Improved Lower Limits for Pheromone Trails in Ant Colony Optimization

Ant Colony Optimization algorithms were inspired by the foraging behavior of ants that accumulate pheromone trails on the shortest paths to food. Some ACO algorithms employ pheromone trail limits to improve exploration and avoid stagnation by ensuring a non-zero probability of selection for all trails. The MAX-MIN Ant System (MMAS) sets explicit pheromone trail limits while the Ant Colony System (ACS) has implicit pheromone trail limits. Stagnation still occurs in both algorithms with the recommended pheromone trail limits as the relative importance of the pheromone trails increases (α > 1). Improved estimates of the lower pheromone trail limit (τmin) for both algorithms help avoid stagnation and improve performance for α > 1. The improved estimates suggest a general rule to avoid stagnation for stochastic algorithms with explicit or implicit limits on exponential values used in proportional selection.