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Phase Transition in Ant Colony Optimization
Version 1
: Received: 17 October 2023 / Approved: 18 October 2023 / Online: 19 October 2023 (08:04:20 CEST)
A peer-reviewed article of this Preprint also exists.
Mori, S.; Nakamura, S.; Nakayama, K.; Hisakado, M. Phase Transition in Ant Colony Optimization. Physics 2024, 6, 123-137. Mori, S.; Nakamura, S.; Nakayama, K.; Hisakado, M. Phase Transition in Ant Colony Optimization. Physics 2024, 6, 123-137.
Abstract
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 $\alpha<\alpha_c$.
Keywords
Ant colony optimization; Polya urn process; phase transition
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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