Abstract and Applied Analysis

Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation

J. A. Tenreiro Machado

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Abstract

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 739464, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450264

Digital Object Identifier
doi:10.1155/2013/739464

Mathematical Reviews number (MathSciNet)
MR3068867

Citation

Tenreiro Machado, J. A. Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 739464, 7 pages. doi:10.1155/2013/739464. https://projecteuclid.org/euclid.aaa/1393450264


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