Metaoptimization of Differential Evolution by Using Productions of Low-Number of Cycles: The Fitting of Rotation Curves of Spiral Galaxies as Case Study

  • Miguel Cárdenas-Montes
  • Miguel Á. Vega-Rodríguez
  • Mercedes Mollá
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8073)


In order to increase the efficiency of Evolutionary Algorithms, practitioners include improvements as new operators or modifications of the canonical operators, or the hybridization with other Evolutionary Algorithms. However, an alternative to obtain high-quality solutions is: to tune the parameters which govern the behaviour of the algorithm to the specific problem to optimize. This parameters adjustment can be performed by using other Evolutionary Algorithm (Metaoptimization). Unfortunately, metaoptimization leads to a critical increment in the execution time. In this work, a measure of the quality of the tuned behavioural parameters when executing very low-number of cycles in the optimizer is performed and compared with the case when executing high-number of cycles. The fundamental aspect of this approach is if there is enough information about the quality of the behavioural parameters in the very initial cycles of the optimizer. By ascertaining if productions based on a low-number of cycles harvest high-quality behavioural parameters, one of the main drawbacks of the metaoptimization process —the large execution time— can be overcome. The performed tests —the fitting of experimental data of rotation curves of spiral galaxies— demonstrate that this approach improves the efficiency of the metaoptimizer, while reducing processing time.


Metaoptimization Differential Evolution Rotation Curve Spiral Galaxy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Storn, R., Price, K.V.: Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J. of Global Optimization 11(4), 341–359 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Price, K.V., Storn, R., Lampinen, J.: Differential Evolution: A practical Approach to Global Optimization. Springer, Berlin (2005)Google Scholar
  3. 3.
    Marquez, I., et al.: Rotation curves and metallicity gradients from HII regions in spiral galaxies. Astron. Astrophys. 393, 389–408 (2002)CrossRefGoogle Scholar
  4. 4.
    Mercer, R., Sampson, J.: Adaptive search using a reproductive metaplan. Kybernetes 7, 215–228 (1978)CrossRefGoogle Scholar
  5. 5.
    Maron, O., Moore, A.W.: The racing algorithm: Model selection for lazy learners. Artif. Intell. Rev. 11(1-5), 193–225 (1997)CrossRefGoogle Scholar
  6. 6.
    Yuan, B., Gallagher, M.: Combining Meta-EAs and Racing for Difficult EA Parameter Tuning Tasks. In: Lobo, F.G., Lima, C.F., Michalewicz, Z. (eds.) Parameter Setting in Evolutionary Algorithms. SCI, vol. 54, pp. 121–142. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Birattari, M., Stützle, T., Paquete, L., Varrentrapp, K.: A racing algorithm for configuring metaheuristics. In: GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, New York, USA, July 9-13, pp. 11–18. Morgan Kaufmann (2002)Google Scholar
  8. 8.
    Birattari, M.: Tuning Metaheuristics. SCI, vol. 197. Springer, Heidelberg (2009)zbMATHCrossRefGoogle Scholar
  9. 9.
    Pedersen, M.E.H.: Good Parameters for Differential Evolution. Technical Report Technical report no. HL1002, Hvass Laboratories, University of Zurich, Department of Informatics (2010)Google Scholar
  10. 10.
    Smit, S.K., Eiben, A.E.: Comparing Parameter Tuning Methods for Evolutionary Algorithms. In: IEEE Congress on Evolutionary Computation (CEC), pp. 399–406 (May 2009)Google Scholar
  11. 11.
    Mezura-Montes, E., Velázquez-Reyes, J., Coello, C.A.C.: A comparative study of differential evolution variants for global optimization. In: GECCO, Genetic and Evolutionary Computation Conference, Seattle, Washington, USA, July 8-12, pp. 485–492. ACM (2006)Google Scholar
  12. 12.
    Matsumoto, M., Nishimura, T.: Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modeling and Computer Simulation 8(1), 3–30 (1999)CrossRefGoogle Scholar
  13. 13.
    Cárdenas-Montes, M., Vega-Rodríguez, M.A., Gómez-Iglesias, A.: Real-world problem for checking the sensitiveness of evolutionary algorithms to the choice of the random number generator. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Graña, M., Cho, S.-B. (eds.) HAIS 2012, Part III. LNCS, vol. 7208, pp. 385–396. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Charbonneau, P.: Genetic algorithms in astronomy and astrophysics. The Astrophysical Journal Supplement Series 101, 309–334 (1995)CrossRefGoogle Scholar
  15. 15.
    Cárdenas-Montes, M., Mollá, M., Vega-Rodríguez, M.A., Rodríguez-Vázquez, J.J., Gómez-Iglesias, A.: Adjustment of observational data to specific functional forms using a particle swarm algorithm and differential evolution: Rotational curves of a spiral galaxy as case study. In: Sarro, L.M., Eyer, L., O’Mullane, W., De Ridder, J. (eds.) Astrostatistics and Data Mining. Springer Series in Astrostatistics, vol. 2, pp. 81–88. Springer, New York (2012)CrossRefGoogle Scholar
  16. 16.
    García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the cec’2005 special session on real parameter optimization. J. Heuristics 15(6), 617–644 (2009)zbMATHCrossRefGoogle Scholar
  17. 17.
    García, S., Fernández, A., Luengo, J., Herrera, F.: A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput. 13(10), 959–977 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Miguel Cárdenas-Montes
    • 1
  • Miguel Á. Vega-Rodríguez
    • 2
  • Mercedes Mollá
    • 1
  1. 1.Department of Fundamental ResearchCentro de Investigaciones Energéticas Medioambientales y TecnológicasMadridSpain
  2. 2.ARCO Research Group, Dept. Technologies of Computers and CommunicationsUniversity of ExtremaduraCáceresSpain

Personalised recommendations