Swarm Intelligence

, Volume 1, Issue 1, pp 59–79 | Cite as

Mathematical runtime analysis of ACO algorithms: survey on an emerging issue



The paper gives an overview on the status of the theoretical analysis of Ant Colony Optimization (ACO) algorithms, with a special focus on the analytical investigation of the runtime required to find an optimal solution to a given combinatorial optimization problem. First, a general framework for studying questions of this type is presented, and three important ACO variants are recalled within this framework. Secondly, two classes of formal techniques for runtime investigations of the considered type are outlined. Finally, some available runtime complexity results for ACO variants, referring to elementary test problems that have been introduced in the theoretical literature on evolutionary algorithms, are cited and discussed.


Analysis of algorithms Ant colony optimization Combinatorial optimization Runtime analysis Runtime complexity 


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Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Statistics and Decision Support SystemsUniversity of ViennaViennaAustria

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