A heuristic approach for the truck and trailer routing problem

In this paper, we propose an approach based on mathematical programming and local search to cope with the truck and trailer vehicle routing problem. The mathematical programming framework models two subproblems that are solved sequentially, that is, the customer-route assignment problem (CAP), with the objective of minimizing the fleet size used to service clients, and the route definition problem, with the objective of minimizing the total tour length given the set of clients assigned to each vehicle. Since the route assignment model can return infeasible solutions, the local search plays the role of possibly retrieving a feasible solution. The mathematical formulations and the local search work iteratively, embedded in a multiple restarting mechanism able to diversify solutions by (i) identifying additional constraints for the CAP formulation to be taken into account during the algorithm progress, (ii) using a tabu like customer-route matrix to avoid assignments already analysed in the previous iterations of the algorithm. Also a lower bound to assess the solution quality is given. Experiments and comparison with competing approaches suggest that the results of the proposed machinery are promising, producing, on average, a smaller total tour lengths on benchmarks.