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

  • Stũtzle T
  • Dorigo M
  • 83


    Mendeley users who have this article in their library.
  • 314


    Citations of this article.


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

Author-supplied keywords

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

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text


Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free