Optimal Estimation of Fractal Models of Digital Sequences by means of Genetic Algorithms

Self-affine and piecewise self-affine IFS fractal models have been used to model several different types of discrete sequences. The parameters of such models must be determined according to an opimization criterion. However, the general optimization problem is quite complex and some constraints have to be introduced. Several different constraints have been considered in this paper, and the best tradeoff between overall performances and computational complexity has been found. The optimal estimation of the fractal models parameters has been obtained by means of Genetic Algorithms and a very good convergence to the global minimum has been obtained. A comparison with suboptimal algorithms will be reported. Several types of discrete sequences have been modeled with the best performing fractal model and the performance results will be reported