Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization

Chapter

Abstract

This chapter introduces two Perl programs that implement graphical tools for exploring the performance of stochastic local search algorithms for biobjective optimization problems. These tools are based on the concept of the empirical attainment function (EAF), which describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space. In particular, we consider the visualization of attainment surfaces and differences between the first-order EAFs of the outcomes of two algorithms. This visualization allows us to identify certain algorithmic behaviors in a graphical way. We explain the use of these visualization tools and illustrate them with examples arising from practice.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This work was supported by the META-X project, an Action de Recherche Concertée funded by the Scientific Research Directorate of the French Community of Belgium. Thomas Stützle acknowledges support from the Belgian F.R.S.-FNRS, of which he is a Research Associate. The authors also acknowledge Carlos M. Fonseca for providing us the code for computing the EAF as well as for helpful discussions on the main topic of this chapter.

References

  1. Ehrgott M (2000) Multicriteria Optimization, Lecture Notes in Economics and Mathematical Systems, vol 491. Springer, Heidelberg, GermanyGoogle Scholar
  2. Fonseca CM, Fleming P (1996) On the performance assessment and comparison of stochastic multiobjective optimizers. In: Voigt HM, Ebeling W, Rechenberg I, Schwefel HP (eds) Proceedings of PPSN-IV, Fourth International Conference on Parallel Problem Solving from Nature, Springer, Lecture Notes in Computer Science, vol 1141, pp 584–593CrossRefGoogle Scholar
  3. Fonseca CM, Grunert da Fonseca V, Paquete L (2005) Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In: Coello CC, Aguirre AH, ,e>Zitzler E (eds) Evolutionary Multi-criterion Optimization (EMO 2005), Springer, Lecture Notes in Computer Science, vol 3410, pp 250–264Google Scholar
  4. Grunert da Fonseca V, Fonseca CM, Hall A (2001) Inferential performance assessment of stochastic optimizers and the attainment function. In: Zitzler E, Deb K, Thiele L, Coello CC, Corne D (eds) Evolutionary Multi-criterion Optimization (EMO 2001), Springer, Lecture Notes in Computer Science, vol 1993, pp 213– 225CrossRefGoogle Scholar
  5. Hoos H, Stützle T (2005) Stochastic Local Search – Foundations and Applications. Morgan Kaufmann Publishers, San Francisco, CAMATHGoogle Scholar
  6. Inselberg A (1985) The plane with parallel coordinates. Visual Computer 1(4):69– 91MATHCrossRefGoogle Scholar
  7. Knowles J, Corne D (2002) On metrics for comparing non-dominated sets. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC’02), IEEE Press, Piscataway, NJ, pp 711–716Google Scholar
  8. Lópe z-Ibáñez M, Paquete L, Stützle T (2006) Hybrid population-based algorithms for the bi-objective quadratic assignment problem. Journal of Mathematical Modelling and Algorithms 5(1):111–137CrossRefMathSciNetGoogle Scholar
  9. Paquete L, Stützle T (2003) A two-phase local search for the biobjective traveling salesman problem. In: Fonseca CM, Fleming P, Zitzler E, Deb K, Thiele L (eds) Proceedings of the Evolutionary Multi-criterion Optimization (EMO 2003), Springer, Lecture Notes in Computer Science, vol 2632, pp 479–493CrossRefGoogle Scholar
  10. Paquete L, Stützle T (2009) Design and analysis of stochastic local search algorithms for the multiobjective traveling salesman problem. Computers and Operations Research 36(9):2619–2631MATHCrossRefMathSciNetGoogle Scholar
  11. R Development Core Team (2008) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL http://www.R-project.org
  12. Steuer RE (1986) Multiple Criteria Optimization: Theory, Computation and Application. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, NYGoogle Scholar
  13. Stützle T, Hoos H (2001) Analysing the run-time behaviour of iterated local search for the travelling salesman problem. In: Hansen P, Ribeiro C (eds) Essays and Surveys on Metaheuristics, Kluwer Academic Publishers, Boston, MA, pp 589– 611Google Scholar
  14. Taillard ÉD (1991) Robust taboo search for the quadratic assignment problem. Parallel Computing 17:443–455CrossRefMathSciNetGoogle Scholar
  15. Zitzler E, Thiele L, Laumanns M, Fonseca CM,Grunert da Fonseca V (2003) Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2):117–132CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.IRIDIA, CoDEUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations