preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202310.1167.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 19 October 2023 (08:04:20 CEST)

Ant Colony Optimization (ACO) is a stochastic optimization algorithm inspired by the foraging behavior of ants. We investigate a simplified computational model of ACO, wherein ants sequentially engage in binary decision-making tasks, leaving pheromone trails contingent upon their choices. The quantity of pheromone left is the number of correct answers. We scrutinize the impact of a salient parameter in the ACO algorithm, specifically, the exponent $\alpha$ that governs the pheromone levels in the stochastic choice function. In the absence of pheromone evaporation, the system is accurately modeled as a multivariate nonlinear P\'{o}lya urn, undergoing a phase transition as $\alpha$ varies. The probability of selecting the correct answer for each question asymptotically approaches the stable fixed point of the nonlinear P\'{o}lya urn. The system exhibits dual stable fixed points for $\alpha\ge \alpha_c$ and a singular stable fixed point for $\alpha<\alpha_c$. When pheromone evaporates over a time scale $\tau$, the phase transition does not occur and leads to a bimodal stationary distribution of probabilities for $\alpha\ge \alpha_c$ and a monomodal distribution for $\alpha<\alpha_c$.

Ant colony optimization; Polya urn process; phase transition

Physical Sciences, Theoretical Physics

* All users must log in before leaving a comment