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.
Highlights
This paper analyzes the fractional order dynamics during the search for the optimal solution in a plane with an hexagonal tessellation by means of a genetic algorithm
The basis of the symbiosis in lichens is that the fungus provides the algal protection and gains nutrients in return. Such examples are merely possible interpretations of the simulation results, but, an abstract formulation is the basis of the proposed study that primarily intends to model the GA evolution with Fractional calculus (FC) tools
We describe the experiments with the GA and we analyse the results in the perspective of fractional dynamics
Summary
This paper analyzes the fractional order dynamics during the search for the optimal solution in a plane with an hexagonal tessellation by means of a genetic algorithm. The basis of the symbiosis in lichens is that the fungus provides the algal protection and gains nutrients in return Such examples are merely possible interpretations of the simulation results, but, an abstract formulation is the basis of the proposed study that primarily intends to model the GA evolution with FC tools. Bearing these ideas in mind this paper is organized as follows.
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