Skip to main content

Population-Based Incremental Learning for Multiobjective Optimisation

  • Conference paper
Book cover Soft Computing in Industrial Applications

Part of the book series: Advances in Soft Computing ((AINSC,volume 39))

Abstract

The work in this paper presents the use of population-based incremental learning (PBIL), one of the classic single-objective population-based optimisation methods, as a tool for multiobjective optimisation. The PBIL method with two different updating schemes of its probability vectors is presented. The performance of the two proposed multiobjective optimisers are measured and compared with four other established multiobjective evolutionary algorithms i.e. niched Pareto genetic algorithm, version 2 of non-dominated sorting genetic algorithm, version 2 of strength Pareto evolutionary algorithm, and Pareto archived evolution strategy. The optimisation methods are implemented to solve 8 bi-objective test problems where design variables are encoded as a binary string. The Pareto optimal solutions obtained from the various methods are compared and discussed. It can be concluded that, with the assigned test problems, the multiobjective PBIL methods are comparable to the previously developed algorithms in terms of convergence rate. The clear advantage in using PBILs is that they can provide considerably better population diversity.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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.

References

  1. Baluja, S.: Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Technical Report CMU_CS_95_163, Carnegie Mellon University (1994)

    Google Scholar 

  2. Bureerat, S., Cooper, J.E.: Evolutionary methods for the optimisation of engineering systems. In: IEE Colloquium Optimisation in Control: Methods and Applications, IEE, London, Uk, pp. 1/1-1/10 (1998)

    Google Scholar 

  3. Bureerat, S., Limtragool, J.: Performance enhancement of evolutionary search for structural topology optimization. Finite Element in Analysis and Design 42, 547–566 (2006)

    Article  MathSciNet  Google Scholar 

  4. Coello, C.C., Romero, C.E.M.: Evolutionary algorithms and multiple objective optimization. In: Ehrgott, M., Gandibleux, X. (eds.) Multicriteria optimization, pp. 277–331 (2002)

    Google Scholar 

  5. Deb, K., Pratap, A., Meyarivan, T.: Constrained test problems for multi-objective evolutionary optimization. KanGAL Report No, 02, Kanpur Genetic Algorithms Laboraotry (KanGAL), Indian Institute of Technology, Kanpur, India (2000)

    Google Scholar 

  6. Deb, K., et al.: A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Trans. On Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  7. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proc. of the 5th Inter. Conf. on Gas, pp. 416–423 (1993)

    Google Scholar 

  8. Fyfe, C.: Structured population-based incremental learning. Soft Computing 2(4), 91–198 (1999)

    MathSciNet  Google Scholar 

  9. Grandhi, R.V., Bharatram, G.: Multiobjective optimization of large-scale structures. AIAA 31(7), 1329–1337 (1993)

    Article  MATH  Google Scholar 

  10. Horn, J., Nafpliotis, N.: Multiobjective optimization using niched Pareto genetic algorithm. Tech. Report I11iGA1 Report 93005, UIUC (1993)

    Google Scholar 

  11. Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched pareto genetic algorithm for multiobjective optimization. In: The 1st IEEE Conf. on Evolutionary Computation, pp. 82–87. IEEE Computer Society Press, Los Alamitos (1994)

    Google Scholar 

  12. Ivvan, S., et al.: Multiobjective shape optimization using estimation distribution algorithms and correlated information. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 664–676. Springer, Heidelberg (2005)

    Google Scholar 

  13. Knowles, J.D., Corne, D.W.: Approximating the non-dominated front using the Pareto archive evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)

    Article  Google Scholar 

  14. Kunakote, T.: Topology optimization using evolutionary algorithms: comparison of the evolutionary methods and checkerboard suppression technique. Master thesis, Khon Kaen University (2004)

    Google Scholar 

  15. Messac, A., Ismail-Yahaya, A., Mattson, C.A.: The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 25(2), 86–98 (2003)

    Article  MathSciNet  Google Scholar 

  16. Schaffer, J.D.: Multiobjective optimization with vector evaluated genetic algorithms. In: GAs and their Application: Proc. of 1st Inter Conf. on Gas, pp. 93–100 (1985)

    Google Scholar 

  17. Sebag, M., Ducoulombier, A.: Extending population-based incremental learning to continuous search spaces. In: Eiben, A.E., et al. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, p. 418. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Srinivas, N., Deb, K.: Multiobjective optimization using non-dominated genetic algorithms. Evolutionary Computation 2(3), 221–248 (1994)

    Google Scholar 

  19. Yuan, B., Gallagher, M.: Playing in continuous spaces: some analysis and extension of population-based incremental learning. In: Proceedings of the 2003 IEEE Congress on Evolutionary Computation, Canberra, Australia, pp. 443–450. IEEE Computer Society Press, Los Alamitos (2003)

    Chapter  Google Scholar 

  20. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation 8(2), 173–195 (2000)

    Article  Google Scholar 

  21. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary Methods for Design, Optimization and Control, Barcelona, Spain (2002)

    Google Scholar 

  22. Zitzler, E., et al.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. on Evolutionary Computation 7(2), 117–132 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ashraf Saad Keshav Dahal Muhammad Sarfraz Rajkumar Roy

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bureerat, S., Sriworamas, K. (2007). Population-Based Incremental Learning for Multiobjective Optimisation. In: Saad, A., Dahal, K., Sarfraz, M., Roy, R. (eds) Soft Computing in Industrial Applications. Advances in Soft Computing, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70706-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-70706-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70704-2

  • Online ISBN: 978-3-540-70706-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics