交通网络复杂性及其优化研究
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摘要
复杂网络理论的出现为人们研究复杂系统又提供了一个非常好的方法。现实世界中的很多复杂系统均可以用复杂网络来描述,应用复杂网络理论来研究复杂系统具有非常明显的实际应用价值。目前的研究热点主要是从复杂网络的拓扑特性出发,进而研究复杂网络上的动力学、同步、传播等特征以及对其建模。相比非空间网络来说,学者们对于空间网络一直没有给予太多的关注。空间网络中的节点与连边都有特定的地理位置,因此不仅要研究其拓扑特性,还要进一步探索其在地理条件限制下的空间特性以及优化设计,进而达到对空间网络进行高效管理,提高其抗灾变与抗攻击能力的目的。
本文首先介绍了国内外复杂网络理论与应用研究发展动态,在此基础上,本文主要在探求交通网络的空间特性和优化方面做了如下工作:
1、经过统计分析,发现了一类度分布符合类高斯分布形式的复杂网络,经验证,中国铁路网络、世界部分国家高速公路网络、部分主要大都市地铁网络度分布均具有此特性;
2、综合分析了部分世界主要城市地铁网络,发现它们拥有如下共性:倾向于选择短边、平均度数接近于2、聚集系数接近于0,直径较大。经对比分析与计算机模拟仿真,发现城市地铁网络具有类似最小生成树样的结构。之后以北京地铁网络为例分析了其鲁棒性与抗毁性,发现其在节点随机故障情况下具有较好的鲁棒性,但在节点遭受恶意攻击情况下是比较脆弱的;
3、综合分析了部分国家高速公路网络,经分析与计算,发现他们具有如下相同特征:倾向于选择短边、平均度数小于4、小的聚集系数与大的直径。之后从此类网络的空间地理特性对其拓扑特征的成因进行了分析;
4、探讨了中国高速公路网络在节点出现随机故障和遭受恶意攻击下的动力学演化过程并分析了其鲁棒性与抗毁性,结果表明采用动态节点介数降序次序攻击的方式对网络的毁灭性最强;
5、改进了高速公路路网布局规划模型,改进后的模型增加了对路网网络特性的考虑,更贴近于实际需求,之后结合复杂网络与经济学理论,从成本收益分析的角度对路网布局优化模型进行了改进,最后基于运筹学中的一般算法与遗传算法,提出了路网结构优化方法,优化之后的路网结构在抗毁能力上有一定的提高。
The emergence of complex network theory affords us another new and good method to study complex systems. Many complex systems in the real world can be described as the complex networks, so, it is obvious that there are great values to research complex systems by complex network theory. At present, the hot field of complex network research is focused on the topologic properties, dynamics, synchronization, epidemic and modeling. In comparison with abstract networks, little attention is paid to spatial networks. All of the nodes and edges of the spatial networks have special geographical position, so, we must concentrate on their spatial characteristics and optimal plan under the restriction of geography conditions besides their topologic properties. Thus we can manage the spatial networks effectively and efficiently to improve their ability on resisting damage or attack.
The dissertation introduces the complex network theory’s development and research actuality of international and domestic. On the respect of searching spatial properties and the optimization of transportation network, the main works of the dissertation are as follows:
First, by statistic analysis, a kind of complex networks whose degree distribution followed a Gaussian-like distribution was put forward. After case study, it was found that the degree distribution of Chinese Railway Network, National Highway System of some countries and Subway Networks of some cities all followed this type;
Second, some big cities’subway networks were analyzed and it was found that they shared some common characteristics: tending to choose short edges, average degree is near to 2, clustering coefficient is almost 0 and large diameter. By computer simulation, it was also found that the structure of subway network was very like minimum spanning tree, and Beijing subway network was robust under random failure but frail under malice attack;
Third, some countries’National Highway Systems were analyzed and it was found that they share follow common characteristics: tending to choose short edges, average degree is small than 4, small clustering coefficient and large diameter. Then, the genesis of above properties was analyzed from the respect of their spatial geographic characteristics;
Fourth, the dynamic evolvement process of Chinese Highway Network under random failure and malice attack was demonstrated, after analyzing it’s robustness and invulnerability, it was found that Chinese Highway Network are frailest under the malice attack of dynamic node betweenness descending order;
Fifth, modified the model of highway network planning, the network topologic properties were added in the new model, and it satisfied true demand more. Then the optimization method of the highway network was also be modified from the respect of cost-benefit based on complex network and economic theory. At last, the structure of Chinese highway network was optimized by genetic algorithm, and the optimized structure was improved on invulnerability.
本文首先介绍了国内外复杂网络理论与应用研究发展动态,在此基础上,本文主要在探求交通网络的空间特性和优化方面做了如下工作:
1、经过统计分析,发现了一类度分布符合类高斯分布形式的复杂网络,经验证,中国铁路网络、世界部分国家高速公路网络、部分主要大都市地铁网络度分布均具有此特性;
2、综合分析了部分世界主要城市地铁网络,发现它们拥有如下共性:倾向于选择短边、平均度数接近于2、聚集系数接近于0,直径较大。经对比分析与计算机模拟仿真,发现城市地铁网络具有类似最小生成树样的结构。之后以北京地铁网络为例分析了其鲁棒性与抗毁性,发现其在节点随机故障情况下具有较好的鲁棒性,但在节点遭受恶意攻击情况下是比较脆弱的;
3、综合分析了部分国家高速公路网络,经分析与计算,发现他们具有如下相同特征:倾向于选择短边、平均度数小于4、小的聚集系数与大的直径。之后从此类网络的空间地理特性对其拓扑特征的成因进行了分析;
4、探讨了中国高速公路网络在节点出现随机故障和遭受恶意攻击下的动力学演化过程并分析了其鲁棒性与抗毁性,结果表明采用动态节点介数降序次序攻击的方式对网络的毁灭性最强;
5、改进了高速公路路网布局规划模型,改进后的模型增加了对路网网络特性的考虑,更贴近于实际需求,之后结合复杂网络与经济学理论,从成本收益分析的角度对路网布局优化模型进行了改进,最后基于运筹学中的一般算法与遗传算法,提出了路网结构优化方法,优化之后的路网结构在抗毁能力上有一定的提高。
The emergence of complex network theory affords us another new and good method to study complex systems. Many complex systems in the real world can be described as the complex networks, so, it is obvious that there are great values to research complex systems by complex network theory. At present, the hot field of complex network research is focused on the topologic properties, dynamics, synchronization, epidemic and modeling. In comparison with abstract networks, little attention is paid to spatial networks. All of the nodes and edges of the spatial networks have special geographical position, so, we must concentrate on their spatial characteristics and optimal plan under the restriction of geography conditions besides their topologic properties. Thus we can manage the spatial networks effectively and efficiently to improve their ability on resisting damage or attack.
The dissertation introduces the complex network theory’s development and research actuality of international and domestic. On the respect of searching spatial properties and the optimization of transportation network, the main works of the dissertation are as follows:
First, by statistic analysis, a kind of complex networks whose degree distribution followed a Gaussian-like distribution was put forward. After case study, it was found that the degree distribution of Chinese Railway Network, National Highway System of some countries and Subway Networks of some cities all followed this type;
Second, some big cities’subway networks were analyzed and it was found that they shared some common characteristics: tending to choose short edges, average degree is near to 2, clustering coefficient is almost 0 and large diameter. By computer simulation, it was also found that the structure of subway network was very like minimum spanning tree, and Beijing subway network was robust under random failure but frail under malice attack;
Third, some countries’National Highway Systems were analyzed and it was found that they share follow common characteristics: tending to choose short edges, average degree is small than 4, small clustering coefficient and large diameter. Then, the genesis of above properties was analyzed from the respect of their spatial geographic characteristics;
Fourth, the dynamic evolvement process of Chinese Highway Network under random failure and malice attack was demonstrated, after analyzing it’s robustness and invulnerability, it was found that Chinese Highway Network are frailest under the malice attack of dynamic node betweenness descending order;
Fifth, modified the model of highway network planning, the network topologic properties were added in the new model, and it satisfied true demand more. Then the optimization method of the highway network was also be modified from the respect of cost-benefit based on complex network and economic theory. At last, the structure of Chinese highway network was optimized by genetic algorithm, and the optimized structure was improved on invulnerability.
引文
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