New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows
针对带时间窗的车辆路径问题，提出了两种增强方法：改进的有限记忆子集行不等式和基于Balas基本不等式的新不等式族，嵌入分支定价切割算法后能求解所有56个100客户的Solomon实例和51个200客户的Gehring-Homberger实例。
The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to satisfy the demands of customers that can be visited within specific time windows. We introduce two enhancements for the exact solution of the VRPTW by branch-price-and-cut (BPC). First, we develop a sharper form of the limited-memory subset-row inequalities by representing the memory as an arc subset rather than a node subset. Second, from the elementary inequalities introduced by Balas in 1977, we derive a family of inequalities that dominate them. These enhancements are embedded into an exact BPC algorithm that includes state-of-the-art features such as bidirectional labeling, decremental state-space relaxation, completion bounds, variable fixing, and route enumeration. Computational results show that these enhancements are particularly effective for the most difficult instances and that our BPC algorithm can solve all 56 Solomon instances with 100 customers and 51 of 60 Gehring and Homberger instances with 200 customers.