Gradient Based Stochastic Mutation Operators in Evolutionary Multi-objective Optimization

  • Pradyumn Kumar Shukla
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4431)


Evolutionary algorithms have been adequately applied in solving single and multi-objective optimization problems. In the single-objective case various studies have shown the usefulness of combining gradient based classical search principles with evolutionary algorithms. However there seems to be a dearth of such studies for the multi-objective case. In this paper, we take two classical search operators and discuss their use as a local search operator in a state-of-the-art evolutionary algorithm. These operators require gradient information which is obtained using a stochastic perturbation technique requiring only two function evaluations. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of hybrid algorithms in solving a large class of complex multi-objective optimization problems.


Mutation Operator Search Operator Binary Indicator Local Search Operator Simultaneous Perturbation 
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.


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  1. 1.
    Bosman, P.A.N., de Jong, E.D.: Exploiting gradient information in numerical multi–objective evolutionary optimization. In: GECCO ’05: Proceedings of the 2005 conference on Genetic and evolutionary computation, pp. 755–762. ACM Press, New York (2005)CrossRefGoogle Scholar
  2. 2.
    Bosman, P.A.N., de Jong, E.D.: Combining gradient techniques for numerical multi-objective evolutionary optimization. In: GECCO ’06: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 627–634. ACM Press, New York (2006)CrossRefGoogle Scholar
  3. 3.
    Brown, M., Smith, R.E.: Effective use of directional information in multi-objective evolutionary computation. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 778–789. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)zbMATHGoogle Scholar
  5. 5.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  6. 6.
    Fliege, J., Svaiter, B.F.: Steepest descent methods for multicriteria optimization. Math. Methods Oper. Res. 51(3), 479–494 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Fonesca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  8. 8.
    Harada, K., Ikeda, K., Kobayashi, S.: Hybridization of genetic algorithm and local search in multiobjective function optimization: recommendation of ga then ls. In: GECCO ’06: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 667–674. ACM Press, New York (2006)CrossRefGoogle Scholar
  9. 9.
    Harada, K., Sakuma, J., Kobayashi, S.: Local search for multiobjective function optimization: pareto descent method. In: GECCO ’06: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 659–666. ACM Press, New York (2006)CrossRefGoogle Scholar
  10. 10.
    Kiwiel, K.C.: Descent methods for nonsmooth convex constrained minimization. In: Nondifferentiable optimization: motivations and applications (Sopron, 1984). Lecture Notes in Econom. and Math. Systems, vol. 255, pp. 203–214. Springer, Berlin (1985)Google Scholar
  11. 11.
    Mukai, H.: Algorithms for multicriterion optimization. IEEE Trans. Automat. Control 25(2), 177–186 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Recchioni, M.C.: A path following method for box-constrained multiobjective optimization with applications to goal programming problems. Math. Methods Oper. Res. 58(1), 69–85 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Schäffler, S., Schultz, R., Weinzierl, K.: Stochastic method for the solution of unconstrained vector optimization problems. Journal of Optimization Theory and Applications 114(1), 209–222 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Shukla, P.K., Deb, K., Tiwari, S.: Comparing Classical Generating Methods with an Evolutionary Multi-objective Optimization Method. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 311–325. Springer, Heidelberg (2005)Google Scholar
  15. 15.
    Spall, J.C.: Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization. IEEE Transactions on Aerospace and Electronic Systems 34(3), 817–823 (1998)CrossRefGoogle Scholar
  16. 16.
    Timmel, G.: Ein stochastisches Suchverrahren zur Bestimmung der optimalen Kompromißlösungen bei statischen polzkriteriellen Optimierungsaufgaben. Wiss. Z. TH Ilmenau 26(5), 159–174 (1980)zbMATHMathSciNetGoogle Scholar
  17. 17.
    Timmel, G.: Modifikation eines statistischen Suchverfahrens der Vektoroptimierung. Wiss. Z. TH Ilmenau 28(6), 139–148 (1982)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)CrossRefGoogle Scholar

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© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Pradyumn Kumar Shukla
    • 1
  1. 1.Institute of Numerical Mathematics, Department of Mathematics, Dresden University of Technology, Dresden PIN 01069Germany

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