Swarm Intell (2007) 1: 135–151
DOI 10.1007/s11721-007-0005-x
Ant colony optimization for real-world vehicle routing
problems
From theory to applications
A.E. Rizzoli, · R. Montemanni · E. Lucibello ·
L.M. Gambardella
Received: 6 December 2006 / Accepted: 10 May 2007 / Published online: 13 September 2007
' Springer Science + Business Media, LLC 2007
Abstract Ant colony optimization (ACO) is a metaheuristic for combinatorial optimization
problems. In this paper we report on its successful application to the vehicle routing problem
(VRP). First, we introduce the VRP and some of its variants, such as the VRP with time
windows, the time dependent VRP, the VRP with pickup and delivery, and the dynamic
VRP. These variants have been formulated in order to bring the VRP closer to the kind of
situations encountered in the real-world.
Then, we introduce the basic principles of ant colony optimization, and we briefly present
its application to the solution of the VRP and of its variants.
Last, we discuss the applications of ACO to a number of real-world problems: a VRP
with time windows for a major supermarket chain in Switzerland; a VRP with pickup and
delivery for a leading distribution company in Italy; a time dependent VRP for freight distri-
bution in the city of Padua, Italy, where the travel times depend on the time of the day; and
an on-line VRP in the city of Lugano, Switzerland, where customers’ orders arrive during
the delivery process.
Keywords Ant colony optimization · Ant colony system · Vehicle routing problem ·
Dynamic VRP · Rich VRP · Real-world VRP
1 Introduction
The vehicle routing problem (VRP) concerns the transport of items between depots and
customers by means of a fleet of vehicles. Examples of VRPs are: milk delivery, mail de-
livery, school bus routing, solid waste collection, heating oil distribution, parcel pick-up
and delivery, dial-a-ride systems, and many others. Although finding the most cost efficient
A.E. Rizzoli, () · R. Montemanni · L.M. Gambardella
Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno, Switzerland
e-mail: andrea@idsia.ch
E. Lucibello
AntOptima, via Fusoni 4, 6900 Lugano, Switzerland

136 Swarm Intell (2007) 1: 135–151
way to distribute goods across the logistic network is the main objective of supply-chain
systems, only in the early ’90s enterprise resource planning software vendors started to in-
tegrate tools to solve the VRP in supply chain management software (a review of software
for supply chain management can be found in Aksoy and Derbez 2003).
The practical interest of the VRP has spawn a number of studies, which tackled the prob-
lem from many sides. Yet, the VRP is combinatorially complex and, therefore, as the size
of the problem increases, it becomes harder and harder to obtain an exact solution for it in
a reasonable amount of time. Thus, even the most advanced exact solution methods impose
particular constraints on the problem instance, which are often violated when dealing with
real-world vehicle routing problems, leaving practitioners unsatisfied with the performance
and applicability of the algorithms.
Given the shortcomings of exact solution methods, researchers in the field of operations
research (OR) started to develop metaheuristics (Blum and Roli 2003), heuristic methods
that can be applied to a wide class of problems. One of the advantages metaheuristics have
over traditional optimization algorithms is their ability to produce a good suboptimal solu-
tion in short time. The integration of optimization algorithms based on metaheuristics, such
as tabu search (Glover and Laguna 1997), simulated annealing (Kirkpatrick et al. 1983), ant
colony optimization (Dorigo et al. 1996, 1999), and iterated local search (Lourenço et al.
2003), with advanced logistic systems for supply chain management opens new perspectives
for operations research applications in industry. In particular, for the solution of VRP and
its variants, a number of metaheuristics have been successfully applied, such as: simulated
annealing (Osman 1993), tabu search (Gendreau et al. 1994; Taillard et al. 1997), granular
tabu search (Toth and Vigo 2003), genetic algorithms (Van Breedam 1996), guided local
search (Kilby et al. 1999), variable neighborhood search (Bräysy 2003), greedy random-
ized adaptive search procedure (Resende and Ribeiro 2003), and ant colony optimization
(Gambardella 1999; Reimann et al. 2003).
In this paper we focus on ant colony optimization (ACO) (Dorigo and Stützle 2004), a
metaheuristic inspired by the foraging behavior of ant colonies. ACO has been used for the
approximate solution of a number of traditional OR problems, among which the job shop
scheduling problem, the quadratic assignment problem, the sequential ordering problem,
the graph coloring problem, and the shortest common supersequence problem (Dorigo and
Stützle 2004). More recently, ACO has been employed in a number of open shop scheduling
problems (Blum 2005), in optimal product design (Albritton and McMullen 2007), and has
also been used in some environmental problems, such as the design of a water distribution
network (Zecchin et al. 2007) or the planning of wells for groundwater quality monitor-
ing (Li and Chan Hilton 2007), thus proving its adaptability to very different domains of
application.
The flexibility of the ACO metaheuristic allowed its application to many vehicle rout-
ing problems where heterogeneous vehicle fleets, limitations on customer accessibility, time
windows, and the order imposed by pick-ups and deliveries considerably complicate the
problem formulation. These kinds of problems have been labeled as rich vehicle routing
problems (Hartl et al. 2006). Yet, real-world problems are even more complex; for instance,
travel times may be uncertain and may depend on traffic conditions, and not all customers’
orders may be perfectly known in time and dimension. These problem variants have been
called dynamic VRP and they are currently attracting a lot of research efforts, because of
their closeness to real-world traffic and distribution models (Zeimpekis et al. 2007). The
objective of this paper is to describe how ant colony optimization can be successfully used
to solve a number of VRP variants, both for some of the basic problem instances (the capac-
itated VRP, the VRP with time windows, the VRP with pickup and delivery) and for some