Computers & Operations Research 34 (2007) 2743 – 2757 www.elsevier.com/locate/cor An efficient variable neighborhood search heuristic for very large scale vehicle routing problems Jari Kytöjoki a , Teemu Nuortio b , Olli Bräysy a , Michel Gendreau c , ∗ a Agora Innoroad Laboratory,Agora Center, University of Jyväskylä, P.O. Box 35, FI-40014, Finland b Department of Environmental Sciences, University of Kuopio, P.O. Box 1627, FI-70211 Kuopio, Finland c Center for Research onTransportation, University of Montreal, P.O.Box 6128, Succursale Centre-ville, Montreal, H3C 3J7, Canada Available online 13 December 2005 Abstract In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.  2005 Elsevier Ltd. All rights reserved. Keywords: Vehicle routing; Heuristics;Variable neighborhood search; Guided local search; Large scale problems 1. Introduction Efficient distribution of goods is of paramount importance, not only for the survival of many logistic service providers, but ultimately for the competitiveness of a region’s economy by lowering the cost of goods to consumers. Cost savings can be achieved, in particular, through the use of high quality routes and schedules for the fleet of vehicles that performs distribution tasks. The vehicle routing problem (VRP), introduced by Dantzig and Ramser [1], holds a central place with regards to the determination of efficient routes in distribution management. Consequently, it has become one of the most widely studied problems in combinatorial optimization. The classical VRP can be formally defined as follows. Let G = (V,E) be a connected digraph where V is a set of n + 1 nodes and E a set of arcs with non-negative weights and associated travel times. One of the nodes represents a depot where the fleet of vehicles is based. With each node i, apart from the depot, is associated a demand q i that can be a delivery from or a pickup to the depot. The problem consists in determining a set of routes starting and ending at the depot such that the total distance traveled is minimized, while the cumulative demand of the customers serviced by any route t, ∑ i ∈t q i , does not exceed the vehicle capacity Q and its ∗ Corresponding author. Tel.: +1 514 3437435; fax: +1 514 3437121. E-mail address: michelg@crt.umontreal.ca (M. Gendreau). 0305-0548/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2005.10.010