铁路网络列车运行调整的优化模型 及其分支定价算法

研究了铁路网络中列车可变更运行线路下的列车运行调整问题,目标是使得所有 列车偏离终到时间之和最小化.首先引入流平衡约束建立基于列车到发时刻的网络流模型,采 用商业软件GUROBI求解.同时构建了基于列车时空路径的整数规划模型,并给出了分支定 价算法,采用伪费用分支和最佳优先搜索策略加快算法的收敛.最后设计算例进行验证,通过 与GUROBI对比说明本文算法是有效的.当列车数为20 列时,求解时间减少91.6%,得到的最 终可行解距离最优解的间隔为9.72%.验证了本文分支策略较最为分数分支策略更优,列车运 行调整可变更线路相比于只能按原始线路行驶平均可降低目标函数值37.4%.     

多约束条件下城市道路环卫车优化配置与路径规划

为有效解决当前城市环卫车调度决策过度依赖人工主观经验造成的车辆配置不合理和作业效率低下问题,本文提出一种多约束条件下的城市道路环卫车优化配置与路径规划方法。通过综合考虑环卫车在现实作业中的作业时限、服务次数、行驶速度和车辆退出节点等多种约束条件,将物理道路网络拓展为时空网络,刻画车辆在路网上的时空运行轨迹,进而将环卫车优化配置与路径规划问题从数学上描述为带多类约束条件的弧路径问题(Arc Routing Problem, ARP)。 在此基础上,构建以车辆配置与出行总成本最小化为目标函数的环卫车优化配置与路径规划模型,并通过设计分支定价算法精确求解模型。将所提方法应用于苏州工业园区19个区域路网的环卫车辆配置与调度管理,从经济成本、作业效率和环保效益这3方面评估所提方法的可行性和有效性。结果表明：本文所提方法能够显著节约环卫运营成本,提升环卫车辆作业效率;同时,可有效降低环卫车辆碳排放量,形成良好的经济和社会效益,为智慧环卫提供了行之有效的新方案。     

Computing 4D near-optimal trajectories for dynamic air traffic flow management with column generation and branch-and-price

Abstract

The current air traffic system faces recurrent saturation problems. Numerous studies are dedicated to this issue, including the present research on a new dynamic regulation filter holding frequent trajectory optimisations in a real-time sliding horizon loop process. We consider a trajectory optimisation problem arising in this context, where a feasible four-dimensional (4D) trajectory is to be built and assigned to each regulated flight to suppress sector overloads while minimising the cost of the chosen policy. We model this problem with a mixed integer linear programme and solve it with a branch-and-price approach. The pricing sub-problem looks for feasible trajectories in a dynamic three-dimensional (3D) network and is solved with a specific algorithm based on shortest path labelling algorithms and on dynamic programming. Each algorithm is tested on real-world data corresponding to a complete traffic day in the European air traffic system; experimental results, including computing times measurement, validate the solution process.