Nothing Special   »   [go: up one dir, main page]

Skip to main content

Constraint-Handling Method for Multi-objective Function Optimization: Pareto Descent Repair Operator

  • Conference paper
Evolutionary Multi-Criterion Optimization (EMO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4403))

Included in the following conference series:

Abstract

Among the multi-objective optimization methods proposed so far, Genetic Algorithms (GA) have been shown to be more effective in recent decades. Most of such methods were developed to solve primarily unconstrained problems. However, many real-world problems are constrained, which necessitates appropriate handling of constraints. Despite much effort devoted to the studies of constraint-handling methods, it has been reported that each of them has certain limitations. Hence, further studies for designing more effective constraint-handling methods are needed.

For this reason, we investigated the guidelines for a method to effectively handle constraints. Based on these guidelines, we designed a new constraint-handling method, Pareto Descent Repair operator (PDR), in which ideas derived from multi-objective local search and gradient projection method are incorporated. An experiment comparing GA that use PDR and some of the existing constraint-handling methods confirmed the effectiveness of PDR.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)

    MATH  Google Scholar 

  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(11-12), 1245–1287 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Knowles, J.D., Corne, D.W.: Memetic algorithms for multiobjective optimization: issues, methods and prospects. In: Krasnogor, N., Smith, J.E., Hart, W.E. (eds.) Recent Advances in Memetic Algorithms, pp. 313–352. Springer, Heidelberg (2004)

    Google Scholar 

  4. Coello, C.A.C.: Treating constraints as objectives for single-objective evolutionary optimization. Engineering Optimization 32(3), 275–308 (2000)

    Article  Google Scholar 

  5. Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311–338 (2000)

    Article  MATH  Google Scholar 

  6. Oyama, A., Shimoyama, K., Fujii, K.: New constraint-handling method for multi-objective multi-constraint evolutionary optimization and its application to space plane design. In: Schilling, R., Haase, W., Periaux, J., Baier, H., Bugeda, G. (eds.) Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2005), pp. 416–428 (2005)

    Google Scholar 

  7. Michalewicz, Z., Nazhiyath, G.: Genocop III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In: Proceedings of the 2nd IEEE International Conference on Evolutionary Computation, vol. 2, pp. 647–651. IEEE Computer Society Press, Los Alamitos (1995)

    Chapter  Google Scholar 

  8. Harada, K., Sakuma, J., Ikeda, K., Ono, I., Kobayashi, S.: Local search for multiobjective function optimization: Pareto descent method ((in Japanese)). Transactions of the Japanese Society for Artificial Intelligence 21(4), 340–350 (2006)

    Google Scholar 

  9. Harada, K., Sakuma, J., Ikeda, K., Ono, I., Kobayashi, S.: Local search for multiobjective function optimization: Pareto descent method. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp. 659–666. ACM Press, New York (2006)

    Chapter  Google Scholar 

  10. Luenberger, D.G.: Linear and Nonlinear Programming. Addison-Wesley, Reading (1984)

    MATH  Google Scholar 

  11. Gellert, W., Gottwald, S., Hellwich, M., Kästner, H., Künstner, H.: VNR Concise Encyclopedia of Mathematics. Van Nostrand Reinhold, New York (1989)

    MATH  Google Scholar 

  12. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  13. Ono, I., Kobayashi, S.: A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: 7th International Conference on Genetic Algorithms (ICGA7), pp. 246–253 (1997)

    Google Scholar 

  14. Knowles, J.D., Corne, D.W.: On metrics for comparing non-dominated sets. In: Proceedings of the 2002 Congress on Evolutionary Computation Conference (CEC02), pp. 711–716. IEEE Computer Society Press, Los Alamitos (2002)

    Google Scholar 

  15. Harada, K., Sakuma, J., Kobayashi, S., Ikeda, K., Ono, I.: Hybridization of genetic algorithm and local search in multiobjective function optimization: Recommendation of GA then LS. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp. 667–674. ACM Press, New York (2006)

    Chapter  Google Scholar 

  16. Harada, K., Ikeda, K., Sakuma, J., Ono, I., Kobayashi, S.: Hybridization of genetic algorithm with local search in multiobjective function optimization: Recommendation of GA then LS ((in Japanese)). Transactions of the Japanese Society for Artificial Intelligence 21(6), 482–492 (2006)

    Article  Google Scholar 

  17. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K., et al. (eds.) EUROGEN 2001, Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pp. 12–21 (2001)

    Google Scholar 

  18. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the Congress on Evolutionary Computation (CEC-2002), pp. 825–830 (2002)

    Google Scholar 

  19. Fliege, J., Svaiter, B.F.: Steepest descent methods for multicriteria optimization. Mathematical Methods of Operations Research 51(3), 479–494 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Shigeru Obayashi Kalyanmoy Deb Carlo Poloni Tomoyuki Hiroyasu Tadahiko Murata

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Harada, K., Sakuma, J., Ono, I., Kobayashi, S. (2007). Constraint-Handling Method for Multi-objective Function Optimization: Pareto Descent Repair Operator. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-70928-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70927-5

  • Online ISBN: 978-3-540-70928-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics