基于量子计算的城市轨道交通网络末班车衔接优化

针对城市轨道交通网络化运营下，各条线路运营时间存在差异性而导致乘客无法成功换乘的问题，本文开展面向城市轨道交通末班车衔接优化问题的研究，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。考虑到线网规模扩大导致模型复杂度高的问题，本文率先将量子计算应用于上述优化模型求解中。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二次无约束二值化优化问题(quadratic unconstrained binary optimization,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。

Quantum Computing-Based Optimization for the Last-Train ConnectionPlanning Problem in Urban Rail Transit Networks

Aiming at the optimization problem of last-train connection planning in urban rail transit networks, which often bringsdifficulties in successful transfers, this study selects the arrival times of the last trains as decision variables and constructs amixed-integer linear programming model to minimize the number of failed passenger transfers. To address the high modelcomplexity caused by the expansion of the network scale, a quantum computing method is adopted to solve the proposed model.First, the original model is reconstructed into a two-stage problem with a smaller computation scale. Then, the first-stage optimizationmodel is transformed into a quadratic unconstrained binary optimization (QUBO) model that can run on a quantum computer.Algorithm development and experimental testing are conducted based on the optical quantum computing technology of thecoherent Ising machine. To verify the effectiveness of the proposed method, we consider the Beijing subway network as anexample. The quantum computing results are compared with those from commercial solvers, confirming the feasibility of both the model transformation method and the quantum computing approach proposed in this study. These findings provide technicalsupport for the further application of quantum computing in solving complex optimization problems in rail transit.