Advertisement

Golomb Rulers: The Advantage of Evolution

  • Francisco B. Pereira
  • Jorge Tavares
  • Ernesto Costa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2902)

Abstract

In this paper we present a new evolutionary algorithm designed to efficiently search for optimal Golomb rulers. The proposed approach uses a redundant random keys representation to codify the information contained in a chromosome and relies on a simple interpretation algorithm to obtain feasible solutions. Experimental results show that this method is successful in quickly identifying good solutions and that can be considered as a realistic alternative to massive parallel approaches that need several months or years to discover high quality Golomb rulers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Golomb, S.: How to Number a Graph. In: Graph Theory and Computing, pp. 23–37. Academic Press, London (1972)Google Scholar
  2. 2.
    Bloom, G., Golomb, S.: Applications of numbered undirected graphs. Proceedings of the IEEE 65, 562–570 (1977)CrossRefGoogle Scholar
  3. 3.
    Dollas, A., Rankin, W., McCracken, D.: New algorithms for golomb ruler derivation and proof of the 19 mark ruler. IEEE Transactions on Information Theory 44, 379–382 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Blum, E., Biraud, F., Ribes, J.: On optimal synthetic linear arrays with applications to radioastronomy. IEEE Transactions on Antennas and Propagation AP-22, 108–109 (1974)Google Scholar
  5. 5.
    Hayes, B.: Collective wisdom. American Scientist 86, 118–122 (1998)Google Scholar
  6. 6.
    Klove, T.: Bounds and construction for difference triangle sets. IEEE Transactions on Information Theory IT-35 (1989) Google Scholar
  7. 7.
    Bean, J.: Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing 6, 154–160 (1994)zbMATHGoogle Scholar
  8. 8.
    Soliday, S., Homaifar, A., Lebby, G.: Genetic algorithm approach to the search for golomb rulers. In: Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA 1995), pp. 528–535. Morgan Kaufmann, San Francisco (1995)Google Scholar
  9. 9.
    Dewdney, A.: Computer recreations. Scientific American, 16–26 (1985)Google Scholar
  10. 10.
    Gardner, M.: Mathematical games. Scientific American, 198–112 (1972)Google Scholar
  11. 11.
    Shearer, J.: Some new optimum golomb rulers. IEEE Transactions on Information Theory IT-36, 183–184 (1990)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Norman, B., Smith, A.: Random keys genetic algorithm with adaptive penalty function for optimization of constrained facility layout problems. In: Proceedings of the Fourth International Conference on Evolutionary Computation, pp. 407–411. IEEE, Los Alamitos (1997)Google Scholar
  13. 13.
    Rothlauf, F., Goldberg, D., Heinzl, A.D.: Network random keys - a tree representation scheme for genetic and evolutionary algorithms. Evolutionary Computation 10, 75–97 (2002)CrossRefGoogle Scholar
  14. 14.
    Magyar, G., Johnsson, G., Nevalainen, O.: An adaptive hybrid genetic algorithm fot the three-matching problem. IEEE Transactions on Evolutionary Computation 4, 135–146 (2000)CrossRefGoogle Scholar
  15. 15.
    Merz, P., Freisleben, B.: Genetic local search for the tsp: New results. In: Back, T., Michalewicz, Z., Yao, X. (eds.) Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 159–164. IEEE Press, Los Alamitos (1997)Google Scholar
  16. 16.
    Moscato, P.: Memetic Algorithms: a Short Introduction. In: New Ideas in Optimization, pp. 221–234. McGraw-Hill, New York (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Francisco B. Pereira
    • 1
    • 2
  • Jorge Tavares
    • 2
  • Ernesto Costa
    • 2
  1. 1.Instituto Superior de Engenharia de CoimbraQuinta da NoraCoimbraPortugal
  2. 2.Centro de Informática e Sistemas da Universidade de CoimbraCoimbraPortugal

Personalised recommendations