Ant Colony Optimization and the Minimum Cut Problem

Timo Kötzing, Per Kristian Lehre, Frank Neumann, Pietro Simone Oliveto

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


    Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was proved successful for the minimum spanning tree problem is studied. Using rigorous runtime analyses we show how the ACO algorithm behaves similarly to Karger and Stein's algorithm for the minimum cut problem as long as the use of pheromone values is limited. Hence optimal solutions are obtained in expected polynomial time. On the other hand, we show that high use of pheromones has a negative effect, and the ACO algorithm may get trapped in local optima resulting in an exponential runtime to obtain an optimal solution. This result indicates that ACO algorithms may be inappropriate for finding minimum cuts.
    Original languageEnglish
    Title of host publicationGECCO '10 Proceedings of the 12th annual conference on Genetic and evolutionary computation
    Publication date2010
    ISBN (Print)978-1-4503-0072-8
    Publication statusPublished - 2010
    Event2010 Genetic and Evolutionary Computation Conference - Portland, United States
    Duration: 7 Jul 201011 Jul 2010


    Conference2010 Genetic and Evolutionary Computation Conference
    Country/TerritoryUnited States
    Internet address


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