中文摘要：

提出了一种优化的迭代降维算法求解混合交通网络设计问题．混合（连续／离散）交通网络设计问题常表示为一个带均衡约束的数学规划问题，上层通过新建路段和改善已有路段来优化网络性能，下层是一个传统的Wardrop用户均衡模型．迭代降维算法的基本思想是降维，先保持一组变量（离影连续）不变，交替地对另一组变量（连续／离散）实现最优化．以迭代的形式反复求解连续网络设计和离散网络设计问题，直至最后收敛到最优解．通过一个数值算例对算法的效果进行了验证．

英文摘要：

An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.