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.

中文翻译：

---

混合蚁群优化算法在多仓库车辆路径问题中的应用

本文讨论了混合蚁群优化算法及其在多站点车辆路径问题（MDVRP）中的应用。该算法结合了概率技术和精确技术。前者基于自然界中蚂蚁在寻找食物时的行为以及模拟的退火原理来实施生物启发的方法。后者是对前者的补充。该算法以有限的迭代次数探索搜索空间。在每次迭代中，确定性局部优化过程可用于改善当前解决方案。首先，介绍了算法的关键部分和特征，特别是与精确的优化过程有关的部分。接下来，本文讨论了针对MDVRP问题进行的实验结果，以验证算法的质量；此外，将这些结果与其他最新方法进行了比较。作为实验，使用了Cordreau的基准实例。实验表明，该算法克服了其他方法，因为它在整个基准实例集上具有最小的平均误差（找到的解决方案与最知名的解决方案之间的差异）。