Advertisement

Automatically Improving the Anytime Behaviour of Multiobjective Evolutionary Algorithms

  • Andreea Radulescu
  • Manuel López-Ibáñez
  • Thomas Stützle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7811)

Abstract

An algorithm that returns as low-cost solutions as possible at any moment of its execution is said to have a good anytime behaviour. The problem of optimising anytime behaviour can be modelled as a bi-objective non-dominated front, where the goal is to minimise both time and cost. Using a unary quality measure such as the hypervolume indicator, the analysis of the anytime behaviour can be converted into a single-objective problem. In this manner, available automatic configuration tools can be applied to improve the anytime behaviour of an algorithm. If we want to optimise the anytime behaviour of multi-objective algorithms, we may apply again unary quality measures to obtain a scalar value for measuring the obtained approximation to the Pareto front. Thus, for multi-objective algorithms, the anytime behaviour may be described in terms of the curve of the hypervolume over time, and the quality of this bi-objective tradeoff curve be evaluated according to its hypervolume. Using this approach, we can automatically improve the anytime behaviour of multi-objective evolutionary algorithms (MOEAs). In this article, we first introduce this approach and then experimentally study the improvements obtained considering three MOEAs, namely, IBEA, NSGA-II and SPEA2.

Keywords

Pareto Front Multiobjective Optimization Multiobjective Optimization Problem Multiobjective Evolutionary Algorithm Nondominated Sorting 
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.
    Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)zbMATHCrossRefGoogle Scholar
  2. 2.
    Birattari, M., Yuan, Z., Balaprakash, P., Stützle, T.: F-race and iterated F-race: An overview. In: Bartz-Beielstein, T., et al. (eds.) Experimental Methods for the Analysis of Optimization Algorithms, pp. 311–336. Springer, Berlin (2010)CrossRefGoogle Scholar
  3. 3.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search spaces. Complex Systems 9(2), 115–148 (1995)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 181–197 (2002)CrossRefGoogle Scholar
  5. 5.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. TR 112, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology, Zürich, Switzerland (2001)Google Scholar
  6. 6.
    Eiben, A.E., Smit, S.K.: Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm and Evolutionary Computation 1(1), 19–31 (2011)CrossRefGoogle Scholar
  7. 7.
    Fonseca, C.M., Paquete, L., López-Ibáñez, M.: An improved dimension-sweep algorithm for the hypervolume indicator. In: Congress on Evolutionary Computation (CEC 2006), pp. 1157–1163. IEEE Press, Piscataway (2006)Google Scholar
  8. 8.
    Hoos, H.H.: Automated algorithm configuration and parameter tuning. In: Hamadi, Y., Monfroy, E., Saubion, F. (eds.) Autonomous Search, pp. 37–71. Springer, Berlin (2012)Google Scholar
  9. 9.
    Hoos, H.H.: Programming by optimization. Communications of the ACM 55(2), 70–80 (2012)CrossRefGoogle Scholar
  10. 10.
    Hoos, H.H., Stützle, T.: Stochastic Local Search—Foundations and Applications. Morgan Kaufmann Publishers, San Francisco (2005)Google Scholar
  11. 11.
    Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T.: ParamILS: an automatic algorithm configuration framework. Journal of Artificial Intelligence Research 36, 267–306 (2009)zbMATHGoogle Scholar
  12. 12.
    Liefooghe, A., Jourdan, L., Talbi, E.G.: A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO. European Journal of Operational Research 209(2), 104–112 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    López-Ibáñez, M., Dubois-Lacoste, J., Stützle, T., Birattari, M.: The irace package, iterated race for automatic algorithm configuration. Tech. Rep. TR/IRIDIA/2011-004, IRIDIA, Université Libre de Bruxelles, Belgium (2011)Google Scholar
  14. 14.
    López-Ibáñez, M., Knowles, J., Laumanns, M.: On Sequential Online Archiving of Objective Vectors. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 46–60. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    López-Ibáñez, M., Liao, T., Stützle, T.: On the Anytime Behavior of IPOP-CMA-ES. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 357–366. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    López-Ibáñez, M., Stützle, T.: Automatically improving the anytime behaviour of optimisation algorithms. Tech. Rep. TR/IRIDIA/2012-012, IRIDIA, Université Libre de Bruxelles, Belgium (2012)Google Scholar
  17. 17.
    Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  18. 18.
    Zilberstein, S.: Using anytime algorithms in intelligent systems. AI Magazine 17(3), 73–83 (1996)Google Scholar
  19. 19.
    Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K., et al. (eds.) Evolutionary Methods for Design, Optimisation and Control, pp. 95–100. CIMNE, Barcelona (2002)Google Scholar
  21. 21.
    Zitzler, E., Thiele, L., Deb, K.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar
  22. 22.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreea Radulescu
    • 1
  • Manuel López-Ibáñez
    • 2
  • Thomas Stützle
    • 2
  1. 1.LINA, UMR CNRS 6241Université de NantesNantesFrance
  2. 2.IRIDIA, CoDEUniversité Libre de Bruxelles (ULB)BrusselsBelgium

Personalised recommendations