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A Generator for Multimodal Test Functions with Multiple Global Optima

  • Jani Rönkkönen
  • Xiaodong Li
  • Ville Kyrki
  • Jouni Lampinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5361)

Abstract

The topic of multimodal function optimization, where the aim is to locate more than one solution, has attracted a growing interest especially in the evolutionary computing research community. To experimentally evaluate the strengths and weaknesses of multimodal optimization algorithms, it is important to use test functions representing different characteristics and of various levels of difficulty. However, the available selection of multimodal test problems with multiple global optima is rather limited at the moment and no general framework exists. This paper describes our attempt in constructing a test function generator to allow the generation of easily tunable test functions. The aim is to provide a general and easily expandable environment for testing different methods of multimodal optimization. Several function families with different characteristics are included. The generator implements new parameterizable function families for generating desired landscapes and a selection of well known test functions from literature, which can be rotated and stretched. The module can be easily imported to any optimization algorithm implementation compatible with C programming language.

Keywords

Multimodal optimization test function generator global optimization 

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References

  1. 1.
    Mahfoud, S.: A comparison of parallel and sequential niching methods. In: Proceedings of 6th International Conference on Genetic Algorithms, pp. 136–143 (1995)Google Scholar
  2. 2.
    De Jong, K.: An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan (1975)Google Scholar
  3. 3.
    Goldberg, D., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Grefenstette, J. (ed.) Proc. of the Second International Conference on Genetic Algorithms, pp. 41–49 (1987)Google Scholar
  4. 4.
    Mahfoud, S.: Niching methods for genetic algorithms. PhD thesis, Urbana, IL, USA (1995)Google Scholar
  5. 5.
    Beasley, D., Bull, D., Martin, R.: A sequential niche technique for multimodal function optimization. Evolutionary Computation 1(2), 101–125 (1993)CrossRefGoogle Scholar
  6. 6.
    Harik, G.: Finding multimodal solutions using restricted tournament selection. In: Eshelman, L. (ed.) Proc. of the Sixth International Conference on Genetic Algorithms, pp. 24–31. Morgan Kaufmann, San Francisco (1995)Google Scholar
  7. 7.
    Pétrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proc. of the 3rd IEEE International Conference on Evolutionary Computation, pp. 798–803 (1996)Google Scholar
  8. 8.
    Li, J., Balazs, M., Parks, G., Clarkson, P.: A species conserving genetic algorithm for multimodal function optimization. Evol. Comput. 10(3), 207–234 (2002)CrossRefGoogle Scholar
  9. 9.
    Wolpert, D., Macready, W., William, G.: No free lunch theorems for search. Technical report, The Santa Fe Institute (1995)Google Scholar
  10. 10.
    Morrison, R., Jong, K.D.: A test problem generator for nonstationary evironments. In: Proceedings of the Congress of Evolutionary Computation, Piscataway, NJ, pp. 1843–1850. IEEE Press, Los Alamitos (1999)Google Scholar
  11. 11.
    Morrison, R.: Designing Evolutionary Algorithms for Dynamic Environments. Springer, Berlin (2004)CrossRefzbMATHGoogle Scholar
  12. 12.
    Branke, J.: Evolutionary Optimization in Dynamic Environments. Kluwer Academic Publishers, Norwell (2002)CrossRefzbMATHGoogle Scholar
  13. 13.
    Gaviano, M., Kvasov, D., Lera, D., Sergeyev, Y.: Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization. ACM Transactions on Mathematical Software 29(4), 469–480 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Michalewicz, Z., Deb, K., Schmidt, M., Stidsen, T.: Test-case generator for nonlinear continuous parameter optimization techniques. IEEE Trans. on Evol. Comput. 4, 197–215 (2000)CrossRefGoogle Scholar
  15. 15.
    Gallagher, M., Yuan, B.: A general-purpose tunable landscape generator. IEEE Transactions on Evolutionary Computation 10, 590–603 (2006)CrossRefGoogle Scholar
  16. 16.
    Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference, Seattle, WA, pp. 1305–1312. ACM Press, New York (2006)Google Scholar
  17. 17.
    Hansen, N., Ostermeier, A.: Completely derandomized self adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)CrossRefGoogle Scholar
  18. 18.
    Press, W., Flannery, B., Teukolsky, S., Vetterling, W.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1992)zbMATHGoogle Scholar
  19. 19.
    Törn, A., Žilinskas, A. (eds.): Global Optimization. LNCS, vol. 350. Springer, Heidelberg (1989)zbMATHGoogle Scholar
  20. 20.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Heidelberg (1996)CrossRefzbMATHGoogle Scholar
  21. 21.
    Ursem, R.: Multinational evolutionary algorithms. In: Proceedings of Congress of Evolutionary Computation (CEC 1999), vol. 3. IEEE Press, Los Alamitos (1999)Google Scholar
  22. 22.
    Shir, O., Bäck, T.: Niche radius adaptation in the cma-es niching algorithm. 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. 142–151. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jani Rönkkönen
    • 1
  • Xiaodong Li
    • 2
  • Ville Kyrki
    • 1
  • Jouni Lampinen
    • 3
  1. 1.Department of Information TechnologyLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.School of Computer Science and ITRMIT UniversityAustralia
  3. 3.Department of Computer ScienceUniversity of VaasaVaasaFinland

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