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考虑城市路网中不同出行方式车流之间相互影响，通过对私家车实行拥挤道路使用收费和增加公交发车频率之间的相互制约关系分析，提出了基于可变公交发车频率的城市拥挤道路收费定价的优化问题. 在分析确定路网上公交车和私家车出行方式的广义出行成本的基础上建立了该问题的双层规划模型，其中上层规划以路网上的出行者消费盈余最大为优化目标，下层规划为弹性需求下的组合出行网络用户平衡模型；并设计了基于模拟退火算法求解的优化算法. 算例分析表明，基于可变公交发车频率的城市拥挤道路收费定价模型和算法能够更有效地解决道路拥挤问题.

Optimization Study on Road Pricing with Variable Bus Frequency

The paper proposes the optimization problem of road pricing with variable bus frequency on the basis of the relations analysis of mutual constraints between road pricing and increasing bus frequency considering the interaction of different travel modes. A bi-level programming model is developed by estimating the generalized travel cost of bus and private car traveling. The upper objective of the model maximizes total consuming surplus of network, while the lower is the user equilibrium model with elastic demand of combined mode. The optimal algorithm is also designed based on the simulated annealing algorithm. A numerical example illustrates that the model and algorithm can effectively solve the problem of road congestion.