A permutation based Genetic Algorithm for minimum span frequency assignment

  • Christine Valenzuela
  • Steve Hurley
  • Derek Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1498)


We describe a Genetic Algorithm (GA) for solving the minimum span frequency assignment problem (MSFAP).The MSFAP involves assigning frequencies to each transmitter in a region, subject to a number of constraints being satisfied, such that the span, i.e. the range of frequencies used, is minimized. The technique involves finding an ordering of the transmitters for use in a sequential (greedy) assignment process. Results are given which show that our GA produces optimal solutions to several practical problem instances, and compares favourably to simulated annealing and tabu search algorithms.


Genetic Algorithm Tabu Search Travel Salesman Problem Travel Salesman Problem Channel Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L.G. Anderson. A simulation study of some dynamic channel assignment algorithms in a high capacity mobile telecommunications system. IEEE Transactions on Communications, COM-21:1294–1301, 1973.CrossRefGoogle Scholar
  2. 2.
    D.J. Cavicchio. Adaptive search using simulated evolution. PhD thesis, University of Michigan, 1970.Google Scholar
  3. 3.
    W. Crompton, S. Hurley, and N.M. Stephens. A parallel genetic algorithm for frequency assignment problems. In Proc. IMACS/IEEE Conference on Signal Processing, Robotics and Neural Networks, pages 81–84, Lille, France, 1994.Google Scholar
  4. 4.
    L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings 9th International Joint Conference on Artificial Intelligence, pages 162–164, 1985.Google Scholar
  5. 5.
    L. Davis. Job shop scheduling with genetic algorithms. In J. Grefenstette, editor, Proceedings International Conference on Genetic Algorithms and their Applications, pages 136–140. Lawrence Erlbaum Associates, 1985.Google Scholar
  6. 6.
    N. Funabiki and Y. Takefuji. A neural network parallel algorithm for channel assignment problems in cellular radio networks. IEEE Transactions on Vehicular Technology, 41(4):430–437, 1992.CrossRefGoogle Scholar
  7. 7.
    A. Gamst. Some lower bounds for a class of frequency assignment problems. IEEE Transactions on Vehicular Technology, 35:8–14, 1986.Google Scholar
  8. 8.
    D.E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, 1989.Google Scholar
  9. 9.
    J.H. Holland. Adaption in natural and artificial systems. University of Michigan Press, Ann Arbor, 1975.Google Scholar
  10. 10.
    S. Hurley and D.H. Smith. Meta-heuristics and channel assignment. In R.A. Leese, editor, Methods and algorithms for channel assignment. Oxford University Press, to appear 1998.Google Scholar
  11. 11.
    S. Hurley, D.H. Smith, and S.U. Thiel. FASoft: A system for discrete channel frequency assignment. Radio Science, 32:1921–1939, 1997.CrossRefGoogle Scholar
  12. 12.
    R. Leese. Tiling methods for channel assignment in radio communication networks. In 3rd ICIAM Congress, 1996.Google Scholar
  13. 13.
    I.M. Oliver, D.J. Smith, and J.R.C. Holland. A study of permutation operators on the travelling salesman problem. In Proceedings 2nd International Conference on Genetic Algorithms, pages 224–230, 1987.Google Scholar
  14. 14.
    K.N. Sivarajan, R.J. McEliece, and J.W. Ketchum. Channel assignment in cellular radio. In Proceedings of 39th Conference, IEEE Vehicular Technolgy Society, pages 846–850, 1989.Google Scholar
  15. 15.
    D.H. Smith, S.M. Allen, and S. Hurley. Lower bounds for channel assignment. In R.A. Leese, editor, Methods and algorithms for channel assignment. Oxford University Press, to appear 1998.Google Scholar
  16. 16.
    D.H. Smith and S. Hurley. Bounds for the frequency assignment problem. Discrete Mathematics, 167/168:571–582, 1997.MathSciNetCrossRefGoogle Scholar
  17. 17.
    D.H. Smith, S. Hurley, and S.U. Thiel. Improving heuristics for the frequency assignment problem. European Journal of Operational Research, to appear 1998.Google Scholar
  18. 18.
    G. Syswerda. Uniform crossover in genetic algorithms. In J.D. Schaffer, editor, Proceedings 3rd International Conference on Genetic Algorithms, pages 2–9. Lawrence Erlbaum Associates, 1989.Google Scholar
  19. 19.
    D. Tcha, Y. Chung, and T. Choi. A new lower bound for the frequency assignment problem. IEEE/ACM Transactions on Networking, 5(1):34–39, 1997.CrossRefGoogle Scholar
  20. 20.
    C.L. Valenzuela. Evolutionary divide and conquer: A novel genetic approach to the TSP. PhD thesis, Imperial College, University of London, 1995.Google Scholar
  21. 21.
    W. Wang and C. Rushforth. An adaptive local search algorithm for the channel assignment problem (cap). IEEE Transactions on Vehicular Technology, 45(3):459–466, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Christine Valenzuela
    • 1
  • Steve Hurley
    • 2
  • Derek Smith
    • 3
  1. 1.School of Computing and MathematicsUniversity of TeessideUK
  2. 2.Department of Computer ScienceCardiff UniversityUK
  3. 3.Division of Mathematics and ComputingUniversity of GlamorganUK

Personalised recommendations