A short convergence proof for a class of ant colony optimization algorithms

In this paper, we prove some convergence properties for a class of ant colony optimization algorithms. In particular, we prove that for any small constant 0 and for a sufficiently large number of algorithm iterations , the probability of finding an optimal solution at least once is ( ) 1 and that this probability tends to 1 for . We also prove that, after an optimal solution has been found, it takes a finite number of iterations for the pheromone trails associated to the found optimal solution to grow higher than any other pheromone trail and that, for , any fixed ant will produce the optimal solution during the th iteration with probability 1 ^( min max), where min and max are the minimum and maximum values that can be taken by pheromone trails.

• Type: Journal
• Year: 2002
• Where: TEC
• Authors: Thomas Stützle, Marco Dorigo
• Keywords: Ant Colony Optimization, Optimal Solution, Pheromone Trails, TEC 2002