The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive and perturbative heuristics to tackle this problem using Deep Learning. In this paper, we join these efforts to develop the Combined Deep Constructor and Perturbator, which combines two powerful constructive and perturbative Deep Learning-based heuristics, using attention mechanisms at their core. Furthermore, we improve the Attention Model-Dynamic for the Capacitated Vehicle Routing Problem by proposing a memory-efficient algorithm that reduces its memory complexity by a factor of the number of nodes. Our method shows promising results. It demonstrates a cost improvement in common datasets when compared against other multiple Deep Learning methods. It also obtains close results to the state-of-the art heuristics from the Operations Research field. Additionally, the proposed memory efficient algorithm for the Attention Model-Dynamic model enables its use in problem instances with more than 100 nodes.
翻译:机动车辆脱轨问题是众所周知的NP-硬性难题,对寻找向多个地点运送产品的车辆的最佳路线提出了挑战。最近,出现了新的努力,以利用深层学习来创造建设性和不稳定的稳健性来解决这一问题。在本文中,我们联合开发了“深层构造和扰动综合体”,将两个强大的建设性和扰动性深层学习的休眠机制结合在一起。此外,我们改进了“注意机动车辆脱轨问题模型-动态”的方法,提出一个记忆高效的算法,通过节点数的一个因素来降低其记忆复杂性。我们的方法显示了有希望的结果。它表明,与其他多层深层学习方法相比,共同数据集的成本有所改善。它也从操作研究领域获取了近乎现代的超高科技。此外,拟议的“注意模型-动态”模型的记忆高效算法,使得其在问题情况下能够使用超过100个节点。