Solving Rotated Multi-objective Optimization Problems Using Differential Evolution

  • Antony W. Iorio
  • Xiaodong Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3339)


This paper demonstrates that the self-adaptive technique of Differential Evolution (DE) can be simply used for solving a multi-objective optimization problem where parameters are interdependent. The real-coded crossover and mutation rates within the NSGA-II have been replaced with a simple Differential Evolution scheme, and results are reported on a rotated problem which has presented difficulties using existing Multi-objective Genetic Algorithms. The Differential Evolution variant of the NSGA-II has demonstrated rotational invariance and superior performance over the NSGA-II on this problem.


Multiobjective Genetic Algorithm Traditional Genetic Algorithm Mass Rapid Transit Multiobjective Optimization Algorithm Automatic Train Operation 
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.
    Salomon, R.: Re-evaluating Genetic Algorithm Performance Under Coordinate Rotation of Benchmark Functions: A Survey of Some Theoretical and Practical Aspects of Genetic Algorithms. Bio. Systems 39(3), 263–278 (1996)CrossRefGoogle Scholar
  2. 2.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  3. 3.
    Price, K.V.: An Introduction to Differential Evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill, London, UK (1999)Google Scholar
  4. 4.
    Price, K.V.: Differential evolution: a fast and simple numerical optimizer. In: Smith, M., Lee, M., Keller, J., Yen, J. (eds.) Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS, pp. 524–527. IEEE Press, New York (1996)Google Scholar
  5. 5.
    Ilonen, J., Kamarainen, J.-K., Lampinen, J.: Differential Evolution Training Algorithm for Feed-Forward Neural Networks. Neural Processing Letters 7(1), 93–105 (2003)CrossRefGoogle Scholar
  6. 6.
    Storn, R.: Differential evolution design of an IIR-filter. In: Proceedings of IEEE International Conference on Evolutionary Computation ICEC 1996, pp. 268–273. IEEE Press, New York (1996)CrossRefGoogle Scholar
  7. 7.
    Rogalsky, T., Derksen, R.W., Kocabiyik, S.: Differential Evolution in Aerodynamic Optimization. In: Proceedings of the 46th Annual Conference of the Canadian Aeronautics and Space Institute, pp. 29–36 (1999)Google Scholar
  8. 8.
    Chang, C.S., Xu, D.Y.: Differential Evolution of Fuzzy Automatic Train Operation for Mass Rapid Transit System. IEEE Proceedings of Electric Power Applications 147(3), 206–212 (2000)CrossRefGoogle Scholar
  9. 9.
    Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto-frontier Differential Evolution Approach for Multi-objective Optimization Problems. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), vol. 2, pp. 971–978 (2001)Google Scholar
  10. 10.
    Abbass, H.A., Sarker, R.: The Pareto Differential Evolution Algorithm. International Journal on Artificial Intelligence Tools 11(4), 531–552 (2002)CrossRefGoogle Scholar
  11. 11.
    Abbass, H.A.: The Self-Adaptive Pareto Differential Evolution Algorithm. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 831–836. IEEE Press, Los Alamitos (2002)CrossRefGoogle Scholar
  12. 12.
    Abbass, H.A.: A memetic pareto evolutionary approach to artificial neural networks. In: Stumptner, M., Corbett, D.R., Brooks, M. (eds.) Canadian AI 2001. LNCS (LNAI), vol. 2256, pp. 1–12. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Madavan, N.K.: Multiobjective Optimization Using a Pareto Differential Evolution Approach. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 2, pp. 1145–1150. IEEE Press, Los Alamitos (2002)CrossRefGoogle Scholar
  14. 14.
    Xue, F.: Multi-Objective Differential Evolution and its Application to Enterprise Planning. In: Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA 2003), vol. 3, pp. 3535–3541. IEEE Press, Los Alamitos (2003)Google Scholar
  15. 15.
    Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based Multi-objective Differential Evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), vol. 2, pp. 862–869. IEEE Press, Los Alamitos (2003)Google Scholar
  16. 16.
    Okabe, T., Jin, Y., Sendhoff, B.: A Critical Survey of Performance Indicies for Multi-Objective Optimisation. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), vol. 2, pp. 878–885. IEEE Press, Los Alamitos (2003)CrossRefGoogle Scholar
  17. 17.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Trans. Evol. Comput. 2(2), 117–132 (2003)CrossRefGoogle Scholar
  18. 18.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Antony W. Iorio
    • 1
  • Xiaodong Li
    • 1
  1. 1.School of Computer Science and Information TechnologyRoyal Melbourne Institute of Technology UniversityMelbourneAustralia

Personalised recommendations