Ant Colony Optimization (ACO) is inspired by the ability of ant colonies to find shortest paths between their nest and a food source. We analyze the running time of different ACO systems for shortest path problems. First, we improve running time bounds by Attiratanasunthron and Fakcharoenphol [Information Processing Letters, 105(3):88–92, 2008] for single-destination shortest paths and extend their results for acyclic graphs to arbitrary graphs. Our upper bound is asymptotically tight for large evaporation factors, holds with high probability, and transfers to the all-pairs shortest paths problem. There, a simple mechanism for exchanging information between ants with different destinations yields a significant improvement. Our results indicate that ACO is the best known metaheuristic for the all-pairs shortest paths problem.


Short Path Directed Acyclic Graph Short Path Problem Outgoing Edge Pheromone Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christian Horoba
    • 1
  • Dirk Sudholt
    • 1
    • 2
  1. 1.LS 2, Fakultät für InformatikTechnische Universität DortmundDortmundGermany
  2. 2.International Computer Science InstituteBerkeleyUSA

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