1. A Nonlinear Multi-agent System designed for Swarm Intelligence: the Logistic MAS
- Author
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Rodolphe Charrier, Christine Bourjot, François Charpillet, Autonomous intelligent machine (MAIA), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematical optimization ,Optimization problem ,Computer science ,Flocking (behavior) ,Stochastic modelling ,business.industry ,Multi-agent system ,Swarm behaviour ,02 engineering and technology ,01 natural sciences ,Swarm intelligence ,Chaos theory ,[INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA] ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Programming paradigm ,020201 artificial intelligence & image processing ,Artificial intelligence ,010306 general physics ,business - Abstract
International audience; Ant algorithms and flocking algorithms are the two main programming paradigms in swarm intelligence. They are built on stochastic models, widely used in optimization problems. However, though this modeling leads to high-performance algorithms, some mechanisms, like the symmetry break in ant decision, are still not well understood at the local ant level. Moreover, there is currently no modeling approach which joins the two paradigms. This paper proposes an entirely novel approach to the mathematical foundations of swarm algorithms: contrary to the current stochastic approaches, we show that an alternative deterministic model exists, which has its origin in deterministic chaos theory. We establish a reactive multi-agent system, based on logistic nonlinear decision maps, and designed according to the influence-reaction scheme. The rewriting of the decision functions leads to a new way of understanding the swarm phenomena in terms of state synchronization, and enables the analysis of their convergence behavior through bifurcation diagrams. We apply our approach on two concrete examples of each algorithm class, in order to demonstrate its general applicability.
- Published
- 2007
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