Advertisement

A Local Search Based Evolutionary Multi-objective Optimization Approach for Fast and Accurate Convergence

  • Karthik Sindhya
  • Kalyanmoy Deb
  • Kaisa Miettinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

A local search method is often introduced in an evolutionary optimization technique to enhance its speed and accuracy of convergence to true optimal solutions. In multi-objective optimization problems, the implementation of a local search is a non-trivial task, as determining a goal for the local search in presence of multiple conflicting objectives becomes a difficult proposition. In this paper, we borrow a multiple criteria decision making concept of employing a reference point based approach of minimizing an achievement scalarizing function and include it as a search operator of an EMO algorithm. Simulation results with NSGA-II on a number of two to four-objective problems with and without the local search approach clearly show the importance of local search in aiding a computationally faster and more accurate convergence to Pareto-optimal solutions. The concept is now ready to be coupled with a faster and more accurate diversity-preserving procedure to make the overall procedure a competitive algorithm for multi-objective optimization.

Keywords

Local Search Multiobjective Optimization Local Search Method Local Search Procedure Multiple Criterion Decision Making 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Belton, V., Stewart, T.: Multiple Criteria Decision Analysis: An integrated Approach. Kluwer, Dordrecht (2002)CrossRefGoogle Scholar
  2. 2.
    Byrd, R.H., Nocedal, J., Waltz, R.A.: KNITRO: An integrated package for nonlinear optimization. In: di Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, pp. 35–59. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Coello Coello, C.A., VanVeldhuizen, D.A., Lamont, G.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)zbMATHGoogle 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.
    Deb, K., Mohan, M., Mishra, S.: Towards a quick computation of well-spread Pareto-optimal solutions. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 222–236. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Goel, T., Deb, K.: Hybrid methods for multi-objective evolutionary algorithms. In: Proceedings of the Fourth Asia-Pacific Conference on Simulated Evolution and Learning (SEAL 2002), pp. 188–192 (2002)Google Scholar
  8. 8.
    Harada, K., Sakuma, J., Kobayashi, S.: Local search for multiobjective function optimization: Pareto descent method. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 659–666 (2006)Google Scholar
  9. 9.
    Ishibuchi, H., Narukawa, K.: Some issues on the implementation of local search in evolutionary multiobjective optimization. In: Deb, K. (ed.) GECCO 2004. LNCS, vol. 3102, pp. 1246–1258. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Jaskiewicz, A.: Genetic local search for multiple objective combinatorial optimization. European Journal of Operational Research 371(1), 50–71 (2002)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Knowles, J.D., Corne, D.: M-PAES: A memetic algorithm for multiobjective optimization. In: Proceedings of Congress on Evolutionary Computation (CEC 2000), pp. 325–332 (2000)Google Scholar
  12. 12.
    Kuhn, H.W., Tucker, A.W.: Nonlinear Programming. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. University of California Press, Berkeley (1951)Google Scholar
  13. 13.
    Kukkonen, S., Deb, K.: A fast and effective method for pruning of non-dominated solutions in many-objective problems. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN IX 2006. LNCS, vol. 4193, pp. 553–562. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., Deb, K.: Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 44–53. Springer, Heidelberg (2002)Google Scholar
  16. 16.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)zbMATHGoogle Scholar
  17. 17.
    Murata, T., Nozawa, H., Tsujimura, Y., Gen, M., Ishinuchi, H.: Effect of local search on the performance of celluar multi-objective genetic algorithms for designing fuzzy rule based classification systems. In: Proceeding of the Congress on Evolutionary Computation (CEC 2002), pp. 663–668 (2002)Google Scholar
  18. 18.
    Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Applications, pp. 468–486. Springer, Berlin (1980)CrossRefGoogle Scholar
  19. 19.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., Tsahalis, D.T., Périaux, J., Papailiou, K.D., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, International Center for Numerical Methods in Engineering (CIMNE), pp. 95–100 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Karthik Sindhya
    • 1
    • 3
  • Kalyanmoy Deb
    • 1
    • 3
  • Kaisa Miettinen
    • 2
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KanpurIndia
  2. 2.Department of Mathematical Information TechnologyUniversity of Jyväskylä(Agora)Finland
  3. 3.Department of Business Technology, Helsinki School of EconomicsHelsinkiFinland

Personalised recommendations