Abstract
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.
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Notes
- 1.
Apparently, in (3), a velocity is added to a position. However, this addition occurs over a single time increment (iteration), so the equation retains its coherency.
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Acknowledgements
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 (http://www.iac.es/consolider-ingenio-gtc), which are acknowledged.
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Cárdenas-Montes, M., Mollá, M., Vega-Rodríguez, M.A., Rodríguez-Vázquez, J.J., Gómez-Iglesias, A. (2012). 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., Eyer, L., O'Mullane, W., De Ridder, J. (eds) Astrostatistics and Data Mining. Springer Series in Astrostatistics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3323-1_7
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DOI: https://doi.org/10.1007/978-1-4614-3323-1_7
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