排阵式交叉口几何设计与信号控制协同鲁棒优化

针对排阵式交叉口在实际交通波动环境中存在车辆滞留排序区，运行效率稳定性难以保障的问题，提出了鲁棒优化方法，平衡交叉口运行的效率和稳定性。在分析排阵式交叉口运行特性的基础上，指出了其运行效率波动性与交叉口几何设计、信号控制、交通需求、饱和流率和运行车速这5个因素有关。确定了将交通需求、饱和流率和运行车速这3个客观波动因素作为模型的输入参数，将几何设计和信号控制这2个可受设计人员控制的要素作为模型的优化控制变量进行协同优化的模型框架。在此基础上，以交叉口车均延误条件风险值最小为目标，考虑了各流向车道数、信号相位相序、排序区车辆清空等方面的约束条件，构建了基于情景的鲁棒优化模型，并建立了遗传算法对模型进行求解。通过案例分析，对鲁棒优化模型的置信水平取值和算法准确性进行了分析，证明了算法可以使目标函数收敛到最小值，并基于蒙特卡洛模拟对优化效益进行了检验。研究发现，所建立的几何设计与信号控制协同鲁棒优化模型可实现在交通需求和供给的波动下，对排阵式交叉口的车道功能、排序区长度以及主、预信号控制进行协同优化。相较于确定性的设计方法，在平均延误层面基本维持原有水平，但对延误标准差和最大值有着较为明显的改善，案例中分别减少了48%和23%。

Joint Robust Optimization of Layout Design and Signal Control for Tandem Intersections

To mitigate the potential risk of vehicles trapped in a sorting area, a robust optimization method is proposed for tandem intersections to balance the operational efficiency and stability in a traffic fluctuation environment. Based on the analysis of the operational characteristics, it was found that the operational fluctuation of the tandem intersection is related to five influencing factors:layout design, signal control, traffic demand, saturated flow rate, and operating speed. The framework of the optimization model was proposed with regard to the traffic demand, saturated flow rate, and operating speed as input parameters. The layout design and signal control, which can be controlled by the designer, were set as the decision variables. A scenario-based robust optimization model was established to minimize the conditional risk value of delay, considering the constraints of the lane number, signal plan, and clearance of vehicles in the sorting area. The proposed model was solved using a genetic-based algorithm. Through the case study, the values of the confidence level and the accuracy of the algorithm were analyzed. It was proved that the algorithm can converge the objective function to a minimum value. Additionally, the optimization benefits were validated based on a Monte Carlo simulation. The results demonstrate that the established joint robust optimization model can achieve the optimal design of the lane assignment, length of the sorting area, and signal timing for the main signal and pre-signal under traffic supply and demand fluctuations. Compared with the traditional deterministic design methods, the proposed model can significantly improve the performance by reducing the standard deviation and maximum delay while maintaining the average delay. In the case study, the reductions attained were 48% and 23%, respectively.