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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-540-70928-2_11
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