A PRUNING BASED ANT COLONY ALGORITHM FOR MINIMUM VERTEX COVER PROBLEM

Ali D. Mehrabi, Saeed Mehrabi, Abbas Mehrabi

Abstract

Given an undirected, unweighted graph G = (V , E) the minimum vertex cover (MVC) problem is a subset of V whose cardinality is minimum subject to the premise that the selected vertices cover all edges in the graph. In this paper, we propose a meta-heuristic based on Ant Colony Optimization (ACO) approach to find approximate solutions to the minimum vertex cover problem. By introducing a visible set based on pruning paradigm for ants, in each step of their traversal, they are not forced to consider all of the remaining vertices to select the next one for continuing the traversal, resulting very high improvement in both time and convergence rate of the algorithm. We compare our algorithm with two existing algorithms which are based on Genetic Algorithms (GAs) as well as its testing on a variety of benchmarks. Computational experiments evince that the ACO algorithm demonstrates much effectiveness and consistency for solving the minimum vertex cover problem.

References

  1. D. Costa and A. Hertz, (1997), "Ants Can Color Graphs", Journal of Operational Research Society 48, pp. 295- 305.
  2. I. Dinur and S. Safra, (2001), "The Importance of Being Biased", Technical Report, Department of Computer Science, Tel Aviv University, Israel.
  3. K. Kotecha and N. Gambhava, (2003) "A Hybrid Genetic Algorithm for Minimum Vertex Cover Problem", In Proc. of the 1th Indian International Conference on Artificial Intelligence, India.
  4. M. Dorigo, V. Maniezzo and A. Colorni, (1991), "Positive Feedback as a Search Strategy", Technical Report, 91- 016, Politecnico idi Milano.
  5. M. Dorigo and L. M. Gambardella, (1997), "Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem", IEEE Transactions on Evolutionary Computation, 1(1) pp. 53-66.
  6. M. Hifi, (1997), "A Genetic Algorithm-based Heuristic for Solving the Weighted Maximum Independent Set and Some Equivalent Problems", Journal of Operational Research.
  7. M. R. Gary and D. S. Johnson, (1979), "Computers and Intractability: A Guide to the Theory of NPCompleteness", San Francisco, CA: W. H. Freeman.
  8. R. M. Karp, (1972), "Reducibility Among Combinatorial Problems", In R. E. Miller and J. W. Theater (eds), Complexity of Computer Computations, New York: Plenum Press, 1972.
  9. S. Khuri and Th. B├Ąck, (1994), "An Evolutionary Heuristic for the Minimum Vertex Cover Problem", J. Hopf., editor: Genetic Algorithms within the Framework of Evolutionary Computation, pp. 86-90, Max Plank Institut fur Informatic, Saarbrucken.
  10. S. Mehrabi, A. Mehrabi and A. D. Mehrabi, (2009), "A New Hybrid Genetic Algorithm for Maximum Independent Set Problem", In Proceedings of the 4th International Conference on Software and Data Technologies (ICSOFT'09), Sofia, Bulgaria.
  11. S. Mehrabi and A. Mehrabi, (2009), "A New Genetic Algorithm for Multiprocessor Scheduling Problem" (in Persian), In Proceedings of the First National Conference on Software Engineering (NSEC'09), pp. 127-132. Tehran, Iran.
  12. C. H. Papadimitriou and K. Steiglitz, (1982), "Combinatorial Optimization: Algorithms and Complexity", Prentice Hall.
  13. C. H. Papadimitriou, (1994), "Computational Complexity", Addison Wesley, Reading, MA.
  14. D. B. West, (2001), "Introduction to Graph Theory", Prentice Hall, Inc.
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Paper Citation


in Harvard Style

D. Mehrabi A., Mehrabi S. and Mehrabi A. (2009). A PRUNING BASED ANT COLONY ALGORITHM FOR MINIMUM VERTEX COVER PROBLEM . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 281-286. DOI: 10.5220/0002313802810286


in Bibtex Style

@conference{icec09,
author={Ali D. Mehrabi and Saeed Mehrabi and Abbas Mehrabi},
title={A PRUNING BASED ANT COLONY ALGORITHM FOR MINIMUM VERTEX COVER PROBLEM},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)},
year={2009},
pages={281-286},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002313802810286},
isbn={978-989-674-014-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)
TI - A PRUNING BASED ANT COLONY ALGORITHM FOR MINIMUM VERTEX COVER PROBLEM
SN - 978-989-674-014-6
AU - D. Mehrabi A.
AU - Mehrabi S.
AU - Mehrabi A.
PY - 2009
SP - 281
EP - 286
DO - 10.5220/0002313802810286