停车需求分布的双层规划模型及算法
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摘要
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.
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.
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.
引文
[1]张秀媛,董苏华,蔡华民,等.城市停车规划与管理[M].北京:中国建筑工业出版社,2006.[ZHANG XY,DONG S H,CAI H M,et al.Urban parking planning and management[M].Beijing:China Architecture&Building Press,2006.]
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[3]李涛,关宏志.考虑用户时间冲突的停车共享方案优化研究[J].交通运输系统工程与信息,2017,17(5):144-150.[LI T,GUAN H Z.Optimization of parking sharing scheme considering user conflict[J].Journal of Transportation Systems Engineering and Information Technology,2017,17(5):144-150.]
[4]秦焕美,刘聪,杨修涵.基于浮动式停车收费的寻泊与出行意向分析[J].交通运输工程与信息学报,2017,15(1):40-46.[QIN H M,LIU C,YANG X H.Analysis on parking behavior and travel preference based on floating parking fees[J].Journal of Transportation Engineering and Information,2017,15(1):40-46.]
[5]段满珍,曹会云,董博,等.面向个体需求的停车场分配模型[J].交通运输系统工程与信息,2016,16(6):153-159.[DUAN M Z,CAO H Y,DONG B,et al.Parking lots distribution model for the individual demand[J].Journal of Transportation Systems Engineering and Information Technology,2016,16(6):153-159.]
[6]吴涛,晏克非.停车需求管理的机理研究[J].城市规划,2002,26(10):85-88.[WU T,YAN K F.The mechanism study on the parking demand management[J].City Planning Review,2002,26(10):85-88.]
[7]SHEFFI Y.Urban transportation networks:Equilibrium analysis with mathematical programming methods[M].New Jersey:Prentice-Hall,1985.
[8]何胜学.基于两阶段行程时间的交通流分配理论[J].交通运输系统工程与信息,2018,18(1):139-144.[HES X.Traffic assignment theory based on two-stage travel time[J].Journal of Transportation Systems Engineering and Information Technology,2018,18(1):139-144.]
[9]MENG Q,YANG H,BELL M G H.An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem[J].Transportation Research Part B,2001,35(1):83-105.
[10]NGUYEN S,DUPIUS C.An efficient method for computing traffic equilibria in networks with asymmetric transportation costs[J].Transportation Science,1984,18(1):185-202.
[2]徐雷,刘冰,张涵双.停车需求预测和泊位供给策略分析[J].交通科技与经济,2014,16(2):39-43.[XU L,LIU B,ZHANG H S.Research and application of parking demand forecasting and parking supply strategy[J].Technology&Economy in Areas of Communication,2014,16(2):39-43.]
[3]李涛,关宏志.考虑用户时间冲突的停车共享方案优化研究[J].交通运输系统工程与信息,2017,17(5):144-150.[LI T,GUAN H Z.Optimization of parking sharing scheme considering user conflict[J].Journal of Transportation Systems Engineering and Information Technology,2017,17(5):144-150.]
[4]秦焕美,刘聪,杨修涵.基于浮动式停车收费的寻泊与出行意向分析[J].交通运输工程与信息学报,2017,15(1):40-46.[QIN H M,LIU C,YANG X H.Analysis on parking behavior and travel preference based on floating parking fees[J].Journal of Transportation Engineering and Information,2017,15(1):40-46.]
[5]段满珍,曹会云,董博,等.面向个体需求的停车场分配模型[J].交通运输系统工程与信息,2016,16(6):153-159.[DUAN M Z,CAO H Y,DONG B,et al.Parking lots distribution model for the individual demand[J].Journal of Transportation Systems Engineering and Information Technology,2016,16(6):153-159.]
[6]吴涛,晏克非.停车需求管理的机理研究[J].城市规划,2002,26(10):85-88.[WU T,YAN K F.The mechanism study on the parking demand management[J].City Planning Review,2002,26(10):85-88.]
[7]SHEFFI Y.Urban transportation networks:Equilibrium analysis with mathematical programming methods[M].New Jersey:Prentice-Hall,1985.
[8]何胜学.基于两阶段行程时间的交通流分配理论[J].交通运输系统工程与信息,2018,18(1):139-144.[HES X.Traffic assignment theory based on two-stage travel time[J].Journal of Transportation Systems Engineering and Information Technology,2018,18(1):139-144.]
[9]MENG Q,YANG H,BELL M G H.An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem[J].Transportation Research Part B,2001,35(1):83-105.
[10]NGUYEN S,DUPIUS C.An efficient method for computing traffic equilibria in networks with asymmetric transportation costs[J].Transportation Science,1984,18(1):185-202.