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

A Dynamics Projected System Based Solution Algorithm for Mixed Network Equilibrium Model with Nonlinear Side Constraints

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.