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针对编制开行方案涉及因素多、建模及求解困难的特点,结合有容量限制的多商品流网络设计问题,建立确定列车开行对数、开行区段、停站方案及编组形式的多目标整数规划模型,运用权重法将多目标规划转化为单目标规划。鉴于标准的列生成算法难以协同处理网络设计与网络配流问题,设计综合使用列生成与行生成策略的启发式算法确定列车的运行路径及停站方案,采用改进分支策略的分支定界算法求解最终模型。最后,以京沪高铁为例进行验证,在有效时间内获得较高质量解,该解与最优解的误差率为2.13%,且优于京沪高铁实际采用的开行方案。
In view of the characteristics of many factors involved in the preparation of the program, modeling and solving difficulties, a multi-objective integer programming that determines the logarithm of the train opening, the opening section, the stopping plan and the formation of the group is established in combination with the problem of capacity-limited multi-commodity flow network design Model, using the weight method to convert multi-objective planning into single-goal planning. Considering that it is difficult for standard column generation algorithms to co-operate with network design and network allocation problems, a heuristic algorithm based on column generation and row generation strategy is designed to determine the running path and stop plan of the train. The branch and bound algorithm with improved branch strategy is used to solve the problem model. Finally, taking the Beijing-Shanghai high-speed rail as an example, we obtain a higher quality solution within the effective time. The error rate between the solution and the optimal solution is 2.13%, which is better than the actual implementation plan of Beijing-Shanghai high-speed rail.