- Stũtzle T
- Dorigo M

IEEE Transactions on Evolutionary Computation (2002) 6(4) 358-365

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We prove some convergence properties for a class of ant colony

optimization algorithms. In particular, we prove that for any small

constant ε > 0 and for a sufficiently large number of algorithm

iterations t, the probability of finding an optimal solution at least

once is P*(t) ⩾ 1 - ε and that this probability tends to 1 for

t→∞. 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 t→∞, any fixed ant will produce

the optimal solution during the tth iteration with probability P ⩾ 1

εˆ(τmin, τmax), where

τmin and τmax are the minimum and maximum

values that can be taken by pheromone trails

- ACO algorithms
- Ant algorithms
- Ant colony optimization
- Approximation algorithms
- Convergence proof
- Heuristics
- Metaheuristics

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