考虑多目标的城市停车换乘选址优化模型及算法

停车换乘选址问题是城市交通网络设计研究的重点领域，已有研究的优化目标多集中在系统总费用方面，而对交通可持续发展方面考虑不足。为此，提出综合考虑多方面目标的停车换乘设施选址优化模型及其求解算法。首先，基于超网络理论，提出多方式城市交通系统的超网络模型并定义O-D (Origin-destination)间的超路径、有效超路径及子路径，结合出行者出行过程及交通网络拥挤特征，给出超路径费用的数学表达；其次，基于多方式交通网络随机均衡配流结果，构建交通总阻抗、污染物排放量以及交通系统公平性等系统优化指标的计算模型，并建立用以描述停车换乘设施选址问题的多目标优化模型；进而，以多目标系统优化模型为上层问题，以超网络下满足Logit分配的多方式交通网络配流模型为下层问题，构建描述城市多方式交通系统停车换乘设施选址问题的双层规划模型，并基于模型特征，结合“记录-搜索”思想设计非支配排序遗传算法进行求解；最后，基于Sioux Falls网络设计算例。研究结果表明：算法能够在有限的步骤内搜索到90%以上的Pareto最优解；平均而言，停车换乘措施使得交通总阻抗减小了0.31%，污染物排放量减少了7.32%；被优化的3个目标之间无直接关联，说明将停车换乘选址问题建立为多目标模型是必要的。模型与算法可为现实城市中的停车换乘设施选址优化设计提供解决思路。

Model and Algorithm for Urban Park-and-ride Locations Considering Multiple Objectives

The location of park-and-ride (P&R) facilities is important in urban transportation network design. Existing studies focus on optimizing the total travel cost, while neglecting sustainability aspects. This paper proposed a model to find optimal locations of park-and-ride stations in urban areas that considered the above objectives simultaneously and presented a solution algorithm. First, a super-network model was proposed for the multimodal transportation system, and then, the super-path, effective super-path, and sub-path between the origin and destination were defined. The mathematical expression of the super-path cost was obtained by combining the travel process and congestion characteristics of the transportation network. Second, based on the results of stochastic equilibrium assignments in a multimodal transportation network, systemic optimization goals, including total travel impedance, pollutant emissions, and equality of transportation system, were suggested, and a multi-objective optimization model for the P&R location problem was established. Furthermore, a bi-level programming model for the P&R location problem was proposed, where the multi-objective optimization model was considered as the upper problem and the stochastic user equilibrium problem of a multimodal transportation network (SUEM) based on the Logit model, was considered as the lower problem. A non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) combining “record and search” was designed based on the characteristics of the model. Finally, the experimental results based on the transportation network of Sioux Falls, South Dakota, USA show that more than 90% of the Pareto optimal solutions can be obtained by the algorithm within a certain step. P&R measures reduce the total travel impedance by 0.31% and pollutant emissions by 7.32%, on average. There is no direct correlation between the three optimized targets, which shows that it is necessary to establish the P&R location problem as a multi-objective model. The model and algorithm can provide a practical solution for the locations of urban P&R facilities.