solving strategy are given.
(2) Three-layer railway network is proposed, forming out of macro network, basic network and micro network to accommodate the schedule modeling strategy in different scenarios. Based on PES analysis methodology and the three-layer network structure, a specific train scheduling theory for high-speed railway is presented. The model is stand-ardized and simplified via double spanning transformation with less complexity and more accessible to the solution. A specific generic algorithm is designed to work out the programming. The validity and feasibility are proved by a sample.
(3)For the requirement of high-speed railway organization practice and applica-tion, a template scheduling methodology is presented. The template refers to certain features of train trajectories and relation between trains, which are abstracted from operation rules of railway system or human experience. The PES based train scheduling technique is fairly suited for the template generating. With this regard, some common problems are discussed for template schedule methodology, such as rectangle railway construc tion window, arrival or departure tracks occupation and fixed time constraints.
(4) Design and develop a PES based high-speed railway train scheduling computer supported system, integrating theory with practice.
(1)综合既有非周期列车运行图和周期运行图的编制建模思想与理论基础,将高速铁路列车运行图归结为离散事件特征与周期特征。因此首先提出并定义了周期事件系统,该系统研究一类数量为有限集,沿有向周期环以固定周期值T循环往复发生的离散事件群体。相对于既有的研究方法,周期事件系统建模更着重对事件间位差序尤其是紧邻序关系,在问题的描述上采用定义在周期环上向量及运算进行刻画。在此基础上提出了周期事件方程和周期向量方程,这两组以向量为核心的等式关系表征了周期事件系统的可行规则和约束,同时也是建模分析的基本工具。结合这两组方程提出了周期事件系统一般模型和问题解决五阶段策略。
(2)建立了宏观路网、基本路网及微观路网三层路网拓扑结构,以适应在不同的场景下针对性的列车运行图编制问题建模策略。提出了基于PES和三层路网架构表述的高速铁路列车运行图编制模型。通过基于周期向量方程二次支撑扩展技术将原模型化简,大为降低了问题的复杂度提高了可解性和解的通用性。设计了一种遗传算法来解决扩展表示后的向量规划,通过算例证明该算法有效。
(3)针对高速铁路列车运行图的实践需求,提出了高速铁路列车运行图模板化编制思路。所谓模板表征了特定的列车轨迹特征及列车群关系特征,这些特征可能来源于列车运行的规则要求,也可能来源于人工经验的总结与表达。基于PES的列车运行图编制理论可以很好的应用于列车运行图的模板化编制问题。在此基础上研究了高速铁路列车运行图编图过程中常见的问题,如矩形施工天窗、到发线判定与安排以及定点约束问题。
(4)设计开发了基于PES的高速铁路列车运行图模板化编制系统,实现理论与实践上的相互契合。
Two basic characteristics can be found in a train scheduling (off-line) problem, the huge discrete solving scale, and the periodic cycle implied in the schedule. According to the modeling c of discrete event dynamic systems (DEDS), the running trajectories of trains are divided into discrete events series by railway network units, which is the most fundamental method to research train scheduling problem via discretization of train through a set of critical event. On the other hand, the relevant studies on periodic event scheduling problem (PESP) are important methods to makeup periodic train timetable. Although being different from regular train timetable in the meaning of "periodic", PESP theory provides methodology support for the description of periodic events. A train scheduling problem is regarded as a NP problem in nature, and the analytical form of undetermined solutions becomes rarely found. With the research on ordinal optimization theory of train scheduling and ordinal relation analysis of train overtaking behavior, it is known that the event value is not important sometimes. As the train sequence is given, the solutions can be work out in a fixed polynomial time that are optimal for the train sequence or proved to be unfeasible. As ordinal optimization problem eventually is converted to event time point value model for solution, a reflec-tion is stimulated about the relationship between the train in train diagram and the implied periodic feature, mentioned previously.
Based on a combination of DEDS and PESP Train Working Diagram methodolog-ies and ordinal train scheduling theory, Periodic Event System concept is defined and modeling of the relationship between trains is proposed. By these preliminary studies, high-speed railway train scheduling problem is discussed. Briefly, the work and innova-tion are reflected in the following aspects:
(1)With the reference of DEDS and PESP train scheduling conception and theore-tical basis, a novel methodology named Periodic Event System (PES) is proposed and defined, which concentrates on the discrete and periodic nature of a train schedule. The PES can be regarded as a finite set of discrete events, occurring constantly along the direction on a periodic ring with a fixed periodic value T. Relative to existing research, PES focuses on the ordinal shaft of the periodic events, especially for the adjoining events. With description mechanism of periodic ring and vectors defined, two analysis equations called periodic events equation and periodic vectors equation are provided as elementary tools, expressing the core feasible rules and constraints. With this under-standing, a PES generic model and a five-stage problem-solving strategy are given.
(2) Three-layer railway network is proposed, forming out of macro network, basic network and micro network to accommodate the schedule modeling strategy in different scenarios. Based on PES analysis methodology and the three-layer network structure, a specific train scheduling theory for high-speed railway is presented. The model is stand-ardized and simplified via double spanning transformation with less complexity and more accessible to the solution. A specific generic algorithm is designed to work out the programming. The validity and feasibility are proved by a sample.
(3)For the requirement of high-speed railway organization practice and applica-tion, a template scheduling methodology is presented. The template refers to certain features of train trajectories and relation between trains, which are abstracted from operation rules of railway system or human experience. The PES based train scheduling technique is fairly suited for the template generating. With this regard, some common problems are discussed for template schedule methodology, such as rectangle railway construc tion window, arrival or departure tracks occupation and fixed time constraints.
(4) Design and develop a PES based high-speed railway train scheduling computer supported system, integrating theory with practice.
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