Journal of Mathematical Modelling and Algorithms

, Volume 6, Issue 3, pp 361–391 | Cite as

Finding Edge-disjoint Paths in Networks: An Ant Colony Optimization Algorithm

  • Maria J. Blesa
  • Christian Blum


One of the basic operations in communication networks consists in establishing routes for connection requests between physically separated network nodes. In many situations, either due to technical constraints or to quality-of-service and survivability requirements, it is required that no two routes interfere with each other. These requirements apply in particular to routing and admission control in large-scale, high-speed and optical networks. The same requirements also arise in a multitude of other applications such as real-time communications, vlsi design, scheduling, bin packing, and load balancing. This problem can be modeled as a combinatorial optimization problem as follows. Given a graph G representing a network topology, and a collection T={(s 1,t 1)...(s k ,t k )} of pairs of vertices in G representing connection request, the maximum edge-disjoint paths problem is an NP-hard problem that consists in determining the maximum number of pairs in T that can be routed in G by mutually edge-disjoint s i t i paths. We propose an ant colony optimization (aco) algorithm to solve this problem. aco algorithms are approximate algorithms that are inspired by the foraging behavior of real ants. The decentralized nature of these algorithms makes them suitable for the application to problems arising in large-scale environments. First, we propose a basic version of our algorithm in order to outline its main features. In a subsequent step we propose several extensions of the basic algorithm and we conduct an extensive parameter tuning in order to show the usefulness of those extensions. In comparison to a multi-start greedy approach, our algorithm generates in general solutions of higher quality in a shorter amount of time. In particular the run-time behaviour of our algorithm is one of its important advantages.


Ant colony optimization Maximum edge-disjoint paths problem 



(maximum) edge-disjoint paths problem


Simple Greedy Algorithm


Multi-start Greedy Algorithm


Ant Colony System


Ant Colony Optimization

Mathematics Subject Classifications (2000)

90-08 68Wxx 68T20 


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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.ALBCOM research group, Dept. Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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