An iterated local search with guided perturbation for the heterogeneous fleet vehicle routing problem with time windows and three-dimensional loading constraints

An Australian company is faced with the logistics problem of distributing small quantities of fibre boards to hundreds of customers every day. The resulting Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints has to be solved within a single hour, hence the use of a heuristic instead of an exact method. In previous work, the loading was performed after optimising the routes, which in some cases generated infeasible solutions in need of a repair mechanism. In this work, the feasibility of the loading constraints is maintained during the route optimisation. Iterated Local Search has proved very effective at solving vehicle routing problems. Its success is mainly due to its biased sampling of locl optima. However, its performance heavily depends on the perturbation procedure. We trialled different perturbation procedures where the first one perturbs the given solution by moving deliveries that incur the highest cost on the objective function, whilst the second one moves deliveries that have been shifted less frequently by the local search in previous iterations. Our industry partner provided six sets of daily orders which have varied characteristics in terms of the number of customers, customer distribution, number of fibre boards and fibre boards’ sizes. Our investigations show that an instance becomes more constrained when the customer order contains many different board sizes, which makes it harder to find feasible solutions. The results show that the proposed perturbation procedures significantly enhances the performance of iterated local search specifically on such constrained problems.