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Mixed-Integer Evolution Strategies with Dynamic Niching

  • Rui Li
  • Jeroen Eggermont
  • Ofer M. Shir
  • Michael T. M. Emmerich
  • Thomas Bäck
  • Jouke Dijkstra
  • Johan H. C. Reiber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

Mixed-Integer Evolution Strategies (MIES) are a natural extension of standard Evolution Strategies (ES) for addressing optimization of various types of variables – continuous, ordinal integer, and nominal discrete – at the same time. Like most Evolutionary Algorithms (EAs), they experience problems in obtaining the global optimum in highly multimodal search landscapes. Niching methods, the extension of EAs to multimodal domains, are designed to treat this issue. In this study we present a dynamic niching technique for Mixed-Integer Evolution Strategies, based upon an existing ES niching approach, which was developed recently and successfully applied to continuous landscapes. The new approach is based on the heterogeneous distance measure that addresses search space similarity in a way consistent with the mutation operators of the MIES. We apply the proposed Dynamic Niching MIES framework to a test-bed of artificial landscapes and show the improvement on the global convergence in comparison to the standard MIES algorithm.

Keywords

Evolution Strategy Barrier Function Integer Variable Manhattan Distance Evolution Strategy 
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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References

  1. 1.
    Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2005, Edinburgh, UK, September 2-4, 2005. IEEE, Los Alamitos (2005)Google Scholar
  2. 2.
    Bäck, Th.: Evolutionary algorithms in theory and practice. Oxford University Press, New York (1996)zbMATHGoogle Scholar
  3. 3.
    Bäck, Th., Schütz, M.: Evolution strategies for mixed-integer optimization of optical multilayer systems. In: Evolutionary Programming, pp. 33–51 (1995)Google Scholar
  4. 4.
    Emmerich, M., Grötzner, M., Groß, B., Schütz, M.: Mixed-integer evolution strategy for chemical plant optimization with simulators. In: Parmee, I.C. (ed.) Evolutionary Design and Manufacture - Selected papers from ACDM 2000, pp. 55–67. Springer, Heidelberg (2000)Google Scholar
  5. 5.
    Kauffman, S.: Towards a general theory of adaptive walks on rugged landscapes. Journal of theoretical biology 128(1), 11–45 (1987)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Li, R., Emmerich, M.T.M., Eggermont, J., Bovenkamp, E.G.P., Bäck, Th., Dijkstra, J., Reiber, J.H.C.: Mixed-Integer NK Landscapes. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 42–51. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Li, R., Emmerich, M.T.M., Eggermont, J., Bovenkamp, E.G.P., Bäck, Th., Dijkstra, J., Reiber, J.H.C.: Mixed-integer optimization of coronary vessel image analysis using evolution strategies. In: Cattolico, M. (ed.) [8], pp. 1645–1652Google Scholar
  8. 8.
    Cattolico, M. (ed.): Proceedings of Genetic and Evolutionary Computation Conference, GECCO 2006. ACM Press, Seattle (2006)Google Scholar
  9. 9.
    Miller, B.L., Shaw, M.J.: Genetic algorithms with dynamic niche sharing for multimodal function optimization. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC 1996), pp. 786–791 (1996)Google Scholar
  10. 10.
    Preuss, M., Schönemann, L., Emmerich, M.T.M.: Counteracting genetic drift and disruptive recombination in (μ + /,λ)-ea on multimodal fitness landscapes. In: Beyer, H.-G., O’Reilly, U.-M. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2005, pp. 865–872. ACM Press, New York (2005)CrossRefGoogle Scholar
  11. 11.
    Rudolph, G.: An evolutionary algorithm for integer programming. In: Davidor, Y., Schwefel, H.-P., Männer, R. (eds.) PPSN 1994. LNCS, vol. 866, pp. 139–148. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  12. 12.
    Schönemann, L., Emmerich, M.T.M., Preuss, M.: On the extinction of evolutionary algorithms sub-populations on multimodal landscapes. Informatica - Special Issue on Bioinspired Optimization 28(4), 345–351 (2004)Google Scholar
  13. 13.
    Schwefel, H.-P.: Evolution and Optimum Seeking: The Sixth Generation. John Wiley & Sons, Inc., New York (1993)Google Scholar
  14. 14.
    Shir, O.M., Bäck, Th.: Dynamic niching in evolution strategies with covariance matrix adaptation. In: Congress on Evolutionary Computation [1], pp. 2584–2591 Google Scholar
  15. 15.
    Shir, O.M., Bäck, Th.: Niching with Derandomized Evolution Strategies in Artificial and Real-World Landscapes. Natural Computing (2008)Google Scholar
  16. 16.
    Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Cattolico, M. (ed.) [8], pp. 1305–1312Google Scholar
  17. 17.
    Stoean, C., Preuss, M., Gorunescu, R., Dumitrescu, D.: Elitist generational genetic chromodynamics - a new radii-based evolutionary algorithm for multimodal optimization. In: Congress on Evolutionary Computation [1], pp. 1839–1846Google Scholar
  18. 18.
    Streichert, F., Stein, G., Ulmer, H., Zell, A.: A clustering based niching method for evolutionary algorithms. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 644–645. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Mahfoud, S.W.: Niching Methods for Genetic Algorithms. PhD thesis, University of Illinois at Urbana Champaign (1995)Google Scholar
  20. 20.
    Wilson, D.R., Martinez, T.R.: Improved heterogeneous distance functions. Journal of Artificial Intelligence Research 6, 1–34 (1997)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rui Li
    • 1
  • Jeroen Eggermont
    • 2
  • Ofer M. Shir
    • 1
  • Michael T. M. Emmerich
    • 1
  • Thomas Bäck
    • 1
  • Jouke Dijkstra
    • 2
  • Johan H. C. Reiber
    • 2
  1. 1.Natural Computing GroupLeiden UniversityCA LeidenThe Netherlands
  2. 2.Division of Image Processing, Department of Radiology C2SLeiden University Medical CenterRC LeidenThe Netherlands

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