A Cultural Algorithm with Differential Evolution to Solve Constrained Optimization Problems

  • Ricardo Landa Becerra
  • Carlos A. Coello Coello
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3315)

Abstract

A cultural algorithm is proposed in this paper. The main novel feature of this approach is the use of differential evolution as a population space. Differential evolution has been found to be very effective when dealing with real valued optimization problems. The knowledge sources contained in the belief space of the cultural algorithm are specifically designed according to the differential evolution population. Furthermore, we introduce an influence function that selects the source of knowledge to apply the evolutionary operators. Such influence function considerably improves the performance when compared to a previous version of the algorithm (developed by the same authors). We use a well-known set of test functions to validate the approach, and compare the results with respect to the best constraint-handling technique known to date in evolutionary optimization.

Keywords

Differential Evolution Knowledge Source Differential Evolution Algorithm Normative Knowledge Acceptance Function 
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.
    Bentley, J.L., Friedman, J.H.: Data Structures for Range Searching. ACM Computing Surveys 11, 397–409 (1979)CrossRefGoogle Scholar
  2. 2.
    Chung, C.J., Reynolds, R.G.: A Testbed for Solving Optimization Problems using Cultural Algorithms. In: Fogel, L.J., Angeline, P.J., Bäck, T. (eds.) Evolutionary Programming V: Proceedings of the Fifth Annual Conference on Evolutionary Programming. MIT Press, Cambridge (1996)Google Scholar
  3. 3.
    Chung, C.J., Reynolds, R.G.: CAEP: An Evolution-based Tool for Real-Valued Function Optimization using Cultural Algorithms. Journal on Artificial Intelligence Tools 7, 239–292 (1998)CrossRefGoogle Scholar
  4. 4.
    Coello Coello, C.A., Landa Becerra, R.: Adding knowledge and efficient data structures to evolutionary programming: A cultural algorithm for constrained optimization. In: Cantú- Paz, E., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2002), San Francisco, California, pp. 201–209. Morgan Kaufmann Publishers, San Francisco (2002)Google Scholar
  5. 5.
    Goldberg, D.E.: GeneticAlgorithms in Search, Optimization and Machine Learning. Addison- Wesley Publishing Company, Reading (1989)Google Scholar
  6. 6.
    Iacoban, R., Reynolds, R.G., Brewster, J.: Cultural Swarms: Modeling the Impact of Culture on Social Interaction and Problem Solving. In: 2003 IEEE Swarm Intelligence Symposium Proceedings, Indianapolis, Indiana, USA, pp. 205–211. IEEE Service Center, Los Alamitos (2003)Google Scholar
  7. 7.
    Jin, X., Reynolds, R.G.: Using Knowledge-Based Evolutionary Computation to Solve Nonlinear Constraint Optimization Problems: a Cultural Algorithm Approach. In: 1999 Congress on Evolutionary Computation, Washington, D.C, pp. 1672–1678. IEEE Service Center, Los Alamitos (1999)Google Scholar
  8. 8.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  9. 9.
    Landa Becerra, R., Coello Coello, C.A.: Culturizing differential evolution for constrained optimization. In: ENC 2004, IEEE Service Center, Los Alamitos (2004) (Accepted for publication)Google Scholar
  10. 10.
    Price, K.V.: An introduction to differential evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill, London (1999)Google Scholar
  11. 11.
    Reynolds, R.G.: An Introduction to Cultural Algorithms. In: Sebald, A.V., Fogel, L.J. (eds.) Proceedings of the ThirdAnnual Conference on Evolutionary Programming, pp. 131–139. World Scientific, River Edge (1994)Google Scholar
  12. 12.
    Reynolds, R.G.: Cultural algorithms: Theory and applications. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 367–377. McGraw-Hill, London (1999)Google Scholar
  13. 13.
    Reynolds, R.G., Michalewicz, Z., Cavaretta, M.: Using cultural algorithms for constraint handling in GENOCOP. In: McDonnell, J.R., Reynolds, R.G., Fogel, D.B. (eds.) Proceedings of the Fourth Annual Conference on Evolutionary Programming, pp. 298–305. MIT Press, Cambridge (1995)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.
    Saleem, S.M.: Knowledge-Based Solution to Dynamic Optimization Problems using Cultural Algorithms. PhD thesis,Wayne State University, Detroit, Michigan (2001)Google Scholar
  16. 16.
    Storn, R.: System Design by Constraint Adaptation and Differential Evolution. IEEE Transactions on Evolutionary Computation 3, 22–34 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ricardo Landa Becerra
    • 1
  • Carlos A. Coello Coello
    • 1
  1. 1.Dpto. de Ing. Elect./Secc. ComputaciónCINVESTAV-IPN (Evolutionary Computation Group)Col. San Pedro ZacatencoMexico

Personalised recommendations