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

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.

Domaines: Système multi-agents [cs.MA]

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⟩