An ant colony-based matheuristic approach for solving a class of vehicle routing problems

We propose a matheuristic approach to solve several types of vehicle routing problems (VRP). In the VRP, a fleet of capacitated vehicles visits a set of customers exactly once to satisfy their demands while obeying problem specific characteristics and constraints such as homogeneous or heterogeneous fleet, customer service time windows, single or multiple depots. The proposed matheuristic is based on an ant colony optimization (ACO) algorithm which constructs good feasible solutions. The routes obtained in the ACO procedure are accumulated in a pool as columns which are then fed to an integer programming (IP) optimizer that solves the set-partitioning (-covering) formulation of the particular VRP. The (near-)optimal solution found by the solver is used to reinforce the pheromone trails in ACO. This feedback mechanism between the ACO and IP procedures helps the matheuristic better converge to high quality solutions. We test the performance of the proposed matheuristic on different VRP variants using well-known benchmark instances from the literature. Our computational experiments reveal competitive results: we report six new best solutions and meet the best-known solution in 120 instances out of 193.