Advertisement

Varying fitness functions in genetic algorithms: Studying the rate of increase of the dynamic penalty terms

  • S. Kazarlis
  • V. Petridis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1498)

Abstract

In this paper we present a promising technique that enhances the efficiency of GAs, when they are applied to constrained optimisation problems. According to this technique, the problem constraints are included in the fitness function as penalty terms, that vary during the GA evolution, facilitating thus the location of the global optimum and the avoidance of local optima. Moreover we proceed to test the effect that the rate of change in the fitness function has on GA performance. The tests are performed on two well-known real-world optimisation problems: the Cutting Stock problem and the Unit Commitment problem. Comparative results are reported.

Keywords

Penalty Function Penalty Term Constraint Violation Penalty Factor Unit Commitment 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Bakirtzis, V. Petridis and S. Kazarlis, “A Genetic Algorithm Solution to the Economic Dispatch Problem”, IEE Proceedings — Generation Transmission Distribution, Vol. 141, No. 4, July 1994, p.p. 377–382.CrossRefGoogle Scholar
  2. [2]
    A. R. Brown, “Optimum packing and Depletion”, American Elsevier Inc., 1971, New York.Google Scholar
  3. [3]
    L. Davis, “Adapting operator probabilities in genetic algorithms”, Proceedings of the Third International Conference on Genetic Algorithms and Their Applications, San Mateo, California, Morgan Kaufman, 1989.Google Scholar
  4. [4]
    H. Dyckhoff, “A Typology of Cutting and Packing Problems”, European Journal of Operational Research 44, 1990, pp. 145–159.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Reading, Mass.: Addison Wesley, 1989.Google Scholar
  6. [6]
    J. A. Joines and C. R. Houck, “On the Use of Non-Stationary Penalty Functions to Solve Nonlinear Constrained Optimisation Problems with GA's,” in Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE Service Center, 1994, pp. 579–584.Google Scholar
  7. [7]
    S. A. Kazarlis, A. G. Bakirtzis and V. Petridis, “A Genetic Algorithm Solution to the Unit Commitment Problem,” IEEE Transactions on Power Systems, Vol. 11, No. 1, February 1996, pp. 83–92.CrossRefGoogle Scholar
  8. [8]
    D. Dasgupta and D. R. McGregor, “Thermal Unit Commitment using Genetic Algorithms,” IEE Proceedings — Part C: Generation, Transmission and Distribution, Vol. 141, No. 5, September 1994, pp. 459–465.CrossRefGoogle Scholar
  9. [9]
    Z. Michalewicz and G. Nazhiyath, “Genocop III: A Co-evolutionary Algorithm for Numerical Optimisation Problems with Nonlinear Constraints,” in Proceedings of the 2nd IEEE International Conference on Evolutionary Computation, Vol. 2, Perth-Australia, 29 Nov. — 1 Dec. 1995, pp. 647–651.Google Scholar
  10. [10]
    J. A. Miller. W. D. Potter, R. V. Gandham and C. N. Lapena, “An Evaluation of Local Improvement Operators for Genetic Algorithms”, in IEEE Transactions on Systems, Man, and Cybernetics, Vol. 23, No. 5, Sep./Oct. 1993.Google Scholar
  11. [11]
    V. Petridis and S. Kazarlis “Varying Quality Function in Genetic Algorithms and the Cutting Problem”, in Proceedings of the First IEEE Conference on Evolutionary Computation (ICEC '94 as part of WCCI'94), IEEE Service Center, 1994, Vol. l, pp. 166–169.Google Scholar
  12. [12]
    V. Petridis, S. Kazarlis and A. Bakirtzis, “Varying Fitness Functions in Genetic Algorithm Constrained Optimisation: The Cutting Stock and Unit Commitment Problems,” accepted for publication at the IEEE Transactions on Systems, Man, and Cybernetics, Vol 28 Part B No 5 issue of October 1998.Google Scholar
  13. [13]
    A. E. Smith and D. M. Tate, “Genetic Optimisation Using A Penalty Function,” in Proceedings of the Fifth International Conference on Genetic Algorithms, S. Forrest, Ed. Los Altos, CA: Morgan Kaufmann, 1993, pp. 499–505.Google Scholar
  14. [14]
    W.M. Spears and K.A. De Jong, “An Analysis of Multi-Point Crossover” in Foundations of Genetic Algorithms, San Mateo California, Morgan Kaufman, 1991, pp. 301–315.Google Scholar
  15. [15]
    Paul. E. Sweeney, Elizabeth Ridenour Paternoster, “Cutting and Packing Problems: A categorized Application — Oriented Research Bibliography”, Journal of the Operational Research Society, Vol. 43, No. 7, p.p. 691–706.Google Scholar
  16. [16]
    A.J. Wood and B.F. Wollenberg, Power Generation Operation and Control, 1984, John Wiley, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • S. Kazarlis
    • 1
  • V. Petridis
    • 1
  1. 1.Department of Electrical and Computer Engineering, Faculty of EngineeringAristotle University of ThessalonikiGreece

Personalised recommendations