Stability analysis of the Ant System dynamics with non-uniform pheromone deposition rules

The paper extends the classical ant systems by considering non-uniform deposition by the ants while constructing pheromone trails. A deterministic solution to the ant system dynamics for both uniform and non-uniform pheromone deposition rules has been obtained to determine the parameters of the dynamics that ensure stability in pheromone trails. Computer simulation confirmed the results of stability analysis. Performance of the extended ant system (with non-uniform pheromone deposition rule) is compared with the classical ant system using the well known traveling salesperson problem. Simulation results reveal that the extended ant system outperforms the classical ant system by a large margin with respect to convergence speed without sacrificing the quality of solution.