Immune Clonal MO Algorithm for ZDT Problems

  • Ronghua Shang
  • Wenping Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4222)


In this paper, we introduce a new multiobjective optimization (MO) algorithm to solve ZDT test problems using the immune clonal principle. This algorithm is termed Immune Clonal MO Algorithm (ICMOA). In ICMOA, the antibody population is split into nondominated antibodies and dominated antibodies. Meanwhile, the nondominated antibodies are allowed to survive and to clone and the nonuniform mutation is adopted. Two metrics proposed by K. Deb et al. are adopted to measure the extent of convergence to a known set of Pareto-optimal solutions and the extent of spread achieved among the obtained solutions. Our algorithm is compared with another algorithm that is representative of the state-of-the-art in evolutionary multiobjective optimization–NSGA-II. Simulation results on ZDT test problems show that ICMOA, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to NSGA-II.


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  1. 1.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland (2001)Google Scholar
  3. 3.
    Jiao, L.C., Gong, M.G., Shang, R.H., Du, H.F., Lu, B.: Clonal Selection with Immune Dominance and energy Based Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 474–489. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Shang, R.H., Jiao, L.C., Gong, M.G., Lu, B.: Clonal Selection Algorithm for Dynamic Multiobjective Optimization. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3801, pp. 846–851. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    de Castro, L.N., Von Zuben, F.J.: Learning and Optimization Using the Clonal Selection Principle. IEEE Transactions on Evolutionary Computation 6(3), 239–251 (2002)CrossRefGoogle Scholar
  6. 6.
    Coello, C.C.A., Nareli, C.C.: An Approach to Solve Multiobjective Optimization Problems Based on an Artificial Immune System. In: Timmis, J., Bentley, P.J. (eds.) Proceedings of the First International Conference on Artificial Immune Systems, pp. 212–221 (2002)Google Scholar
  7. 7.
    Du, H.F., Jiao, L.C., Wang, S.A.: Clonal Operator and Antibody Clone Algorithms. In: Proceedings of the First International Conference on Machine Learning and Cybernetics, Beijing, pp. 506–510 (2002)Google Scholar
  8. 8.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Program. Springer, Berlin (1992)Google Scholar
  9. 9.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)CrossRefGoogle Scholar
  10. 10.
    Madavan, N.K.: Multiobjective optimization using a Pareto differential evolution approach. In: Congress on Evolutionary Computation (CEC 2002), Piscataway, New Jersey, vol. 2, pp. 1145–1150. IEEE Service Center, Los Alamitos (2002)Google Scholar
  11. 11.
    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), Canberra, Australia, vol. 2, pp. 862–869. IEEE Press, Los Alamitos (2003)Google Scholar
  12. 12.
    Jiao, L., Wang, L.: A novel genetic algorithm based on immunity. IEEE Transactions on Systems, Man and Cybernetics, Part A 30(5) (September 2000)Google Scholar
  13. 13.
    Jiao, L., Liu, J., Zhong, W.: An organizational coevolutionary algorithm for classification. IEEE Trans. Evol. Comput. 10(1), 67–80 (2006)CrossRefGoogle Scholar
  14. 14.
    Liu, J., Zhong, W., Jiao, L.: A multiagent evolutionary algorithm for constraint satisfaction problems. IEEE Trans. Syst., Man, and Cybern. B. 36(1), 54–73 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ronghua Shang
    • 1
  • Wenping Ma
    • 1
  1. 1.Institute of Intelligent Information ProcessingXidian UniversityXi’anP.R. China

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