Hybrid ant colony optimization algorithm applied to the multi-depot vehicle routing problem

The article deals with the hybrid Ant Colony Optimization algorithm and its application to the Multi-Depot Vehicle Routing Problem (MDVRP). The algorithm combines both probabilistic and exact techniques. The former implements the bio-inspired approach based on the behaviour of ants in the nature when searching for food together with simulated annealing principles. The latter complements the former. The algorithm explores the search space in a finite number of iterations. In each iteration, the deterministic local optimization process may be used to improve the current solution. Firstly, the key parts and features of the algorithm are presented, especially in connection with the exact optimization process. Next, the article deals with the results of experiments on MDVRP problems conducted to verify the quality of the algorithm; moreover, these results are compared to other state-of-the-art methods. As experiments, Cordreau's benchmark instances were used. The experiments showed that the proposed algorithm overcomes the other methods as it has the smallest average error (the difference between the found solution and the best known solution) on the entire set of benchmark instances.