The algorithm uses a branch-and-bound method based on Lagrangian relaxation and dual search. 该算法是一个基于拉格朗日松弛和对偶搜索的分枝定界方法。
Then, the branch-and-bound algorithm is applied to the train scheduling. When a potential conflict in front of the running train is predicted, the branch-and-bound algorithm is applied to search the optimal solution for rescheduling train operation plan. 结合典型实例阐述分支定界算法主要思想,并将分支定界算法运用到列车调度中,在实时预测到列车运行前方存在潜在冲突时,调用分支定界算法搜索列车运行调整计划的最优解。
In the search process, the upper bound and lower bound of the train travel time, as well as the alternative-graph-based branch-and-bound rules, are used to cut the branches dissatisfying the conditions to reduce the search time and ensure the real-time character of train scheduling. 在搜索过程中,利用列车运行时间上界和下界值以及基于替换图的分支定界规则对不满足条件的分支进行剪枝,减少搜索时间,保证列车调度的实时性。