Constraints, 5, 389–414 (2000) c  2000 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. A Comparison of Traditional and Constraint-based Heuristic Methods on Vehicle Routing Problems with Side Constraints PHILIP KILBY * phil.kilby@cmis.csiro.au CSIRO MIS, GPO Box 664, Canberra ACT 2601, Australia PATRICK PROSSER pat@cs.strath.ac.uk Department of Computer Science, University of Strathclyde, Glasgow, Scotland PAUL SHAW shaw@ilog.fr ILOG S.A., BP 85, 9 rue de Verdun, 94253 Gentilly Cedex, France Abstract. The vehicle routing problem (VRP) is a variant of the familiar travelling salesperson problem (TSP). In the VRP we are to perform a number of visits, using a number of vehicles of limited capacity, while typically minimizing the distance travelled. VRPs can be complicated by imposing time windows or deadlines on visits, sequencing constraints between visits, and so on. In this paper, we use a constraint-based toolkit for solving vehicle routing problems to study the effect of different heuristic techniques. We investigate the performance of a number of construction and improvement techniques, and show that as the size of the solution space is decreased through addition of side constraints, certain conventional techniques fail while constraint directed techniques continue to perform acceptably. This suggests that constraint programming techniques are particularly suited to VRPs with side constraints. Keywords: vehicle routing, side constraints, construction and improvement techniques 1. Introduction In vehicle routing problems, we must find a feasible route for each vehicle in a fleet, such that all customers are visited, and all other constraints are satisfied (e.g. capacity constraints and time windows). The goal is to minimize the costs of operation. In benchmarks, travel distance is typically used as a cost measure. This is an extremely important problem. A parcel delivery service is a typical application, and the operating cost of such a service may run to millions of dollars per year. Even modest savings—around 5 percent—can equate to large dollar values and large savings in time, fuel and vehicle wear and tear. Most research on vehicle routing problems to date has assumed a fairly simple model which included capacity and time restrictions on the vehicles. More effort has gone into methods for reducing the cost of solutions than supporting rich models. However, the problems faced in industry often require rich models and include a variety of side constraints such as which vehicles or drivers can perform particular visits, what goods can be carried * This work was carried out while all authors were working in the Apes group at the University of Strathclyde.