A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems

  • Saku Kukkonen
  • Kalyanmoy Deb
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)


Diversity maintenance of solutions is an essential part in multi-objective optimization. Existing techniques are suboptimal either in the sense of obtained distribution or execution time. This paper proposes an effective and relatively fast method for pruning a set of non-dominated solutions. The proposed method is based on a crowding estimation technique using nearest neighbors of solutions in Euclidean sense, and a technique for finding these nearest neighbors quickly. The method is experimentally evaluated, and results indicate a good trade-off between the obtained distribution and execution time. Distribution is good also in many-objective problems, when number of objectives is more than two.


Multiobjective Optimization Vector Quantization Pruning Method Strength Pareto Evolutionary Algorithm Crowd Distance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of the Third Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2001), Athens, Greece, pp. 95–100 (2002)Google Scholar
  2. 2.
    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
  3. 3.
    Jensen, M.T.: Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms. IEEE Transactions on Evolutionary Computation 7(5), 503–515 (2003)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multiobjective Optimization. In: Evolutionary Multiobjective Optimization, pp. 105–145. Springer, London (2005)CrossRefGoogle Scholar
  5. 5.
    Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. In: Proceedings of the 2006 Congress on Evolutionary Computation (CEC 2006), Vancouver, BC, Canada (2006) (accepted for publication)Google Scholar
  6. 6.
    Guan, L., Kamel, M.: Equal-average hyperplane partioning method for vector quantization of image data. Pattern Recognition Letters 13(10), 693–699 (1992)CrossRefGoogle Scholar
  7. 7.
    Ra, S.W., Kim, J.K.: A fast mean-distance-ordered partial codebook search algorithm for image vector quantization. IEEE Transactions on Circuits and Systems-II 40(9), 576–579 (1993)CrossRefGoogle Scholar
  8. 8.
    Baek, S., Sung, K.M.: Fast K-nearest-neighbour search algorithm for nonparametric classification. IEE Electronics Letters 36(21), 1821–1822 (2000)CrossRefGoogle Scholar
  9. 9.
    Bei, C.D., Gray, R.M.: An improvement of the minimum distortion encoding algorithm for vector quantization. IEEE Transactions on Communications COM-33(10), 1132–1132 (1985)Google Scholar
  10. 10.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. Prentice-Hall, Englewood Cliffs (1990)MATHGoogle Scholar
  11. 11.
    Vaidya, P.M.: An O(n logn) algorithm for the all-nearest-neigbors problem. Discrete & Computational Geometry 4, 101–115 (1989)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kukkonen, S., Lampinen, J.: GDE3: The third evolution step of Generalized Differential Evolution. In: Proceedings of the 2005 Congress on Evolutionary Computation (CEC 2005), Edinburgh, Scotland, pp. 443–450 (2005)Google Scholar
  13. 13.
    Price, K.V., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Berlin (2005)MATHGoogle Scholar
  14. 14.
    Inorio, A., Li, X.: Solving rotated multi-objective optimization problems using Differential Evolution. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 861–872. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester, England (2001)MATHGoogle Scholar
  16. 16.
    Kukkonen, S.: A fast and effective method for pruning of non-dominated solutions in many-objective problems, results (2006) (June 15, 2006), Available: http://www.it.lut.fi/ip/evo/pruning

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Saku Kukkonen
    • 1
  • Kalyanmoy Deb
    • 2
  1. 1.Department of Information TechnologyLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Kanpur Genetic Algorithms Laboratory (KanGAL)Indian Institute of Technology KanpurKanpurIndia

Personalised recommendations