南通大学学报（自然科学版）

分析了交通网络中考虑交叉口转向延误最短路问题(shortest path problem with turning delay，SPPTD)的特点，用具体示例说明在SPPTD中传统的最优性递推原理不再成立。在目前的各种求解SPPTD算法基础上，提出一个新的计算方法。该方法先构建出求解SPPTD的0-1整数规划模型，然后进一步论证对模型的部分0-1变量进行松弛后的混合整数规划模型可以获得与原模型相同的最优解，根据该性质设计了求解模型的改进Benders分解算法，算法将模型分成主子两级交替求解，其中主模型在有限Benders割条件下生成目标函数的下界，主模型的约束条件保证了算法迭代过程中解始终是网络中起点到终点的路径，子模型在每次迭代获得的新路径下得到目标函数的上界与再带入主模型的新Benders割条件。最后在Nguyen-Dupuis网络算例中验证了方法的正确性与可行性，为城市道路交叉口转向延误最短路问题的求解提供了新的解决方法。

This paper analyzes the characteristics of the shortest path problem with turning delay (SPPTD) in traffic networks. A specific example demonstrates that the traditional optimality recursive principle no longer holds for SPPTD. Based on various existing algorithms for solving SPPTD， a novel computational method is proposed. This method first constructs a 0-1 integer programming model for solving SPPTD. It further demonstrates that a mixed integer programming model， after relaxing some of the model's 0-1 variables， can yield the same optimal solution as the original model. Based on this property， an improved Benders decomposition algorithm for solving the model is designed. This algorithm divides the model into two levels， a master and a sub-level， and solves them alternately. The master model generates a lower bound for the objective function under finite Benders cut conditions. The constraints of the master modelensure that the solution is always a path from the starting point to the end point in the network during the algorithm iterations. The sub-level model obtains an upper bound for the objective function based on the new path obtained in each iteration， which is then fed into the new Benders cut conditions of the master model. Finally， the correctness and feasibility of the method are verified on a Nguyen-Dupuis network example， providing a new approach to solving the shortest path problem with turning delay at urban road intersections.