Branch-and-Price Heuristics: A Case Study on the Vehicle Routing Problem with Time Windows

Branch-and-price is a powerful framework to solve hard combinatorial problems. It is an interesting alternative to general purpose mixed integer programming as column generation usually produces at the root node tight lower bounds (when minimizing) that are further improved when branching. Branching also helps to generate integer solutions, however branch-and-price can be quite weak at producing good integer solutions rapidly because the solution of the relaxed master problem is rarely integer-valued. In this paper, we propose a general cooperation scheme between branch-and-price and local search to help branch-and-price finding good integer solutions earlier. This cooperation scheme extends to branch-and-price the use of heuristics in branch-and-bound and it also generalizes three previously known accelerations of branch-and-price. We show on the vehicle routing problem with time windows (Solomon benchmark) that it consistently improves the ability of branch-and-price to generate good integer solutions ea rly while retaining the ability of branch-and-price to produce good lower bounds.