Abstract
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 methods with evolutionary algorithms. However there seems to be limited number of such studies for the multi-objective case. In this paper, we take two classical methods for unconstrained multi-optimization problems and discuss their use as a local search operator in a state-of-the-art multi-objective evolutionary algorithm. These operators require gradient information which is obtained using finite difference method and 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 resulting hybrid algorithms in solving a large class of complex multi-objective optimization problems. We also discuss a new convergence metric which is useful as a stopping criteria for problems having an unknown Pareto-optimal front.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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, Washington DC, USA, pp. 755–762. ACM Press, New York (2005), doi:10.1145/1068009.1068138
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)
Branke, J., Kauβler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 499–507 (2001)
Branke, J., Deb, K.: Integrating User Preferences into Evolutionary Multi-Objective Optimization. In: Jin, Y. (ed.) Knowledge Incorporation in Evolutionary Computation, pp. 461–477. Springer, Heidelberg (2005)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
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)
Deb, K., Zope, P., Jain, A.: Distributed computing of pareto-optimal solutions using multi-objective evolutionary algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 535–549. Springer, Heidelberg (2003)
Ehrgott, M.: Multicriteria Optimization. Springer, Heidelberg (2000)
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.) Parallel Problem Solving from Nature - PPSN IV. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)
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)
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)
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)
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)
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)
Shukla, P.K., Dutta, J., Deb, K.: Approximate solutions in multiobjective optimization. Technical report, KanGal Report No. 2004009, Indian Institute Of Technology Kanpur, India (2004)
Spall, J.C.: Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization. IEEE Transactions on Aerospace and Electronic Systems 34(3), 817–823 (1998)
Timmel, G.: Ein stochastisches Suchverrahren zur Bestimmung der optimalen Kompromißlösungen bei statischen polzkriteriellen Optimierungsaufgaben. Wiss. Z. TH Ilmenau 26(5), 159–174 (1980)
Timmel, G.: Modifikation eines statistischen Suchverfahrens der Vektoroptimierung. Wiss. Z. TH Ilmenau 28(6), 139–148 (1982)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms – A comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Shukla, P.K. (2007). On Gradient Based Local Search Methods in Unconstrained Evolutionary Multi-objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-70928-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70927-5
Online ISBN: 978-3-540-70928-2
eBook Packages: Computer ScienceComputer Science (R0)