Documentation of objfractal
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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)
Chrom - Matrix containing the chromosomes of the current
population. Each row corresponds to one individual's
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.
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
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
% continuous variant of the Fractal function with default box
% dimension BoxDim = 1.85
% 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 document is part of version 3.8
GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab -
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© 1994-2006 Hartmut Pohlheim, All Rights Reserved,