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Deterministic Nonlinear Modeling of Ant Algorithm with Logistic Multi-Agent System

Rodolphe Charrier 1 Christine Bourjot 1 François Charpillet 1
1 MAIA - Autonomous intelligent machine
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Ant algorithms are one of the main programming paradigms in swarm intelligence. They are built on stochastic decision functions, which can also be found in other types of bio-inspired algorithms with the same mathematical form. However, though this modeling leads to high-performance algorithms, some phenomena, like symmetry break, are still not well understood or modeled at the ant level. This paper proposes an original analysis of the problem : we establish a reactive multi-agent system based on logistic nonlinear decision maps, and designed according to the influence-reaction scheme. Our proposition is an entirely novel approach to the mathematical foundations of ant algorithms : contrary to the current stochastic approaches, we show that an alternative deterministic model exists, which has its origin in deterministic chaos theory. The rewriting of the decision functions leads to a new way of understanding and visualizing the convergence behavior of ant algorithms. We apply our approach on a concrete example, namely the binary bridge problem.
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Rodolphe Charrier, Christine Bourjot, François Charpillet. Deterministic Nonlinear Modeling of Ant Algorithm with Logistic Multi-Agent System. International Conference on Autonomous Agents and Multiagent Systems - AAMAS'07, May 2007, Honolulu Hawaii, United States. pp.920-922, ⟨10.1145/1329125.1329293⟩. ⟨inria-00168313⟩

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