混合网络均衡模型的求解算法研究  

Study of Solution Algorithm for Mixed Network Equilibrium Model

作　　者：隆冰[1] 朱晓宁[1] 

机构地区：[1]北京交通大学交通运输学院,北京100044

出　　处：《公路交通科技》2014年第3期112-118,共7页Journal of Highway and Transportation Research and Development

基　　金：国家自然科学基金项目(60870014);高等学校博士学科点专项科研基金项目(20130009110001)

摘　　要：为了解决不同属性用户路径选择相互影响的混合交通均衡分配问题,利用变分不等式描述了混合网络中用户平衡UE、系统最优SO、古诺-纳什均衡CN这3类用户的路径选择行为。分别采用基于路段的对角化算法和基于路径的双重投影算法对混合网络均衡模型进行求解,以Sioux Falls网络为例,从计算效率、收敛精度2个方面对其进行对比分析。分析结果表明:对角化算法前期收敛较快,但拖尾严重,很难通过多次迭代达到较高的精度;双重投影算法即使经过上千次迭代,精度仍可提高。在多种混合比例下,SO、CN用户控制流量比越大,系统总阻抗越小,而SO用户流量比低于0.5时,系统总阻抗下降很快,随着流量比增大,下降速度随之变缓。In order to solve the problem of mixed traffic equilibrium assignment with mutual influence of different kinds of users, a variational inequality is adopted to describe the routing behaviors of user equilibrium （UE）, system optimum （SO）, and Cournot-Nash equilibrium （CN） users in mixed network. The link based diagonalization algorithm and the path based double projection algorithm are provided to solve the mixed network equilibrium problem respectively. Comparative analysis is conducted in the aspects of computational efficiency and convergence precision between the 2 algorithms in the Sioux Falls network. The result shows that （ 1 ） link based diagonalization algorithm converges faster in the beginning, but it tails badly and is difficult to achieve high precision through multiple iterations; （2） computational accuracy can beimproved by path based double projection algorithm even after 1 000 iterations; （3） with various mixed proportions, the more the flow ratio controlled by SO and CN users, the smaller the total system impedance will be; （3） system impedance decreases very fast when flow ratio is less than 0.5 controlled by SO users, however, the drop speed of system impedance turns slowly with the increase of flow ratio.

关 键 词：交通工程 混合网络 变分不等式 交通分配 双重投影算法 

分 类 号：U491.123[交通运输工程—交通运输规划与管理]