停车需求分布的双层规划模型及算法

针对停车需求给定条件下的停车设施选择问题，建立了描述停车设施选择和出行路线选择行为的双层规划模型，并基于在部分增广乘子法中嵌套Frank-Wolfe算法的思路设计了求解模型的有效算法.上层模型在满足停车需求和设施停放车辆数有限条件下，力图最小化实际停车需求分布与期望分布间的差异.下层模型假设出行者路线选择行为遵循用户均衡原则.上下层模型通过设施选择概率函数实现有效关联.部分增广乘子法中嵌套Frank-Wolfe 算法求解上层模型可以有效利用上层模型的单纯形式约束特征.算例分析验证了新模型与算法的有效性.研究结论拓展了现有理论的应用场景，为相关研究提供了新的建模分析思路.

Bi-level Programming Model and Algorithm of Parking Demand Distribution

To deal with the parking facility choosing problem with given parking demand, a bi- level programming model is constructed to describe the parking facility choosing behaviors and travel route choosing behaviors. An effective solution method for the bi- level model is designed based on the partial augmented Lagrange multiplier method nested with Frank- Wolfe algorithm. With the constraints of satisfying the parking demand and restriction to number of the parking vehicles at facility, the upper level model tries to minimize the difference between actual parking distribution and the expected distribution. The lower level model assumes that the user equilibrium principle is followed by users to choose travel paths. The connection between the upper and lower level models is realized by the probability function of choosing facility. The partial augmented Lagrange multiplier method nested Frank- Wolfe algorithm to solve the upper level model can make use of the simplex feature of constraints. The numerical example verifies the effectiveness and efficiency of the new model and method. The research result not only extends the application setting of the existing theory, but also provides a new way to formulate and analyze the related problems.