一种求解容量制约下交通网络流模型的新梯度方法

容量制约下的交通网络流模型是一个非线性规划问题，表现为在路段容量约束条件下的用户均衡网络的优化，这个模型能够描述交通网络的拥挤特征．容量制约下的交通网络流模型可以转换成传统的用户均衡模型的形式，为此对于任意一个给定的结点对，定义了一个新梯度，这个新梯度等于所有使用路径的费用的均值．利用新梯度的特征，并结合惩罚函数方法，可以获得容量制约下的交通网络流的解．数值实验表明所提出的方法表现出优良的收敛性能．

New Gradient Method for the Capacitated Network Flow Model

The capacitated network flow model is formulated in general nonlinear optimization problem with explicit link capacity constraints. The model is expected to describe a congested network due to the link capacity constraints. For utilizing properties of the conventional user equilibrium model, the capacitated flow model can be turned into the form of the conventional user equilibrium model. A new gradient which is equal to the average cost of all the used paths within the given origin-destination pair is defined. The Newton method with the new gradient is combined with the interior penalty method to obtain the capacitated network flow solution. Numerical experiment demonstrates the excellent performances of the proposed methods over the small network.