Documentation of objfletwell

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Function Synopsis

`ObjVal = objfletwell(Chrom, P1, P2)`

Help text

``` OBJective function after FLETcher and PoWELL

This function implements the function after Fletcher and Powell
and a discretization of this objective function. The function
after Fletcher and Powell is highly multimodal and a
representative of nonlinear parameter estimation.

For the computation of this objective function two random matrices
A, B and a random vector alpha are used. Therefore the function is
not symmetric and the extrema are randomly distributed over the
search space. The random values of A, B and alpha are retrieved
by the private function getFletwellData.

This function was first introduced by Fletcher and Powell in:
Fletcher, R. and Powell, M.J.D., A rapidly convergent descent
method for minimization. Computer Journal, 6:163-168, 1963.

In connection with Evolution Strategies the function was used in:
Schwefel, H.-P., Numerische Optimierung von Computer-Modellen
mittels der Evolutionsstrategie, volume 26 of Interdisciplinary
Systems Research. Basel: Birkhaeuser, 1977, pp. 327-328.

Baeck, T., Evolutionary Algorithms in Theory and Practice.
New York-Oxford: Oxford University Press, 1996, pp. 143-144.

Syntax: ObjVal = objfletwell(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 discrete version
is used (P1 = 1).

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 function after Fletcher and Powell
>> objfletwell(Chrom)

% discrete variant of the function after Fletcher and Powell
>> objfletwell(Chrom, 1)

Author:   Hartmut Pohlheim
History:  08.11.99    file created
```

Cross-Reference Information

This function is called by
 GEATbx: Main page  Tutorial  Algorithms  M-functions  Parameter/Options  Example functions  www.geatbx.com

This document is part of version 3.8 of the GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab - www.geatbx.com.
The Genetic and Evolutionary Algorithm Toolbox is not public domain.