Ant colony optimization and the minimum cut problem

Authors:
Timo Kötzing;Per Kristian Lehre;Frank Neumann;Pietro Simone Oliveto
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;University of Birmingham, Birmingham, United Kingdom;Max-Planck-Institut für Informatik, Saarbrücken, Germany;University of Birmingham, Birmingham, United Kingdom
Venue:
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Year:
2010

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Abstract

Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was proved successful for the minimum spanning tree problem is studied. Using rigorous runtime analyses we show how the ACO algorithm behaves similarly to Karger and Stein's algorithm for the minimum cut problem as long as the use of pheromone values is limited. Hence optimal solutions are obtained in expected polynomial time. On the other hand, we show that high use of pheromones has a negative effect, and the ACO algorithm may get trapped in local optima resulting in an exponential runtime to obtain an optimal solution. This result indicates that ACO algorithms may be inappropriate for finding minimum cuts.