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

  • Miguel Cárdenas-Montes
  • Mercedes Mollá
  • Miguel A. Vega-Rodríguez
  • Juan José Rodríguez-Vázquez
  • Antonio Gómez-Iglesias
Part of the Springer Series in Astrostatistics book series (SSIA, volume 2)


The fitting of experimental or observational data to specific functional forms requires high computational capacities in order to tackle the complexity of the calculations. This complexity makes compulsory the use of efficient search procedures such as evolutionary algorithms. Evolutionary algorithms have proved their capability to find suboptimal, high-quality solutions to problems with large search spaces. In this context, a particle swarm algorithm and differential evolution are used to fit a data set to a serial expansion of Legendre polynomials. Concerning the data set, 56 rotation curves of spiral galaxies are used to build up a serial expansion—physically meaningless—retaining the essential information of the curves. The ultimate goal of this work is twofold: first, to provide a theoretical functional form representing the features of the rotational curves of spiral galaxies in order to couple it to other computational models; and second, to demonstrate the applicability of evolutionary algorithms to the matching between astronomical data sets and theoretical models.


Differential Evolution Legendre Polynomial Rotation Curve Spiral Galaxy Differential Evolution Algorithm 
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.



This work was partially supported by DGICYT Grant AYA2010–21887–C04–02 and by the Comunidad de Madrid under Grant CAM S2009/ESP-1496 (AstroMadrid) and by the Spanish MICINN under the Consolider-Ingenio 2010 Program Grant CSD2006-00070: First Science with the GTC (, which are acknowledged.


  1. 1.
    Charbonneau P (1995) Astrophys J Suppl S 101:309ADSCrossRefGoogle Scholar
  2. 2.
    Alba E, Tomassini M (2002) IEEE Trans Evol Comput 6(5):443CrossRefGoogle Scholar
  3. 3.
    Kennedy J, Eberhart RC (1995) Proc IEEE Int Conf Neural Networks IV:1942Google Scholar
  4. 4.
    Eberhart RC, Shi Y, Kennedy J (2001) Swarm intelligence (The Morgan Kaufmann Series in Artificial Intelligence). Morgan Kaufmann, 1st ednGoogle Scholar
  5. 5.
    Eberhart RC, Kennedy J (1995) 39–43. DOI 10.1109/MHS.1995.494215Google Scholar
  6. 6.
    Price KV, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer-Verlag, Berlin, GermanyMATHGoogle Scholar
  7. 7.
    Storn R, Price K (1997) J Global Optim 11(4):341. DOI Google Scholar
  8. 8.
    Montgomery D, Runger G (2002) Applied statistics and probability for engineers. John Wiley and Sons Ltd, New York, USAGoogle Scholar
  9. 9.
    Press W, Flannery B, Teukolsky S, Vetterling W (1992) Numerical recipes in C: the art of scientific computing. Cambridge University PressGoogle Scholar
  10. 10.
    Matsumoto M, Nishimura T (1998) ACM Trans Model Comput Simul 8(1):3MATHCrossRefGoogle Scholar
  11. 11.
    Marquez I, et al (2002) Astron Astrophys 393:389. DOI 10.1051/0004-6361:20021036ADSCrossRefGoogle Scholar
  12. 12.
    García S, Fernández A, Luengo J, Herrera F (2009) Soft Comput 13(10):959CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Miguel Cárdenas-Montes
    • 1
  • Mercedes Mollá
    • 1
  • Miguel A. Vega-Rodríguez
    • 2
  • Juan José Rodríguez-Vázquez
    • 1
  • Antonio Gómez-Iglesias
    • 3
  1. 1.Department of Fundamental ResearchCentro de Investigaciones Energéticas Medioambientales y TecnológicasMadridSpain
  2. 2.Dept. Technologies of Computers and CommunicationsUniversity of Extremadura, ARCO Research GroupCáceresSpain
  3. 3.National Fusion LaboratoryCentro de Investigaciones Energéticas Medioambientales y TecnológicasMadridSpain

Personalised recommendations