约束可松弛的网络绿波模型

为解决区域交通信号协调控制领域中常规网络绿波模型可行域窄或无解的问题，提出了约束可松弛的网络绿波模型。应用混合整数线性规划方法构建模型，以所有路段双向绿波带宽加权和最大为优化目标，利用约束松弛方法，将干线约束和网络外圈闭环约束转变为可松弛的不等式约束。模型针对每条路段引入了0~1二元变量，表示路段的绿波是否被打断。通过模型求解，获得网络中必要的松弛路段，并打断相应的路段绿波，去除外圈闭环约束，以扩大可行域并找到最优解。算例对不同控制方案下提出的模型和其他绿波模型的绿波优化结果进行比较分析。算例显示，当网络各个交叉口采用同一化控制方案时，易于在不打断任何路段绿波的条件下找到最优解。此时，所提出的模型的解和常规网络绿波模型的解等价。当网络各交叉口采取差异化控制方案时，常规网络绿波模型无可行解，Gartner网络绿波模型仅获得非最优的可行解，而所提出的模型能够获得全局最优解。算例中只有1条路段的绿波被打断，而网络的其他路段均获得有效绿波带，且任意相交的干线绿波能够合理协调。算例优化结果表明：所提出的模型优于常规网络绿波模型和Gartner网络绿波模型，更适合复杂的城市交通网络信号优化设计。

Network Green-wave Band Model Permitting Relaxation of Constraints

To solve the problem of the regional traffic signal control domain in which the feasible region becomes narrow or even empty in a network green-wave band model, a novel model permitting the relaxation of constraints is proposed. The model was constructed as a mixed integer linear program in which the weighted sum of the green waves' bandwidths of all road segments was taken as the objective function. A constraint relaxation method was used to transform the constraints related to arterials and the network outer loops into relaxation-enabled inequality constraints. The model introduced a 0-1 binary variable for each road segment, indicating whether the green wave of the segment is interrupted. In this way, the model relaxed the outer loop constraints, thereby expanding the feasible region and finding the optimal solution. The optimized results of different models under different signal timing schemes were compared in an example network. When the intersections of the network adopted the homogeneous signal-timing scheme, it was easy to find the optimal solution without interrupting the green wave of any road segment.In this case, the solution of the proposed model was equivalent to the solution of the traditional network green wave model.When the intersections of the network adopted the heterogeneous signal timing schemes, the regular network green wave model failed to find solutions and the network green wave model built by Gartner only obtained non-optimally feasible solutions. In contrast, the proposed model could obtain a global optimal solution. Under this circumstance, the green wave of only one road segment was interrupted, while the other road segments achieved effective green wavebands and the arbitrary intersecting green waves could be reasonably coordinated. The results indicate that the proposed model is better than the regular network green wave model and the network green-wave model built by Gartner; the proposed model is more suitable for complex urban traffic network signal optimization.