Penalty Function Methods for Constrained Optimization with Genetic Algorithms: A Statistical Analysis

  • Angel Fernando Kuri-Morales
  • Jesús Gutiérrez-García
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2313)


Genetic algorithms (GAs) have been successfully applied to numerical optimization problems. Since GAs are usually designed for unconstrained optimization, they have to be adapted to tackle the constrained cases, i.e. those in which not all representable solutions are valid. In this work we experimentally compare 5 ways to attain such adaptation. Our analysis relies on the usual method of selecting an arbitrary suite of test functions (25 of these) albeit applying a methodology which allows us to determine which method is better within statistical certainty limits. In order to do this we have selected 5 penalty function strategies; for each of these we have further selected 3 particular GAs. The behavior of each strategy and the associated GAs is then established by extensively sampling the function suite and finding the worst case best values from Chebyshev’s theorem. We have found some counter- intuitive results which we discuss and try to explain.


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  1. 1.
    Coello, C., “Theoretical and Numerical Constraint-Handling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art”, Computer Methods in Applied Mechanics and Engineering, 2001 (to be published).Google Scholar
  2. 2.
    Homaiffar A., Qi C. & Lai S., “Constrained Optimization Via Genetic Algorithms“. Simulation, 62:4, pp. 242–254, 1994.CrossRefGoogle Scholar
  3. 3.
    Joines, J and Houck, C., "On the Use of Non-Stationary Penalty Functions to Solve Nonlinear Constrained Optimization Problems with GA’s". Proceedings of first IEEE Conference on Evolutionary Computation, pp. 579–584, 1994.Google Scholar
  4. 4.
    Shoenauer, M. and Xanthakis, S., "Constrained GA Optimization". Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 573–580, 1993.Google Scholar
  5. 5.
    Kuri, A., A Comprehensive Approach to Genetic Algorithms in Optimization and Learning. Theory and Applications, Vol. 1. Instituto Politécnico Nacional, pp 270, 1999.Google Scholar
  6. 6.
    Powell, D. and Skolnick, M., "Using Genetic Algorithms in Engineering Design Optimization with Non-linear Constraints". Proceedings of the Fifth International Conference on Genetic Algorithms. pp. 424–430, 1993.Google Scholar
  7. 7.
    Kuri, A., "A universal Eclectic Genetic Algorithm for Constrained Optimization". Proceedings 6th European Congress on Intelligent Techniques & Soft Computing, EUFIT’98, pp. 518–522, 1998.Google Scholar
  8. 8.
    Richardson J., Palmer M., Liepins G. & Hilliard M., “Some Guidelines for Genetic Algorithms with Penalty Functions”. Proceedings of the IEEE International Conference on Evolutionary Computation, pp.191–197, 1989.Google Scholar
  9. 9.
    Back, T., Evolutionary Algorithms in Theory and Practice, Oxford University Press, New York, 1996.Google Scholar
  10. 10.
    Coello, C., “Use of a Self-Adaptive Penalty Approach for Engineering Optimization Problems”, Computers in Industry, 41(2):113–127, 2000.Google Scholar
  11. 11.
    Fogel, D., Evolutionary Computation. Toward a New Philosophy of Machine Intelligence, the Institute of Electrical and Electronic Engineers, New York, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Angel Fernando Kuri-Morales
    • 1
  • Jesús Gutiérrez-García
    • 2
  1. 1.Instituto Tecnológico Autónomo de MéxicoMéxico D.F.
  2. 2.Centro de Investigación en ComputaciónInstituto Politécnico NacionalMéxico D.F.

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