Since it is computationally expensive to solve the vehicle routing problem (VRP) optimally, as this problem is NP-hard, in this technical note we study how to accurately approximate the optimal VRP tour length. In our previous papers, we developed a linear regression model including the mean and standard deviation of the modified Clarke and Wright heuristic solution values, which was able to predict the optimal VRP tour length fairly well. In this note, we find that by doing a small amount of extra work to include the minimum of the modified Clarke and Wright heuristic solution values, we can improve the predictive results substantially.

由于最优地解决车辆路径问题 (VRP) 的计算成本很高，并且该问题是 NP 难问题，因此在本技术说明中，我们研究如何准确地近似最佳 VRP 游览长度。在我们之前的论文中，我们开发了一个线性回归模型，包括修正后的 Clarke 和 Wright 启发式解值的平均值和标准差，该模型能够很好地预测最佳 VRP 游览长度。在这篇文章中，我们发现通过做少量的额外工作来包含修改后的克拉克和赖特启发式解决方案值的最小值，我们可以大大改进预测结果。