非对称网络容量约束用户均衡交通分配仿真算法
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摘要
针对非对称网络路段容量约束交通均衡分配模型计算困难,设计了一种带路段容量约束的用户均衡交通分配仿真算法。在算法迭代过程中,将按全有全无法在当前最短路上分配流量与前一轮迭代所得到的流量加权组合,各O-D对的组合系数依Logit模型来确定;并不断自适应调节路段排队延误因子和误差因子来模拟实际路段行驶时间,使路段流量逐步低于路段容量,从而达到广义用户均衡,克服了容量约束均衡分配计算量大及Logit随机分配法要求枚举所有路径的困难。随后证明了算法的收敛性,并对一个小型路网进行了数值试验。
In the asymmetric network,an efficient algorithm is presented for user equilibrium traffic assignment problem with link capacity constraints to circumvent the costly solution of the constrained equilibrium assignment model.In each iteration process,the path flow volumes on each path are updated by weighted summing the path flow volume assigned to current shortest paths and the ones obtained in an early iteration,and the weight coefficient is determined by Logit model in each O-D pair.The method ensures gradually the links flow lower than corresponding capacity and trends to generalized user equilibrium by simulating realistic link travel time and adaptively regulating the delay and error factors.It is superior to the Logit-based stochastic equilibrium method owing to avoiding the paths numeration.Both the convergence result and the numerical example show this algorithm is effective and efficient.
In the asymmetric network,an efficient algorithm is presented for user equilibrium traffic assignment problem with link capacity constraints to circumvent the costly solution of the constrained equilibrium assignment model.In each iteration process,the path flow volumes on each path are updated by weighted summing the path flow volume assigned to current shortest paths and the ones obtained in an early iteration,and the weight coefficient is determined by Logit model in each O-D pair.The method ensures gradually the links flow lower than corresponding capacity and trends to generalized user equilibrium by simulating realistic link travel time and adaptively regulating the delay and error factors.It is superior to the Logit-based stochastic equilibrium method owing to avoiding the paths numeration.Both the convergence result and the numerical example show this algorithm is effective and efficient.
引文
1 Larsson T,Patriksson M.An augmented lagrangian dual algorithm forlink capacity side constrained traffic assignment problems.Transpor-tation Research,1995;29:433—455
2 Nie Y,Zhang H M.Models and algorithms for the traffic assignmentProblem with link capacity constraints.Transportation Research,2004;38:285—312
3 Xu Y D,Li S J,Teo K L.Vector network equilibrium problems withcapacity constraints of arcs.Transportation Research Part E,2012;48:567—577
4 Sheffi Y.Urban transportation networks:Equilibrium analysis withmathematical program methods.New Jersey,Prentice-Hall,INC,En-glewood Cliffs,1985
5 Chiou Suh-wen.A novel algorithm for area traffic capacity control withelastic travel demands.Applied Mathematical Model,2011;35:650—666
6 Meng Qiang,Khoo Hooiling.A computational model for the probit-based dynamic stochastic user optimal traffic assignment problem.JAdv Transp,2012;46:80—94
7 Szeto W Y,Solayappan M,Yu Jiang.Reliability-Based transit as-signment for congested stochastic transit networks.Computer-AidedCivil and Infrastructure Engineering,2011;26:311—326
8 D’Acierno L,Gallo M,Montella B.An ant colony optimisation algo-rithm for solving the asymmetric traffic assignment problem.EuropeanJournal of Operational Research,2012;217:459—469
9黄崇超,刘炳全.非平衡交通分配的Frank-Wolfe迭代算法.数学的实践与认识,2009;39(8):19—26
10 Yang Hai,Huang Haijun.Mathematica and economic theory of roadpricing.Elsevier,2005
2 Nie Y,Zhang H M.Models and algorithms for the traffic assignmentProblem with link capacity constraints.Transportation Research,2004;38:285—312
3 Xu Y D,Li S J,Teo K L.Vector network equilibrium problems withcapacity constraints of arcs.Transportation Research Part E,2012;48:567—577
4 Sheffi Y.Urban transportation networks:Equilibrium analysis withmathematical program methods.New Jersey,Prentice-Hall,INC,En-glewood Cliffs,1985
5 Chiou Suh-wen.A novel algorithm for area traffic capacity control withelastic travel demands.Applied Mathematical Model,2011;35:650—666
6 Meng Qiang,Khoo Hooiling.A computational model for the probit-based dynamic stochastic user optimal traffic assignment problem.JAdv Transp,2012;46:80—94
7 Szeto W Y,Solayappan M,Yu Jiang.Reliability-Based transit as-signment for congested stochastic transit networks.Computer-AidedCivil and Infrastructure Engineering,2011;26:311—326
8 D’Acierno L,Gallo M,Montella B.An ant colony optimisation algo-rithm for solving the asymmetric traffic assignment problem.EuropeanJournal of Operational Research,2012;217:459—469
9黄崇超,刘炳全.非平衡交通分配的Frank-Wolfe迭代算法.数学的实践与认识,2009;39(8):19—26
10 Yang Hai,Huang Haijun.Mathematica and economic theory of roadpricing.Elsevier,2005