Population-Based Incremental Learning for Multiobjective Optimisation

  • Sujin Bureerat
  • Krit Sriworamas
Part of the Advances in Soft Computing book series (AINSC, volume 39)


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.


Multiobjective Evolutionary Optimisation Population-Based Incremental Learning Non-dominated Solutions Pareto Archive Performance Comparison 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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. 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. 3.
    Bureerat, S., Limtragool, J.: Performance enhancement of evolutionary search for structural topology optimization. Finite Element in Analysis and Design 42, 547–566 (2006)CrossRefMathSciNetGoogle Scholar
  4. 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. 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. 6.
    Deb, K., et al.: A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Trans. On Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  7. 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. 8.
    Fyfe, C.: Structured population-based incremental learning. Soft Computing 2(4), 91–198 (1999)MathSciNetGoogle Scholar
  9. 9.
    Grandhi, R.V., Bharatram, G.: Multiobjective optimization of large-scale structures. AIAA 31(7), 1329–1337 (1993)zbMATHCrossRefGoogle Scholar
  10. 10.
    Horn, J., Nafpliotis, N.: Multiobjective optimization using niched Pareto genetic algorithm. Tech. Report I11iGA1 Report 93005, UIUC (1993)Google Scholar
  11. 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. 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. 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)CrossRefGoogle Scholar
  14. 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. 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)CrossRefMathSciNetGoogle Scholar
  16. 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. 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)CrossRefGoogle Scholar
  18. 18.
    Srinivas, N., Deb, K.: Multiobjective optimization using non-dominated genetic algorithms. Evolutionary Computation 2(3), 221–248 (1994)Google Scholar
  19. 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)CrossRefGoogle Scholar
  20. 20.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar
  21. 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. 22.
    Zitzler, E., et al.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. on Evolutionary Computation 7(2), 117–132 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sujin Bureerat
    • 1
  • Krit Sriworamas
    • 1
  1. 1.Department of Mechanical Engineering, Faculty of Engineering, Khon, Kaen University, 40002Thailand

Personalised recommendations