出口道左转交叉口信号控制鲁棒优化方法

为了提高出口道左转交叉口在现实交通需求和供给波动环境中的适应性，权衡运行效率与稳定性，对其鲁棒优化方法进行研究。在对出口道左转交叉口运行特点和饱和流率进行分析的基础上，提出从交通需求分布、基本饱和流率分布和实际运行车速分布3个方面考虑交通的波动性，以适应出口道左转交叉口交通供给波动与控制方案相关联的特征。在此基础上，分别以平均值-标准差最小、条件风险值最小和最大值最小化为目标，建立3种信号控制鲁棒优化方法，并基于遗传算法建立求解算法。通过算例分析，对鲁棒优化算法的准确性、平均值-标准差模型的参数取值和3种鲁棒优化方法优化效益进行分析。研究结果表明：所建立的鲁棒优化方法可实现交通需求和供给波动下出口道左转交叉口信号控制与设计车速的优化设计，相较于传统控制方案其在保证效率的前提下提高了控制方案运行的稳定性；平均值-标准差模型和条件风险值模型对于各项指标均表现较好，可在保障平均延误维持较优值的基础上（案例中车均延误增加小于3%）显著改善运行效果的稳定性（案例中延误标准差减少约40%）；最小-最大模型对延误最大值的优化效果最佳，但其对于控制方案的整体效率会造成较大的负面影响（案例中车均延误增加了8.19%）。

Robust Optimization of Exit-lanes for Left-turn Intersections

In order to improve the adaptability of exit-lanes for left-turn (EFL) intersections, in an environment of fluctuating traffic demand and supply, and to balance operational efficiency and stability, a robust optimization method was studied. Based on an analysis of the operational characteristics and the saturated flow rate of EFL intersections, it is proposed that the fluctuation of traffic should be considered from three aspects:the distribution of traffic demand, the distribution of basic saturated flow rate, and the distribution of vehicular running speed. This enables the characteristics of the EFL intersection, the fluctuations of the traffic supply are related to the control scheme, to be taken into account. On this basis, three types of robust optimization model for signal control were established, with the aim of minimizing the combined value of mean and variance, conditional value-at-risk, and the value of the worst-case scenario. The proposed models were solved by a genetic-based algorithm. A case study was used to analyze the accuracy of the algorithm, the value of the weighting parameter in the mean-standard deviation model, and the optimization benefits of the three robust optimization methods. The results show that the established robust optimization method can optimally design the signal control and speed at EFL intersections under fluctuating traffic demand and supply. Compared with the traditional method, the stability of the robust control scheme is improved while maintaining efficiency. Among the models, the mean-variance (MSD) model and the conditional value-risk (MCVaR) model perform well for each indicator, and can significantly improve the operational stability, on the basis of maintaining the average delay at low values (less than 3% increase in the case study) and reducing the standard deviation (by about 40%). The minimum-maximum (MNMX) model is optimal in terms of the maximum delay, but it also has a negative impact on the overall efficiency (8.19% increase in average delay).