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).
    P2        - Additional parameter

 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.
© 1994-2006 Hartmut Pohlheim, All Rights Reserved, (support@geatbx.com).