Advertisement

An Improved Version of Volume Dominance for Multi-Objective Optimisation

  • Khoi Le
  • Dario Landa-Silva
  • Hui Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5467)

Abstract

This paper proposes an improved version of volume dominance to assign fitness to solutions in Pareto-based multi-objective optimisation. The impact of this revised volume dominance on the performance of multi-objective evolutionary algorithms is investigated by incorporating it into three approaches, namely SEAMO2, SPEA2 and NSGA2 to solve instances of the 2-, 3- and 4- objective knapsack problem. The improved volume dominance is compared to its previous version and also to the conventional Pareto dominance. It is shown that the proposed improved volume dominance helps the three algorithms to obtain better non-dominated fronts than those obtained when the two other forms of dominance are used.

Keywords

Pareto Front Nondominated Solution Pareto Dominance Multiobjective Evolutionary Algorithm True Pareto Front 
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.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multi-Objective Optimisation. Evolution Computation 10(3), 263–282 (2002)CrossRefGoogle Scholar
  2. 2.
    Koppen, M., Vicente-Garcia, R., Nickolay, B.: Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 399–412. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Burke, E.K., Landa-Silva, D.: The Influence of the Fitness Evaluation Method on the Performance of Multiobjective Search Algorithms. European Journal of Operational Research 169(3), 875–897 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Le, K., Landa-Silva, D.: Obtaining Better Non-Dominated Sets Using Volume Dominance. In: Proceedings of the 2007 Congress on Evolutionary Computation (CEC 2007), pp. 3119–3126. IEEE Press, Los Alamitos (2007)Google Scholar
  5. 5.
    Pareto, V.: Cours D’Economie Polotique. F. Rouge, Lausanne (1896)Google Scholar
  6. 6.
    Dasgusta, P., Chakrabarti, P.P., DeSarkar, S.C.: Multiobjective Heuristic Search: An Introduction to Intelligent Search Methods for Multicriteria Optimization. Computational Intelligence (1999)Google Scholar
  7. 7.
    Yu, P.L.: Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives. Journal of Optimization Theory and Applications 14(3), 319–377 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kokolo, I., Hajime, K., Shigenobu, K.: Failure of Pareto-based MOEAS: Does Non-dominated Really Mean Near to Optimal? In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), pp. 957–962. IEEE Press, Los Alamitos (2001)Google Scholar
  9. 9.
    Jin, H., Wong, M.L.: Adaptive Diversity Maintenance and Convergence Guarantee in Multiobjective Evolutionary Algorithms. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), pp. 2498–2505. IEEE Press, Los Alamitos (2003)Google Scholar
  10. 10.
    Peng, J., Mok, H.M., Tse, W.: Fuzzy Dominance Based on Credibility Distributions. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS, vol. 3613, pp. 295–303. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Sato, H., Aguirre, H., Tanaka, K.: Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar
  13. 13.
    Mumford, C.: Simple Population Replacement Strategies for a Steady-State Multi-objective Evolutionary Algorithm. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 1389–1400. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), pp. 95–100 (2002)Google Scholar
  15. 15.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  16. 16.
    Wu, J., Azarm, S.: Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set. Journal of Mechanical Design 123(1), 18–25 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Khoi Le
    • 1
  • Dario Landa-Silva
    • 1
  • Hui Li
    • 1
  1. 1.Automated Scheduling, Optimisation and Planning Research Group School of Computer ScienceThe University of NottinghamUK

Personalised recommendations