基于复杂网络理论的城市公交网络生成与优化研究
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摘要
目前，我国汽车产业得到前所未有的发展，城市居民出行结构发生了深刻的变化，小汽车出行比例大幅度增加，居民出行机动性提高，同时导致道路资源极度短缺，交通拥堵现象从最初的北上广逐渐向二线城市蔓延，目前已成为我国各大中城市屡见不鲜的事情，并越来越严重。如何缓解和治理城市交通拥堵是摆在交通学者面前的一道难题。大力发展城市公共交通来缓解城市交通拥堵已成为共识，但城市公共交通尤其是常规公交，与小汽车共享道路资源，交通拥堵对其影响较大，为使城市公共交通有效应对交通拥堵，最大限度发挥其优势，必须合理生成和优化城市公交网络。
城市公交网络的生成与优化是一项复杂性较强的研究，复杂网络理论研究全面展开后，许多学者便将其用于城市公交网络复杂性的研究，探索它的演化机制和形成机理，但对于公交网络生成与优化层面，多是通过研究公交网络复杂统计指标分布规律，定性分析其存在的问题，并提出一些措施对网络进行优化，对于公交网络应具有的网络拓扑结构特征及其生成优化的数学模型鲜有研究，同时在公交网络生成与优化模型中，考虑交通拥堵对公交系统和居民出行需求的影响，现有文献尚未对其进行有针对性的研究。
为此本文在国内外研究的基础上，依托国家自然科学基金项目“城市公交网络一体化设计中关键模型与算法研究（51078168）”，基于复杂网络理论和交通拥堵分析，对城市公交网络生成与优化相关方法进行研究，以站点研究为切入点，分别设计了基于效率驱动的复杂公交网络生成算法、基于引力驱动的复杂公交网络生成算法和基于边介数的城市公交网络优化模型，并对城市公交站间距优化进行了研究。本文所完成的科研成果具体如下：
1.以城市公交站点为研究中心，首先对城市公交站点进行分析，然后基于分形理论对站点需求特征进行了分析，结果表明统计间隔为2min时，站点需求具有明显的分形特征；对公交站点类型进行分析，并根据客流量对首末站点、中途站点的数量确定和网络生成优化中的处理方法进行了分析，在交通小区OD矩阵已知的基础上，基于双约束重力模型研究了公交站点OD矩阵的预测方法。
2.对城市公交网络生成与优化的基础问题进行研究，在分析Dijkstra算法的基础上，设计了基于k-1最短路的k最短路算法；分析城市公共交通线网规划的规划目标和约束条件，设计了基于站点容量限制的城市公交效率网络生成算法。
3.为解决最优城市公交网络问题，分析随机网络、小世界网络和无标度网络三种典型的复杂网络，在网络中客流需求较大的情况下，无标度网络的优势比较突出，这是由其拓扑性质决定的。以Barabasi和Albert提出的经典BA模型为基础，基于增长机制和偏好机制提出两个复杂公交网络生成算法：基于效率驱动的复杂公交网络生成算法和基于引力驱动的复杂公交网络生成算法，它们都遵循运输效率最高，网络容量最大的公交网络生成目标，不同之处在于前者以运输效率为驱动，后者考虑了站点之间的阻抗和线路方向的问题，以站点之间的引力为驱动。
4.为优化城市公交网络时缓解交通拥堵对公交系统的影响，通过分析居民出行策略和拓展边介数，引入相关参数以模拟居民在交通拥堵时的出行策略变化，并定义了有效权重、有效路径、有效线路和有效网络，从而构建基于边介数的城市公交网络优化模型及其求解算法；分析零流网络效率、拥挤网络效率、网络效率损失、平均出行时间、平均出行距离、平均出行速度等网络指标与模型参数的关系，确定模型参数的物理意义，并对其进行标定。
5.为结合数学模型和经验设置站点的优势，提出二步骤法计算实际站间距。第一步根据模型假设，建立了站间距最优模型，计算理想条件下的最优站间距；第二步通过分析站间距影响因素，将其归为五个综合因素，即当量加速度、车辆区间平均速度、车辆站点停车时间、乘客平均出行距离和乘客平均到站速度，从而建立站间距修正模型，通过对最优站间距的修正，完成城市公交站点的设置。
6.借鉴《长春经济技术开发区公共交通规划（2011-2020）》项目的相关成果，对本文提出的模型和算法进行实证。首先分析长春经开区公交概况，确定首末站点和中途站点数量及布局，并对站点需求进行预测；然后生成长春经开区的新增线路、优化其现有不合理线路；最后对公交站间距重新进行优化和布局，并对长春经开区公交网络生成优化结果进行评价分析。
本文的研究成果可拓展复杂网络理论的应用范围，丰富城市公共交通规划理论体系，提高城市公交网络对交通拥堵的应对能力，促进城市公交系统健康有序的发展，具有较高的理论价值和实际意义。
China's automobile industry had obtained an unprecedented developmentduring the global economic crisis. The urban trips structure had undergone profoundchanges. The proportion of car trips had obtained a significant increase. Residents′travel mobility had improved. These had caused roads blocked and the phenomenonis spreading from initial Beijing, Shanghai, Guangzhou to second-tier cities. NowTraffic congestion has been common things in the cities and it has been more andmore serious. The scholars have to solve the problem that how to relieve and governurban traffic congestion. Vigorously developing urban public transport to ease urbantraffic congestion has become a consensus. But urban public transport, especially thecommon bus, has to share the road resources with cars. Therefore traffic congestionhas comparatively large effects on it. In order to make urban public transporteffectively deal with traffic congestion and play to its maximized advantages wehave to reasonably generate and optimize the urban public transport network.
Urban public transport network generation and optimization are complexstudies. Multi scholars used complex network theory for the complexity of the urbanpublic transport network after the beginning of its studies. They explored itsevolution mechanism and formation mechanism. But for transit network generationand optimization these scholars studied the distribution law of its complex statisticalindicators, qualitatively analyzed its problems and proposed measures to optimizethe network. They rarely study the bus network topology characteristics and thenetwork mathematical models. When generating and optimizing bus network,consider the effects of traffic congestion on the public transport system and residentstravel demand. The existing literature has not yet targeted research on it.
Therefore the paper relies on the National Natural Science Foundation of“Research on the key models and its algorithms in urban transit network integrateddesign（51078168）” to study transit network on the base of domestic and foreignstudies. Make the station research as an entry point, Three models were established,namely complex public transport network model based on efficiency-driven, complex public transport network model based on gravitation-driven and urbantransit network optimization model based on the edge betweenness. Then urban busstop spacing optimization was studied. The completed research results are asfollows:
1. Make urban bus station as research center. Firstly analyze urban bus station,then analyze station demand characteristics on the base of Fractal Theory. Theresults show that when the statistics interval is2min the station demand haveapparent fractal characteristics. Analyze bus stop type, then according to the trafficdetermine the number of first and last stop, the middle stop and their treatmentmethods. Apply double constrained gravity model to predict the bus stops OD matrixwith obtaining traffic zone OD matrix.
2. Study the basic issue of urban public transport network generation andoptimization. Design k shortest path algorithm with k-1shortest path on the base ofDijkstra algorithm. Analyze planning objectives and constraints of urban publictransit network planning, build urban public transport efficiency networkinfrastructure model based on station capacity restrictions.
3. In order to obtain best urban transit network, analyze three typical complexnetworks of random networks, small world networks and scale-free networks. Whenlarge passenger demand appear in the network the scale-free networks get theadvantage because of their topological properties. Analyze classic BA model fromBarabasi and Albert, propose two complex public transport network generationalgorithms based on growth mechanisms and preferences mechanism, namelycomplex public transport network generation algorithm based on efficiency-drivenand complex public transport network generation algorithm based on thegravity–driven. They all follow the maximized transport efficiency and networkcapacity as bus networks generation targets. The difference is that the former wasdriven by transport efficiency and the latter had considered the impedance betweenthe stations and the line direction, it is driven by the gravitation between the stations.
4. In order to relieve traffic congestion on the public transport system in theurban public transport network optimization this research introduced relevantparameters to simulate the residents travel strategy changes in the traffic congestionby analyzing the residents travel strategy and expanding the edge betweenness, Thendefine the effective weight, the effective path, the effective lines and the effectivenetwork to build the urban public transport network optimization model and its algorithm based on edge betweenness. It also determined the physical meaning of themodel parameters and their calibration by analyzing the relationship between themodel parameters and network indicators such as zero-flow network efficiency, thecrowded network efficiency, network efficiency loss, the average travel time, theaverage trip distance, the average trip speed etc.
5. The paper proposed a two-step method which could calculate the actualstation spacing to combine the advantage of mathematical models and experience toset up stations. The first step is to establish the station spacing optimal model tocalculate the optimal station spacing under the ideal conditions based on modelassumes. The second step is to analyze the affect factors of station spacing andclassify them into five combination factors, namely the equivalent acceleration, thespace mean speed of the vehicle, the parking time of vehicle at stop, averagepassenger trip distance and average arrival speed of passenger. This researchcompleted the setting of urban bus stops through building a station spacingcorrection model to correct the optimal station spacing.
6. By learning from the related outcomes about the project of “Public transportplanning in Changchun Economic and Technological Development Zone(2011-2020)”, the paper made the empirical study on the proposed model andmethod. Firstly analyze the current situation of public transit in Changchun,determine the number and layout of the first and last station and middle station, thenpredict station requirements. Next generate new lines in Changchun and optimizetheir existing unreasonable lines. Finally re-optimized the station spacing, evaluatethe generation and optimization results of transit network in Changchun Economicand Technological Development Zone.
The results of this research can expand the range of applications of complexnetwork theory, rich urban public transport planning theory system, improve theresponse capacity of urban public transport network to traffic congestion, promotethe healthy and orderly development of the urban public transport system, have hightheoretical value and practical significance.
城市公交网络的生成与优化是一项复杂性较强的研究，复杂网络理论研究全面展开后，许多学者便将其用于城市公交网络复杂性的研究，探索它的演化机制和形成机理，但对于公交网络生成与优化层面，多是通过研究公交网络复杂统计指标分布规律，定性分析其存在的问题，并提出一些措施对网络进行优化，对于公交网络应具有的网络拓扑结构特征及其生成优化的数学模型鲜有研究，同时在公交网络生成与优化模型中，考虑交通拥堵对公交系统和居民出行需求的影响，现有文献尚未对其进行有针对性的研究。
为此本文在国内外研究的基础上，依托国家自然科学基金项目“城市公交网络一体化设计中关键模型与算法研究（51078168）”，基于复杂网络理论和交通拥堵分析，对城市公交网络生成与优化相关方法进行研究，以站点研究为切入点，分别设计了基于效率驱动的复杂公交网络生成算法、基于引力驱动的复杂公交网络生成算法和基于边介数的城市公交网络优化模型，并对城市公交站间距优化进行了研究。本文所完成的科研成果具体如下：
1.以城市公交站点为研究中心，首先对城市公交站点进行分析，然后基于分形理论对站点需求特征进行了分析，结果表明统计间隔为2min时，站点需求具有明显的分形特征；对公交站点类型进行分析，并根据客流量对首末站点、中途站点的数量确定和网络生成优化中的处理方法进行了分析，在交通小区OD矩阵已知的基础上，基于双约束重力模型研究了公交站点OD矩阵的预测方法。
2.对城市公交网络生成与优化的基础问题进行研究，在分析Dijkstra算法的基础上，设计了基于k-1最短路的k最短路算法；分析城市公共交通线网规划的规划目标和约束条件，设计了基于站点容量限制的城市公交效率网络生成算法。
3.为解决最优城市公交网络问题，分析随机网络、小世界网络和无标度网络三种典型的复杂网络，在网络中客流需求较大的情况下，无标度网络的优势比较突出，这是由其拓扑性质决定的。以Barabasi和Albert提出的经典BA模型为基础，基于增长机制和偏好机制提出两个复杂公交网络生成算法：基于效率驱动的复杂公交网络生成算法和基于引力驱动的复杂公交网络生成算法，它们都遵循运输效率最高，网络容量最大的公交网络生成目标，不同之处在于前者以运输效率为驱动，后者考虑了站点之间的阻抗和线路方向的问题，以站点之间的引力为驱动。
4.为优化城市公交网络时缓解交通拥堵对公交系统的影响，通过分析居民出行策略和拓展边介数，引入相关参数以模拟居民在交通拥堵时的出行策略变化，并定义了有效权重、有效路径、有效线路和有效网络，从而构建基于边介数的城市公交网络优化模型及其求解算法；分析零流网络效率、拥挤网络效率、网络效率损失、平均出行时间、平均出行距离、平均出行速度等网络指标与模型参数的关系，确定模型参数的物理意义，并对其进行标定。
5.为结合数学模型和经验设置站点的优势，提出二步骤法计算实际站间距。第一步根据模型假设，建立了站间距最优模型，计算理想条件下的最优站间距；第二步通过分析站间距影响因素，将其归为五个综合因素，即当量加速度、车辆区间平均速度、车辆站点停车时间、乘客平均出行距离和乘客平均到站速度，从而建立站间距修正模型，通过对最优站间距的修正，完成城市公交站点的设置。
6.借鉴《长春经济技术开发区公共交通规划（2011-2020）》项目的相关成果，对本文提出的模型和算法进行实证。首先分析长春经开区公交概况，确定首末站点和中途站点数量及布局，并对站点需求进行预测；然后生成长春经开区的新增线路、优化其现有不合理线路；最后对公交站间距重新进行优化和布局，并对长春经开区公交网络生成优化结果进行评价分析。
本文的研究成果可拓展复杂网络理论的应用范围，丰富城市公共交通规划理论体系，提高城市公交网络对交通拥堵的应对能力，促进城市公交系统健康有序的发展，具有较高的理论价值和实际意义。
China's automobile industry had obtained an unprecedented developmentduring the global economic crisis. The urban trips structure had undergone profoundchanges. The proportion of car trips had obtained a significant increase. Residents′travel mobility had improved. These had caused roads blocked and the phenomenonis spreading from initial Beijing, Shanghai, Guangzhou to second-tier cities. NowTraffic congestion has been common things in the cities and it has been more andmore serious. The scholars have to solve the problem that how to relieve and governurban traffic congestion. Vigorously developing urban public transport to ease urbantraffic congestion has become a consensus. But urban public transport, especially thecommon bus, has to share the road resources with cars. Therefore traffic congestionhas comparatively large effects on it. In order to make urban public transporteffectively deal with traffic congestion and play to its maximized advantages wehave to reasonably generate and optimize the urban public transport network.
Urban public transport network generation and optimization are complexstudies. Multi scholars used complex network theory for the complexity of the urbanpublic transport network after the beginning of its studies. They explored itsevolution mechanism and formation mechanism. But for transit network generationand optimization these scholars studied the distribution law of its complex statisticalindicators, qualitatively analyzed its problems and proposed measures to optimizethe network. They rarely study the bus network topology characteristics and thenetwork mathematical models. When generating and optimizing bus network,consider the effects of traffic congestion on the public transport system and residentstravel demand. The existing literature has not yet targeted research on it.
Therefore the paper relies on the National Natural Science Foundation of“Research on the key models and its algorithms in urban transit network integrateddesign（51078168）” to study transit network on the base of domestic and foreignstudies. Make the station research as an entry point, Three models were established,namely complex public transport network model based on efficiency-driven, complex public transport network model based on gravitation-driven and urbantransit network optimization model based on the edge betweenness. Then urban busstop spacing optimization was studied. The completed research results are asfollows:
1. Make urban bus station as research center. Firstly analyze urban bus station,then analyze station demand characteristics on the base of Fractal Theory. Theresults show that when the statistics interval is2min the station demand haveapparent fractal characteristics. Analyze bus stop type, then according to the trafficdetermine the number of first and last stop, the middle stop and their treatmentmethods. Apply double constrained gravity model to predict the bus stops OD matrixwith obtaining traffic zone OD matrix.
2. Study the basic issue of urban public transport network generation andoptimization. Design k shortest path algorithm with k-1shortest path on the base ofDijkstra algorithm. Analyze planning objectives and constraints of urban publictransit network planning, build urban public transport efficiency networkinfrastructure model based on station capacity restrictions.
3. In order to obtain best urban transit network, analyze three typical complexnetworks of random networks, small world networks and scale-free networks. Whenlarge passenger demand appear in the network the scale-free networks get theadvantage because of their topological properties. Analyze classic BA model fromBarabasi and Albert, propose two complex public transport network generationalgorithms based on growth mechanisms and preferences mechanism, namelycomplex public transport network generation algorithm based on efficiency-drivenand complex public transport network generation algorithm based on thegravity–driven. They all follow the maximized transport efficiency and networkcapacity as bus networks generation targets. The difference is that the former wasdriven by transport efficiency and the latter had considered the impedance betweenthe stations and the line direction, it is driven by the gravitation between the stations.
4. In order to relieve traffic congestion on the public transport system in theurban public transport network optimization this research introduced relevantparameters to simulate the residents travel strategy changes in the traffic congestionby analyzing the residents travel strategy and expanding the edge betweenness, Thendefine the effective weight, the effective path, the effective lines and the effectivenetwork to build the urban public transport network optimization model and its algorithm based on edge betweenness. It also determined the physical meaning of themodel parameters and their calibration by analyzing the relationship between themodel parameters and network indicators such as zero-flow network efficiency, thecrowded network efficiency, network efficiency loss, the average travel time, theaverage trip distance, the average trip speed etc.
5. The paper proposed a two-step method which could calculate the actualstation spacing to combine the advantage of mathematical models and experience toset up stations. The first step is to establish the station spacing optimal model tocalculate the optimal station spacing under the ideal conditions based on modelassumes. The second step is to analyze the affect factors of station spacing andclassify them into five combination factors, namely the equivalent acceleration, thespace mean speed of the vehicle, the parking time of vehicle at stop, averagepassenger trip distance and average arrival speed of passenger. This researchcompleted the setting of urban bus stops through building a station spacingcorrection model to correct the optimal station spacing.
6. By learning from the related outcomes about the project of “Public transportplanning in Changchun Economic and Technological Development Zone(2011-2020)”, the paper made the empirical study on the proposed model andmethod. Firstly analyze the current situation of public transit in Changchun,determine the number and layout of the first and last station and middle station, thenpredict station requirements. Next generate new lines in Changchun and optimizetheir existing unreasonable lines. Finally re-optimized the station spacing, evaluatethe generation and optimization results of transit network in Changchun Economicand Technological Development Zone.
The results of this research can expand the range of applications of complexnetwork theory, rich urban public transport planning theory system, improve theresponse capacity of urban public transport network to traffic congestion, promotethe healthy and orderly development of the urban public transport system, have hightheoretical value and practical significance.
引文
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