A spatial parallel heuristic approach for solving very large-scale vehicle routing problems

The vehicle routing problem (VRP) is one of the most prominent problems in spatial optimization because of its broad applications in both the public and private sectors. This article presents a novel spatial parallel heuristic approach for solving large-scale VRPs with capacity constraints. A spatial partitioning strategy is devised to divide a region of interest into a set of small spatial cells to allow the use of a parallel local search with a spatial neighbor reduction strategy. An additional local search and perturbation mechanism around the border area of spatial cells is used to improve route segments across spatial cells to overcome the border effect. The results of one man-made VRP benchmark and three real-world super-large-scale VRP instances with tens of thousands of nodes verify that the presented spatial parallel heuristic approach achieves a comparable solution with much less computing time.