用户均衡网络中的敏感度分析方法

以确定性交通网络用户均衡问题为研究对象,在分析了确定性用户均衡模型与优化条件的基础上,从非线性规划理论出发推导出确定性用户均衡模型的敏感度分析方程.与变分不等式的敏感度分析方法相比较,该方法只需要一般的数学规划知识,很容易被交通规划师和工程师所接受;提供一种获得均衡网络路径解的方法,该方法根据路径费用的大小决定路径解集的取舍,最终可以找到与各OD相对应的多条最短路径,该路径解可以直接用于网络敏感度分析.实例说明了该算法的有效性和敏感度分析在交通规划、建设与管理中的应用.

Solutions to Sensitivity Analysis for the Equilibrium Network Flow

The equilibrium network flow problem is formulated in its general form as a mathematical programming, and sensitivity analysis are developed for the mathematical programming. The sensitivity analysis is to calculate the derivatives of the equilibrium link flows with respect to perturbations, which are of the cost functions, of the origin-destination matrix and of the link capacities. At the same time, a path-based gradient projection with variable step is proposed, and adopted in the sensitivity. The numerical example illustrates the applications of sensitivity analysis in traffic planning, construction and operations.