On the Finite-Time Dynamics of Ant Colony Optimization

Walter J. Gutjahr ()
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Walter J. Gutjahr: University of Vienna

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 1, 105-133

Abstract: Abstract An analytical framework for investigating the finite-time dynamics of ant colony optimization (ACO) under a fitness-proportional pheromone update rule on arbitrary construction graphs is developed. A limit theorem on the approximation of the stochastic ACO process by a deterministic process is demonstrated, and a system of ordinary differential equations governing the process dynamics is identified. As an example for the application of the presented theory, the behavior of ACO on three different construction graphs for subset selection problems is analyzed and compared for some basic test functions. The theory enables first rough theoretical predictions of the convergence speed of ACO.

Keywords: Ant colony optimization; Convergence speed; Probabilistic algorithms; Stochastic approximation; Stochastic optimization (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s11009-006-7291-4

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