解集束法在训练时刻表问题中的应用
Disaggregation in Bundle Methods: Application to the Train Timetabling Problem
摘要：
束方法常用于解决大规模最优化问题的拉格朗日松弛所产生的对偶问题。这样的问题的一个例子是训练调度问题。针对训练编组优化程序中拉格朗日松弛法产生的对偶问题进行了求解。对偶问题的解决使用束方法。我们制定和比较两种不同的捆绑方法的性能：聚集的方法，这是一个标准的方法，和一个新的，非聚集的方法，这是在这里提出的。这两种方法进行了测试，从铁矿石铁路线的现实训练调度方案。数值结果表明，新的非集计方法一般产生更快的收敛速度比标准的聚集方法。
英文摘要：
Bundle methods are often used to solve dual problems that arise from Lagrangian relaxations of large scale optimization problems. An example of such problems is the train timetabling problem. This paper focuses on solving a dual problem that arises from Lagrangian relaxation of a train timetabling optimization program. The dual problem is solved using bundle methods. We formulate and compare the performances of two different bundle methods: the aggregate method, which is a standard method, and a new, disaggregate, method which is proposed here. The two methods were tested on realistic train timetabling scenarios from the Iron Ore railway line. The numerical results show that the new disaggregate approach generally yields faster convergence than the standard aggregate approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
