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Rodolphe Charrier, Cyrille Bertelle
This paper investigates the possibility of using parametric one-dimensional chaotic maps within a swarm of ant-like agents to perform optimization tasks. Ant algorithms derive from a stochastic modeling based on specific probability laws. We consider in this paper a full deterministic model of chaotic ants which use a chaotic map –like the quadratic map – to govern the decision behavior of ant-like agents. This chaotic map can produce pseudo-randomness for simulating stochastic behaviors with specific distributions. The main advantage of this approach lies in the possibility of controlling the chaotic properties of the iterated map through a single parameter per map. We deal actually with a decentralized swarm of agents individually controlled by only one parameter. This resulting chaotic swarm is driven by a “pheromone field”, as classical ant algorithms do, which modifies each individual control parameter in respect with the perceived values of the field. To summarize, the proposed algorithm in this paper
operates a distributed parametric control on agent’s internal decisions by means of a global pheromone field. Finally we illustrate and test this approach on a Travelling Salesman Problem (TSP) instance, and compare the results with the original Ant System algorithm.
On the one hand, this change of the modeling paradigm — deterministic versus stochastic — implies a novel view of the internal mechanisms involved during the searching and optimizing process of ants. On the other hand, the obtained results prove the efficiency of this algorithm design.
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