近年来我国城市轨道交通网络化进程的快速推进。在末班车时段，各条线路运营时间存在差异性经常导致乘客无法成功换乘。因此，制定合理的网络末班车衔接方案是当前城市轨道交通运营面临的重要问题。针对网络末班车衔接优化问题，本文选取末班车到发时间为决策变量，以最小化失败换乘乘客数量为目标，构建了混合整数线性规划模型。针对线网规模扩大导致模型复杂度高的问题，首先将原始模型重构为计算规模更小的两阶段问题；进而将第一阶段优化模型转换为可以运行在量子计算机上的QUBO模型，并基于相干伊辛机的光量子计算技术完成了算法开发和真机实测。为了验证所提方法的有效性，以北京地铁为例，将量子计算结果与商业求解器进行比较，验证了本文提出模型转换方法和量子计算方法的可行性，为进一步应用量子计算解决轨道交通行业复杂优化问题提供了技术支撑。

In recent years, there has been a rapid development in the process of urban rail transit networks construction in China. During the last train service period, the operational times of different rail lines vary, often causing passengers difficulties in successful transfers. Therefore, it has become an important issue to formulate a reasonable last-train connection scheme. Aiming at the optimization problem of last-train connection planning in urban rail transit network, this paper selects the arrival time of last trains as decision variables, and constructs a mixed-integer linear programming model to minimize the number of failed transfer passengers. To address the high model complexity caused by the expansion of network scale, firstly, the original model is reconstructed into a two-stage problem with smaller computation scale; subsequently, the first-stage optimization model is transformed into a QUBO (Quadratic Unconstrained Binary Optimization) model that can run on a quantum computer. The algorithm development and experimental testing are carried out based on the coherent Ising machine's optical quantum computing technology. To verify the effectiveness of the proposed method, this paper takes Beijing subway network as an example. Quantum computing results are compared with those from commercial solvers, confirming the feasibility of the model transformation method and quantum computing approach proposed in this paper. This provides technical support for the further application of quantum computing in solving complex optimization problems in the rail transit.

U231

国家自然科学基金(资助编号：U2368204)