Global Index (all files) (short | long) | Local contents | Local Index (files in subdir) (short | long)

ObjVal = objfractal(Chrom, P1, P2)

OBJective function Fractal Mandelbrot This function implements a fractal function and its discretization. The Fractal function is highly multimodal and emulates noisy real-world objective functions. The objective function is obtained by an approximation of the simplified real part C(x) of the Weierstrass-Mandelbrot function. C(x) is continuous but has no derivative at any point. With the box-dimension BoxDim (1 < BoxDim < 2) of this function the ruggedness of the surface can be controlled. Higher values for BoxDim increase the complexity of this objective function and vice versa. The Weierstrass-Mandelbrot function is described in: Mandelbrot, B.B. The fractal geometry of nature. New York: Freeman, 1983. Syntax: ObjVal = objfractal(Chrom, P1, P2) Input parameters: Chrom - Matrix containing the chromosomes of the current population. Each row corresponds to one individual's string representation. If Chrom == [NaN xxx] or Chrom == [NaN xxx yyy], then special values will be returned, see Output parameters xxx == 1 (or []) return boundaries xxx == 2 return title yyy == 0 return title of continuous variant yyy == 1 return title of discrete variant xxx == 3 return value of global minimum P1 - (Optional) Number indicating which variant is used, if Chrom is not NaN or []. P1 = 1 use discrete version P1 = 0 use continuous version If P1 is omitted or P1 = [] the continuos version is used (P1 = 0). P2 - (Optional) Scalar containing the box dimension BoxDim (1 < BoxDim < 2) of this objective function. If P2 is omitted, empty or out of range, then the default value BoxDim = 1.85 is used. Output parameters: ObjVal - Column vector containing the objective values of the individuals in the current population. if called with Chrom == [NaN xxx] or Chrom == [NaN xxx yyy], then ObjVal contains xxx == 1 (or []), matrix with the boundaries of the varaibles xxx == 2, text with the title of the function yyy omitted: title of continuous variant yyy = 0 title of continuous variant yyy = 1 title of discrete variant xxx == 3, value of global minimum Examples: % continuous variant of the Fractal function with default box % dimension BoxDim = 1.85 >> objfractal(Chrom) % discrete variant of the Fractal function with default box % dimension BoxDim = 1.85 >> objfractal(Chrom, 1) % discrete variant of the Fractal function with box dimension % BoxDim = 1.4. >> objfractal(Chrom, 1, 1.4)

This function is called by | |
---|---|

GEATbx: |
Main page Tutorial Algorithms M-functions Parameter/Options Example functions www.geatbx.com |

This document is part of

The Genetic and Evolutionary Algorithm Toolbox is