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Module: OptimizationModel OptimizationModel.py

A Collection of optimization functions as testing targets for optimization procedures (e.g for evolution strategy).

Each of the functions is wrapped by a descendant of class OptimizationModel.

Each function maps a vector to a scalar error value and has a one ore more optimum points (multimodal problem) of lowest error (minimization problem) respectively highest quality (maximization problem).

Imported modules   
from Numeric import array, asarray, arrayrange, zeros, ones, sum
from math import sqrt
Functions   
MandelbrotIteration
sqr
  MandelbrotIteration 
MandelbrotIteration ( p,  n )

Mandelbrot iteration. Do at most n iterations of the complex mapping X(i+1) = XiČ + c with parameter c and X0 = 0 until it diverges (max. n times), divergence criterium is | Xi | > 2.0. Periodicity checking is also done. Arguments: - p(ro): List of length one containing complex constant c. This also represents X1. Return value: - number of iterations done in case of divergence - minus period in case of periodicity - n else. Also on return list p will contain the iteration sequence (X0 excluded).

  sqr 
sqr ( x )

Classes   

EllipsoidModel

Hyper ellipsoid model with optimum in the origin

MandelbrotModel

The fractal mandelbrot set (discovered by Benoit Mandelbrot from IBM)

OptimizationModel

Abstract quality function model.

ParabolicRidgeModel

Parabolic ridge directed in the main diagonal of the search space.

RosenbrockModel

Rosenbrock's valley, De Jong's function 2 (also called banana valley)

SphereModel

Hyper sphere model with Optimum in the origin.


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