Advertisement

Defining and Optimizing Indicator-Based Diversity Measures in Multiobjective Search

  • Tamara Ulrich
  • Johannes Bader
  • Lothar Thiele
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6238)

Abstract

In this paper, we elaborate how decision space diversity can be integrated into indicator-based multiobjective search. We introduce DIOP, the diversity integrating multiobjective optimizer, which concurrently optimizes two set-based diversity measures, one in decision space and the other in objective space. We introduce a possibility to improve the diversity of a solution set, where the minimum proximity of these solutions to the Pareto-front is user-defined. Experiments show that DIOP is able to optimize both diversity measures and that the decision space diversity can indeed be improved if the required maximum distance of the solutions to the front is relaxed.

Keywords

Diversity Measure Multiobjective Optimization Objective Space Quality Constraint Decision Space 
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.
    Conover, W.J.: Practical Nonparametric Statistics, 3rd edn. John Wiley, Chichester (1999)Google Scholar
  2. 2.
    Deb, K., Agrawal, S.: A niched-penalty approach for constraint handling in genetic algorithms. In: ICANNGA (1999)Google Scholar
  3. 3.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multi-Objective Optimization. TIK Report 112, ETH Zurich (2001)Google Scholar
  4. 4.
    Deb, K., Tiwari, S.: Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization. EJOR 185(3), 1062–1087 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Gaston, K.J., Spicer, J.I.: Biodiversity: An Introduction, 2nd edn. Wiley-Blackwell, Chichester (2004)Google Scholar
  6. 6.
    Izsák, J., Papp, L.: A link between ecological diversity indices and measures of biodiversity. Ecological Modelling 130(1-3), 151–156 (2000)CrossRefGoogle Scholar
  7. 7.
    Li, X., Zheng, J., Xue, J.: A Diversity Metric for Multi-objective Evolutionary Algorithms. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 68–73. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Rudolph, G., Naujoks, B., Preuss, M.: Capabilities of EMOA to detect and preserve equivalent pareto subsets. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 36–50. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Sarma, J., Jong, K.A.D.: An analysis of the effects of neighborhood size and shape on local selection algorithms. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 236–244. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  10. 10.
    Shimodaira, H.: A diversity-control-oriented genetic algorithm (dcga): Performance in function optimization. In: Genetic and Evolutionary Computation Conference, p. 366 (2000)Google Scholar
  11. 11.
    Shir, O.M., Preuss, M., Naujoks, B., Emmerich, M.: Enhancing decision space diversity in evolutionary multiobjective algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 95–109. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Solow, A.R., Polasky, S.: Measuring biological diversity. Environmental and Ecological Statistics 1(2), 95–103 (1994)CrossRefGoogle Scholar
  13. 13.
    Squillero, G., Tonda, A.P.: A novel methodology for diversity preservation in evolutionary algorithms. In: GECCO, pp. 2223–2226. ACM, New York (2008)CrossRefGoogle Scholar
  14. 14.
    Srinivas, N., Deb, K.: Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 2(3), 221–248 (1994)CrossRefGoogle Scholar
  15. 15.
    Toffolo, A., Benini, E.: Genetic diversity as an objective in multi-objective evolutionary algorithms. Evolutionary Computation 11(2), 151–167 (2003)CrossRefGoogle Scholar
  16. 16.
    Tsutsui, S., Fujimoto, Y., Ghosh, A.: Forking genetic algorithms: Gas with search space division schemes. Evolutionary Computation 5(1), 61–80 (1997)CrossRefGoogle Scholar
  17. 17.
    Ulrich, T., Bader, J., Zitzler, E.: Integrating Decision Space Diversity into Hypervolume-based Multiobjective Search. In: Genetic and Evolutionary Computation Conference (to appear, 2010)Google Scholar
  18. 18.
    Ursem, R.K.: Diversity-guided evolutionary algorithms. In: Congress on Evolutionary Computation, pp. 1633–1640 (2002)Google Scholar
  19. 19.
    Weitzman, M.: On diversity. The Quarterly Journal of Economics 107(2), 363–405 (1992)zbMATHCrossRefGoogle Scholar
  20. 20.
    Zhou, A., Zhang, Q., Jin, Y.: Approximating the set of pareto optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Transactions on Evolutionary Computation (2009) (accepted)Google Scholar
  21. 21.
    Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization (Revised Version). TIK Report 300, ETH Zurich (2008)Google Scholar
  22. 22.
    Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization. IEEE Transactions on Evolutionary Computation (2009) (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tamara Ulrich
    • 1
  • Johannes Bader
    • 1
  • Lothar Thiele
    • 1
  1. 1.Computer Engineering and Networks LaboratoryETH ZurichZurichSwitzerland

Personalised recommendations