A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET PROBLEM

Saeed Mehrabi, Abbas Mehrabi, Ali D. Mehrabi

Abstract

In recent years, Genetic Algorithms (GAs) have been frequently used for many search and optimization problems. In this paper, we use genetic algorithms for solving the NP-complete maximum independent set problem (MISP). We have developed a new heuristic independent crossover (HIX) especially for MISP, introducing a new hybrid genetic algorithm (MIS-HGA). We use a repair operator to ensure that our offsprings are valid after mutation. We compare our algorithm, MIS-GA, with an efficient existing algorithm called GENEsYs. Also, a variety of benchmarks are used to test our algorithm. As the experimental results show: 1) our algorithm outperforms GENEsYs, and, 2) applying HIX to genetic algorithms with an appropriate mutation rate, gives far better performance than the classical crossover operators.

References

  1. Bodenhofer, U.: (2003) "Genetic Algorithms: Theory and Applications". Lecture Notes. 3rd edition.
  2. Chu, P. C., Beasley, J. E.: (2004) "A Genetic Algorithm for Set Covering Problem". European Journal of Operational Research 94, 392-904.
  3. Goldberg, D. E.: (1989) "Genetic Algorithms in Search, Optimization and Machine Learning". Massachusetts: Addison Wesley.
  4. Hifi, M.: (1997) "A Genetic Algorithm-based Heuristic for Solving the Weighted Maximum Independent Set and Some Equivalent Problems". J. of Operational Research.
  5. Holland, J. H.: (1992) "Adaptation in natural and artificial systems". MA: MIT Press.
  6. Khuri, S., B├Ąck, Th.: (1994) "An Evolutionary Heuristic for the Maximum Independent Set Problem". In proceedings of the IEEE Conference on Evolutionary Computation, vol. 2, 531-535.
  7. Lio, X., Sakamoto, A., Shimamoto, T.: (1997) A Genetic Approach for Maximum Independent Set Problems". IEIC Transactions on Fundamentals of Electronics, Communications and Computer Sciences, No. 3 pp. 551-556.
  8. Mehrabi, S., Mehrabi, A.: (2009a) "A New Genetic Algorithm for Multiprocessor Scheduling Problem", (in Persian). In Proc. of the National Conference on Software Engineering (NSEC'09), Tehran, Iran.
  9. Mehrabi, A., Mehrabi, S.: (2009b) "A Genetic Algorithm for Multiprocessor Task Assignment Problem with Limited Memory". 14th International CSI Symposium on Intelligent Systems and Soft Computing (CSICC2009), Tehran, Iran. Submitted.
  10. Papadimitriou, C. H., Steiglitz, K.: (1982), "Combinatorial Optimization: Algorithms and Complexity". Prentice Hall.
  11. West, D. B.: (2001) "Introduction to Graph Theory". Prentice Hall, Inc.
  12. Whitley, D.: (1995) "Modeling Hybrid Genetic Algorithms", Genetic Algorithms in Engineering and Computer Science. Wiley, 1995.
  13. Neil J. A. Sloane.: (2009) Challenge Problems: Independent Sets in Graphs, online available at: http:// www.research.att.com/njas/doc/graphs.html
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Paper Citation


in Harvard Style

Mehrabi S., Mehrabi A. and D. Mehrabi A. (2009). A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET PROBLEM . In Proceedings of the 4th International Conference on Software and Data Technologies - Volume 2: ICSOFT, ISBN 978-989-674-010-8, pages 314-317. DOI: 10.5220/0002253403140317


in Bibtex Style

@conference{icsoft09,
author={Saeed Mehrabi and Abbas Mehrabi and Ali D. Mehrabi},
title={A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET PROBLEM},
booktitle={Proceedings of the 4th International Conference on Software and Data Technologies - Volume 2: ICSOFT,},
year={2009},
pages={314-317},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002253403140317},
isbn={978-989-674-010-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Software and Data Technologies - Volume 2: ICSOFT,
TI - A NEW HYBRID GENETIC ALGORITHM FOR MAXIMUM INDEPENDENT SET PROBLEM
SN - 978-989-674-010-8
AU - Mehrabi S.
AU - Mehrabi A.
AU - D. Mehrabi A.
PY - 2009
SP - 314
EP - 317
DO - 10.5220/0002253403140317