A Hybrid of Differential Evolution and Genetic Algorithm for Constrained Multiobjective Optimization Problems

  • Min Zhang
  • Huantong Geng
  • Wenjian Luo
  • Linfeng Huang
  • Xufa Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4247)


Two novel schemes of selecting the current best solutions for multiobjective differential evolution are proposed in this paper. Based on the search biases strategy suggested by Runarsson and Yao, a hybrid of multiobjective differential evolution and genetic algorithm with (N+N) framework for constrained MOPs is given. And then the hybrid algorithm adopting the two schemes respectively is compared with the constrained NSGA-II on 4 benchmark functions constructed by Deb. The experimental results show that the hybrid algorithm has better performance, especially in the distribution of non-dominated set.


Genetic Algorithm Differential Evolution Hybrid Algorithm Benchmark Function Multiobjective Evolutionary Algorithm 
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.
    Rosenberg, R.S.: Simulation of genetic populations with biochemical properties. Ph.D. thesis, University of Michigan, Ann Harbor, Michigan (1967)Google Scholar
  2. 2.
    David Schaffer, J.: Multiple objective optimization with vector evaluated genetic algorithms. In: Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, pp. 93–100. Lawrence Erlbaum, Mahwah (1985)Google Scholar
  3. 3.
    Coello Coello, C.A.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine 1(1), 28–36 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation 2(3), 221–248 (1994)CrossRefGoogle Scholar
  5. 5.
    Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the 1st CEC, June 1994, vol. 1, pp. 82–87 (1994)Google Scholar
  6. 6.
    Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective Optimization: Formulation, discussion and generalization. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423 (1993)Google Scholar
  7. 7.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRefGoogle Scholar
  8. 8.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. In: EUROGEN 2001. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pp. 95–100 (2002)Google Scholar
  9. 9.
    Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 263–282 (2002)CrossRefGoogle Scholar
  12. 12.
    Coello Coello, C.A., Toscano Pulido, G., Salazar Lechuga, M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)CrossRefGoogle Scholar
  13. 13.
    Robič, T., Filipič, B.: DEMO: Differential Evolution for Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Runarsson, T.P., Yao, X.: Search Biases in Constrained Evolutionary Optimization. IEEE Trans. Syst. Man Cybern. Part C-Appl. Rev. 35(2), 233–243 (2005)CrossRefGoogle Scholar
  15. 15.
    Runarsson, T.P., Yao, X.: Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)CrossRefGoogle Scholar
  16. 16.
    Storn, R., Price, K.: Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimiz. 11(4), 341–359 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRefGoogle Scholar
  18. 18.
    Fieldsend, J.E., Everson, R.M., Singh, S.: Using unconstrained elite archives for multiobjective optimization. IEEE Trans. Evol. Comput. 7(2), 305–323 (2003)CrossRefGoogle Scholar
  19. 19.
    Zhang, M., Geng, H.T., Luo, W.J., Huang, L.F., Wang, X.F.: A Novel Search Biases Selection Strategy for Constrained Evolutionary Optimization. In: CEC 2006 (to appear, 2006)Google Scholar
  20. 20.
    Deb, K., Pratap, A., Meyarivan, T.: Constrained Test Problems for Multi-objective Evolutionary Optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 284–298. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. 21.
    Mezura-Montes, E., Velázquez-Reyes, J., Coello Coello, C.A.: Promising infeasibility and multiple offspring incorporated to differential evolution for constrained optimization. In: GECCO 2005, pp. 225–232 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Min Zhang
    • 1
  • Huantong Geng
    • 1
  • Wenjian Luo
    • 1
  • Linfeng Huang
    • 1
  • Xufa Wang
    • 1
  1. 1.Nature Inspired Computation and Applications Laboratory, Department of Computer, Science and TechnologyUniversity of Science and Technology of ChinaHefei, AnhuiChina

Personalised recommendations