An advanced hybrid meta-heuristic algorithm for the vehicle routing problem with backhauls and time windows

•A new model is built up for vehicle routing problem with backhauls and time windows.•A hybrid algorithm which includes tabu search and simulated annealing is proposed.•The nearest neighbor method is improved for initial solution generation.•Proposed hybrid meta-heuristic algorithm outperforms the existing methods.•34 new best solutions are obtained for 45 instances.

This paper presents an advanced hybrid meta-heuristic algorithm (HMA) to solve the vehicle routing problem with backhauls and time windows (VRPBTW). The VRPBTW is an extension of the vehicle routing problem with time windows (VRPTW) and the vehicle routing problem with backhauls (VRPB) that includes capacity, backhaul and time window constraints. In this problem, the customers are divided into two subsets consisting of linehaul and backhaul customers. Each vehicle starts from the depot, and goods are delivered from the depot to the linehaul customers. Goods are subsequently returned to the depot from the backhaul customers. The objective is to minimize the total distance that satisfies all of the constraints. The proposed meta-heuristic method is tested on a problem data set obtained from Solomon’s VRPTW benchmark problems which includes 25, 50 and 100 demand nodes. The results of the computational studies show that the HMA outperforms the existing studies and provides better solutions than the best known solutions in practical computational times.