A Branch and Price Heuristic Algorithm for the Vehicle Routing Problem with Time Windows

The branch and price heuristic (BPH) algorithm is proposed to deal with the vehicle routing problem with time windows (VRPTW). Firstly, the greedy algorithm based on the nearest neighbor strategy is designed to obtain the initial columns of the master problem. Secondly, the bee algorithm (BA) with two swap-based operators is devised to solve the pricing subproblem within a reasonable running time. Finally, an arc branching strategy is developed to branch each node with non-integer solution in the branch-and-bound tree to get the integer solution ultimately. Computational experiments are conducted on the Solomon benchmark instances and the results manifest that the proposed BPH algorithm can effectively address the VRPTW.