InforLorV4, Main, Curation, bibRecord, 004952

Convergence and rate of convergence of a simple ant model

Identifieur interne : 004952 ( Main/Curation ); précédent : 004951; suivant : 004953

Convergence and rate of convergence of a simple ant model

Auteurs : Amine Boumaza [France] ; Bruno Scherrer [France]

Source :

RBID : Hal:inria-00170186

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.

Url:

https://hal.inria.fr/inria-00170186

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<front><div type="abstract" xml:lang="en">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.</div>
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Convergence and rate of convergence of a simple ant model

Convergence and rate of convergence of a simple ant model

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