Convergence and rate of convergence of a simple ant model

Amine Boumaza 1 Bruno Scherrer 1
1 MAIA - Autonomous intelligent machine
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present a simple ant model that solves a discrete foraging problem. We describe simulations and provide a complete convergence analysis: we show that the ant population computes the solution of some optimal control problem and converges in some well defined sense. We discuss the rate of convergence with respect to the number of ants: we give experimental and theoretical arguments that suggest that this convergence rate is superlinear with respect to the number of agents. Furthermore, we explain how this model can be extended in order to solve optimal control problems in general and argue that such an approach can be applied to any problem that involves the computation of the fixed point of a contraction mapping. This allows to design a large class of formally well understood ant like algorithms.
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Submitted on : Wednesday, December 20, 2006 - 11:30:56 AM
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Amine Boumaza, Bruno Scherrer. Convergence and rate of convergence of a simple ant model. [Research Report] 2007, pp.8. ⟨inria-00121341⟩

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