Efficiently solving very large-scale routing problems

Abstract

The vehicle routing problem is among the most-studied and practically relevant problems in combinatorial optimization. Yet, almost all research thus far has been targeted at solving problems with not more than a few hundred customers. In this paper, we explore how to design a local search heuristic that computes good solutions for very large-scale instances of the capacitated vehicle routing problem in a reasonable computational time. We investigate different ways to reduce the time complexity with pruning and sequential search, as well as the space complexity by restricting the amount of stored information. The resulting algorithm outperforms a previously introduced heuristic for instances of 10,000 and more customers in relatively short computational time. In order to stimulate more research in this domain, we introduce a new set of benchmark instances that are based on a real-world problem and contain up to 30,000 customers and use our heuristic to solve them.