Advertisement

Constrained Optimization by the ε Constrained Hybrid Algorithm of Particle Swarm Optimization and Genetic Algorithm

  • Tetsuyuki Takahama
  • Setsuko Sakai
  • Noriyuki Iwane
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3809)

Abstract

The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison that compares search points based on the constraint violation of them. We proposed the ε constrained particle swarm optimizer εPSO, which is the combination of the ε constrained method and particle swarm optimization. The εPSO can run very fast and find very high quality solutions, but the εPSO is not very stable and sometimes can only find lower quality solutions. On the contrary, the εGA, which is the combination of the ε constrained method and GA, is very stable and can find high quality solutions, but it is difficult for the εGA to find higher quality solutions than the εPSO. In this study, we propose the hybrid algorithm of the εPSO and the εGA to find very high quality solutions stably. The effectiveness of the hybrid algorithm is shown by comparing it with various methods on well known nonlinear constrained problems.

Keywords

Hybrid Algorithm Constrain Optimization Problem Constraint Violation Nonlinear Optimization Problem High Quality Solution 
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.
    Michalewicz, Z., Nazhiyath, G.: GENOCOP III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In: Proc. of the 2nd IEEE International Conference on Evolutionary Computation, Perth, Australia, vol. 2, pp. 647–651 (1995)Google Scholar
  2. 2.
    Coello, C.A.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 191, 1245–1287 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Coath, G., Halgamuge, S.K.: A comparison of constraint-handling methods for the application of particle swarm optimization to constrained nonlinear optimization problems. In: Proc. of IEEE Congress on Evolutionary Computation, Canberra, Australia, pp. 2419–2425 (2003)Google Scholar
  4. 4.
    Hu, X., Eberhart, R.C.: Solving constrained nonlinear optimization problems with particle swarm optimization. In: Proc. of the Sixth World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida (2002)Google Scholar
  5. 5.
    Homaifar, A., Lai, S.H.Y., Qi, X.: Constrained optimization via genetic algorithms. Simulation 62, 242–254 (1994)CrossRefGoogle Scholar
  6. 6.
    Joines, J., Houck, C.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Proc. of the First IEEE Conference on Evolutionary Computation, Orlando, Florida, pp. 579–584 (1994)Google Scholar
  7. 7.
    Michalewicz, Z., Attia, N.F.: Evolutionary optimization of constrained problems. In: Proc. of the 3rd Annual Conference on Evolutionary Programming, Singapore, pp. 98–108 (1994)Google Scholar
  8. 8.
    Hadj-Alouane, A.B., Bean, J.C.: A genetic algorithm for the multiple-choice integer program. Operations Research 45, 92–101 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Coello, C.A.C.: Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry 41, 113–127 (2000)CrossRefGoogle Scholar
  10. 10.
    Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization method for constrained optimization problems. In: Sincak, P., Vascak, J., et al. (eds.) Intelligent Technologies — Theory and Application: New Trends in Intelligent Technologies. Frontiers in Artificial Intelligence and Applications, vol. 76, pp. 214–220. IOS Press, Amsterdam (2002)Google Scholar
  11. 11.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311–338 (2000)zbMATHCrossRefGoogle Scholar
  12. 12.
    Takahama, T., Sakai, S.: Tuning fuzzy control rules by the α constrained method which solves constrained nonlinear optimization problems. Electronics and Communications in Japan 83, 1–12 (2000)Google Scholar
  13. 13.
    Takahama, T., Sakai, S.: Constrained optimization by ε constrained particle swarm optimizer with ε-level control. In: Proc. of the 4th IEEE International Workshop on Soft Computing as Transdisciplinary Science and Technology (WSTST 2005), Muroran, Japan, pp. 1019–1029 (2005)Google Scholar
  14. 14.
    Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4, 284–294 (2000)CrossRefGoogle Scholar
  15. 15.
    Camponogara, E., Talukdar, S.N.: A genetic algorithm for constrained and multiobjective optimization. In: 3rd Nordic Workshop on Genetic Algorithms and Their Applications, Vaasa, Finland, pp. 49–62 (1997)Google Scholar
  16. 16.
    Surry, P.D., Radcliffe, N.J.: The COMOGA method: Constrained optimisation by multiobjective genetic algorithms. Control and Cybernetics 26, 391–412 (1997)MathSciNetGoogle Scholar
  17. 17.
    Coello, C.A.C.: Constraint-handling using an evolutionary multiobjective optimization technique. Civil Engineering and Environmental Systems 17, 319–346 (2000)CrossRefGoogle Scholar
  18. 18.
    Ray, T., Liew, K., Saini, P.: An intelligent information sharing strategy within a swarm for unconstrained and constrained optimization problems. Soft Computing – A Fusion of Foundations, Methodologies and Applications 6, 38–44 (2002)zbMATHCrossRefGoogle Scholar
  19. 19.
    Takahama, T., Sakai, S.: Learning fuzzy control rules by α-constrained simplex method. System and Computers in Japan 34, 80–90 (2003)CrossRefGoogle Scholar
  20. 20.
    Takahama, T., Sakai, S.: Constrained optimization by applying the α constrained method to the nonlinear simplex method with mutations. IEEE Trans. on Evolutionary Computation (to appear)Google Scholar
  21. 21.
    Takahama, T., Sakai, S.: Constrained optimization by α constrained genetic algorithm (αGA). Systems and Computers in Japan 35, 11–22 (2004)CrossRefGoogle Scholar
  22. 22.
    Takahama, T., Sakai, S.: Constrained optimization by the α constrained particle swarm optimizer. Journal of Advanced Computational Intelligence and Intelligent Informatics 9, 282–289 (2005)Google Scholar
  23. 23.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)Google Scholar
  24. 24.
    Himmelblau, D.M.: Applied Nonlinear Programming. McGrow-Hill, New York (1972)zbMATHGoogle Scholar
  25. 25.
    Gen, M., Cheng, R.: Genetic Algorithms & Engineering Design. Wiley, New York (1997)Google Scholar
  26. 26.
    Rao, S.S.: Engineering Optimization, 3rd edn. Wiley, New York (1996)Google Scholar
  27. 27.
    Kannan, B.K., Kramer, S.N.: An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Journal of mechanical design, Transactions of the ASME 116, 318–320 (1994)CrossRefGoogle Scholar
  28. 28.
    Sandgren, E.: Nonlinear integer and discrete programming in mechanical design. In: Proc. of the ASME Design Technology Conference, Kissimine, Florida, pp. 95–105 (1988)Google Scholar
  29. 29.
    Deb, K.: GeneAS: A robust optimal design technique for mechanical component design. In: Dasgupta, D., Michalewicz, Z. (eds.) Evolutionary Algorithms in Engineering Applications, pp. 497–514. Springer, Berlin (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tetsuyuki Takahama
    • 1
  • Setsuko Sakai
    • 2
  • Noriyuki Iwane
    • 1
  1. 1.Hiroshima City UniversityHiroshimaJapan
  2. 2.Hiroshima Shudo UniversityHiroshimaJapan

Personalised recommendations