基于动态投影系统的带非线性边界约束混行路网均衡模型求解算法
|
摘要
针对路网中考虑电动汽车出行能耗与燃油汽车环境排放情形下混合交通流的非线性边界约束路网均衡问题,设计了一种基于动态投影系统的算法。将复杂非线性边界约束的双车型路网均衡模型转换成变分不等式模型,利用拉格朗日乘子法得到模型的库恩塔克(KKT)条件以及模型的非线性互补问题,通过引入投影算子建立动态投影系统找到模型的最优解。分析模型可确定燃油汽车和电动汽车一般出行成本函数,电动汽车混行条件下交通网络的均衡条件,以及路网均衡条件下两种车型的拥堵外部性并获取混合交通流下路网的运行特征。最后构建数值仿真评估动态投影算法的有效性,结果表明模型收敛于系统的平衡点,且具有指数收敛性质。
Traffic equilibrium problems for electric vehicles(EVs) with battery energy consumption and gasoline vehicles(GVs) with environmental emission constraints generally admit complex nonlinear constraints rendering the equilibrium problem difficult to solve,to address this challenge,a projected dynamics was proposed based algorithm. The complex nonlinear side-constrained traffic equilibrium model is converted into a variational inequality problem(VIP). A set of equivalent Karush-Kuhn-Tucker(KKT) conditions are obtained to yield a nonlinear mixed complementarity reformulation of the equilibrium model. Based on the complementarity reformulation a projected dynamics whose equilibrium corresponds to the solution of the above VIP is devised. The projected dynamics can determine the general travel cost,equilibrium condition mixed with traffic flows and its congestion externality.Finally,a numerical example was conducted to evaluate the solution algorithm. The results show that the algorithm exponentially converges to the equilibrium point of the VIP,which proves the effectiveness and efficiency of the proposed algorithm.
Traffic equilibrium problems for electric vehicles(EVs) with battery energy consumption and gasoline vehicles(GVs) with environmental emission constraints generally admit complex nonlinear constraints rendering the equilibrium problem difficult to solve,to address this challenge,a projected dynamics was proposed based algorithm. The complex nonlinear side-constrained traffic equilibrium model is converted into a variational inequality problem(VIP). A set of equivalent Karush-Kuhn-Tucker(KKT) conditions are obtained to yield a nonlinear mixed complementarity reformulation of the equilibrium model. Based on the complementarity reformulation a projected dynamics whose equilibrium corresponds to the solution of the above VIP is devised. The projected dynamics can determine the general travel cost,equilibrium condition mixed with traffic flows and its congestion externality.Finally,a numerical example was conducted to evaluate the solution algorithm. The results show that the algorithm exponentially converges to the equilibrium point of the VIP,which proves the effectiveness and efficiency of the proposed algorithm.
引文
1赵蒙,安实,王健,等.基于时空网络建模的分时租赁系统电动汽车优化调度方法[J].科学技术与工程,2018,18(23):122-127Zhao Meng,An Shi,Wang Jian,et al.Space-time network modeling based electric vehicle optimal dispatching method for carsharing system[J].Science Technology and Engineering,2018,18(23):122-127
2 He F,Yin Y F,Lawphonganich S.Network equilibrium models with battery electric vehicles[J].Transportation Research Part B:Methodological,2014,67:306-319
3 Jiang N,Xie C.Computing and analyzing mixed equilibrium network flows with gasoline and electric vehicles[J].Computer-aided Civil and Infrastructure Engineering,2014,29(8):626-641
4 Xu M,Meng Q,Liu K.Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints[J].Transportation Research Part B:Methodological,2017,99:138-166
5连静,郑宁安,周雅夫,等.基于电池荷电状态和行驶工况辨识的电动汽车续驶里程估算[J].科学技术与工程,2016,16(13):1671-1815Lian Jing,Zheng Ning'an,Zhou Yafu,et al.Driving range estimation for electric vehicles based on battery soc and driving cycle identification[J].Science Technology and Engineering,2016,16(13):1671-1815
6杨扬,姚恩建,王梅英,等.电动汽车混入条件下的随机用户均衡分配模型[J].中国公路学报,2015,28(9):91-97Yang Yang,Yao Enjian,Wang Meiying,et al.Stochastic user equilibrium assignment model for electric vehicle under hybrid traffic condition[J].China Journal of Highway and Transport,2015,28(9):91-97
7 Galus D,Waraich A,Noembrini F,et al.Integrating power systems,transport systems and vehicle technology for electric mobility impact assessment and efficient control[J].IEEE Transactions on Smart Grid,2012,3(2):934-949
8 Xu X D,Chen A,Cheng L.Reformulating environmentally constrained traffic equilibrium via a smooth gap function[J].International Journal of Sustainable Transportation,2015,9(6):419-430
9 Mokhtar B,Hanif S,Shetty C.Nonlinear programming:Theory and algorithm[M].New Jersey:John Wiley&Sons,Inc Press,2005
10 Sheffi Y.Urban transportation network[M].New Jersey:Pretince Hall Press,1985
11 Xia Y,Feng G,Kamel M.Development and analysis of a neural dynamical approach to nonlinear programming problems[J].IEEETransactions on Automatic Control,2007,52(11):2154-2159
12 Xia Y.An extended projection neural network for constrained optimization[J].Neural Computation,2004,16(4):863-883
13 Xia Y.Further results on global convergence and stability of globally projected dynamical systems[J].Journal of Optimization Theory and Applications,2004,122(3):627-649
2 He F,Yin Y F,Lawphonganich S.Network equilibrium models with battery electric vehicles[J].Transportation Research Part B:Methodological,2014,67:306-319
3 Jiang N,Xie C.Computing and analyzing mixed equilibrium network flows with gasoline and electric vehicles[J].Computer-aided Civil and Infrastructure Engineering,2014,29(8):626-641
4 Xu M,Meng Q,Liu K.Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints[J].Transportation Research Part B:Methodological,2017,99:138-166
5连静,郑宁安,周雅夫,等.基于电池荷电状态和行驶工况辨识的电动汽车续驶里程估算[J].科学技术与工程,2016,16(13):1671-1815Lian Jing,Zheng Ning'an,Zhou Yafu,et al.Driving range estimation for electric vehicles based on battery soc and driving cycle identification[J].Science Technology and Engineering,2016,16(13):1671-1815
6杨扬,姚恩建,王梅英,等.电动汽车混入条件下的随机用户均衡分配模型[J].中国公路学报,2015,28(9):91-97Yang Yang,Yao Enjian,Wang Meiying,et al.Stochastic user equilibrium assignment model for electric vehicle under hybrid traffic condition[J].China Journal of Highway and Transport,2015,28(9):91-97
7 Galus D,Waraich A,Noembrini F,et al.Integrating power systems,transport systems and vehicle technology for electric mobility impact assessment and efficient control[J].IEEE Transactions on Smart Grid,2012,3(2):934-949
8 Xu X D,Chen A,Cheng L.Reformulating environmentally constrained traffic equilibrium via a smooth gap function[J].International Journal of Sustainable Transportation,2015,9(6):419-430
9 Mokhtar B,Hanif S,Shetty C.Nonlinear programming:Theory and algorithm[M].New Jersey:John Wiley&Sons,Inc Press,2005
10 Sheffi Y.Urban transportation network[M].New Jersey:Pretince Hall Press,1985
11 Xia Y,Feng G,Kamel M.Development and analysis of a neural dynamical approach to nonlinear programming problems[J].IEEETransactions on Automatic Control,2007,52(11):2154-2159
12 Xia Y.An extended projection neural network for constrained optimization[J].Neural Computation,2004,16(4):863-883
13 Xia Y.Further results on global convergence and stability of globally projected dynamical systems[J].Journal of Optimization Theory and Applications,2004,122(3):627-649