基于演化博弈理论的城市交通网络路径选择模型与算法研究

Urban traffic congestion, as a problems in the world, has affected the economic development and operating efficiency of many cities. Based on evolutionary game theory, the evolutionary game models are going to be eatablished between traffic managers and travelers under the different conditions, and several algorithms are going to be designed. By analyzing the game relationship between traffic managers and travelers, the feasibility would be explained for the evolutionary game theory which would be applied to the route choice problem in urban traffic network. The characteristics of traveler's route choice with mult-attribute are to be analyzed,and based on information entropy and optimization theory, the comprehensive attribute value will be obtained by combining subjective preference with objective attributes. Let Ant Colony algorithm be the learning mechanism of evolutionary game model, then several game models will be built, and simulation experiments will be executed also. Based on network reliability, different route choices are set for travelers, and a game model will be built to discuss the reliability and validity quantitatively. By using factor theory of graph and defining a non-negative function for each vertex, the existence of subgraph will be discussed when the topological structure changed, and evolutionary game model is to be built to study the influence to traffic managers and travelers among the change. The research of this project has good theoretical and practical meaning for guiding traffic and alleviating traffic congestion.

城市交通拥堵作为世界性问题，已经严重影响了城市的经济发展和运行效率。项目基于演化博弈理论，建立不同条件下以交通管理者与出行者为博弈双方的演化博弈模型并设计求解算法，用于指导实践。分析管理者与出行者之间的博弈关系，阐述演化博弈理论应用于城市交通网络路径选择问题的可行性；研究多属性条件下出行者进行路径选择的性质与特点，基于信息熵与网络优化理论获得出行者主观偏好和路径客观属性相结合的路径综合属性值；以蚁群算法作为演化博弈的学习机制，建立博弈双方之间的演化博弈模型，并设计算法进行仿真实验；基于网络可靠性设定多个路径选择方向，建立演化博弈模型，并定量讨论其可靠性及有效性；对交通网络中的节点定义非负整值函数，利用图的因子理论来证明网络的拓扑结构发生变化时子网络的存在性，进一步建立演化博弈模型定量研究对博弈双方的影响。项目研究成果对指导交通诱导、缓解城市交通拥堵提供方案和平台，具有一定的理论与现实意义。

基于演化博弈理论，研究了不同条件下的出行者路径选择问题，通过建立博弈模型并设计算法，对问题进行了求解。完全信息静态条件下，在没有纳什均衡或有多个纳什均衡时，经典的划线法就失效了，引入极值法并通过定义出行时的得益函数，求出混合策略下的纳什均衡解。不完全信息静态条件下，给出不同策略下出行者的收益值，建立路径选择博弈模型，并通过设计算法求解纯策略与混合策略条件下的纳什均衡解，进而得出博弈模型的贝叶斯纳什均衡。不完全信息动态条件下，建立了出行者之间的动态博弈模型，运用海萨尼转换求解精炼贝叶斯纳什均衡，并对不同策略下的收益值，采用贝叶斯先验概率进行设定，得出动态博弈的精炼贝叶斯纳什均衡解；建立了出行者与路径事故之间的动态博弈模型，并以出行者的期望效用最大为目标，构造了期望效用函数，根据贝叶斯均衡法则求解精炼贝叶斯纳什均衡解。不完全信息动态条件下，研究了企业激励机制路径选择问题，在静态博弈中，得到企业进行柔性动态激励机制路径博弈的支付矩阵及相应的概率矩阵，构建了博弈模型，并依据博弈纳什均衡的求解，给出不同企业的激励机制路径选择策略；在动态博弈中，依据企业之间的博弈关系，定义了混合策略博弈理论下的支付函数，利用极值法得到博弈模型的纳什均衡解。