Documentation of obj4wings

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Function Synopsis

ObjVal = obj4wings(Chrom, P1, P2)

Help text

 OBJective function FOUR-WINGS.

 This function implements the continuous and discrete variant of the
 Four-Wings function. The continuous version is a unimodal function
 with niveaulines resembling conjugated hyperbolas. Because of the
 low slope the surface of the discrete version consists of wide
 plateaus. The area of the plateaus increase with their niveau. 
 
 This function is defined as stepfun4 function in:%
  Jain, Clusterbasierte Abbruchkriterien fuer den Evolutionaeren Test. 
     Diploma-thesis, Technical University of Berlin, Department of 
     Computer Science, chapter 5.1, 1999.

 Syntax: ObjVal = obj4wings(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        - 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 Four-Wings function
  >> obj4wings(Chrom)

  % discrete variant of the Four-Wings function
  >> obj4wings(Chrom, 1)

Cross-Reference Information

Listing of function obj4wings

% Author:   Hartmut Pohlheim
% History:  08.11.99    file created


function ObjVal = obj4wings(Chrom, P1, P2)

% Compute population parameters
   [Nind, Nvar] = size(Chrom);

% Define default values
   doDiscr = 0;      % use discrete variant

% Check size of Chrom and do the appropriate thing
   % if Chrom is [], then reset to [NaN P1], P2
   if isempty(Chrom),
      if nargin < 2, P1 = []; end, if isempty(P1), P1 = 1; end
      if nargin < 3, P2 = []; end, if isempty(P2), P2 = doDiscr; end
      Chrom = [NaN, P1]; P1 = P2; Nind = 1;
   end

   % check the additional parameters
   if nargin < 2, P1 = []; end, if isempty(P1), P1 = doDiscr; end, if P1 == 0, doDiscr = 0; end

   % if Chrom is [NaN xxx] define size of boundary-matrix and others
   if all([Nind == 1, isnan(Chrom(1))]),
      % If only NaN is provided
      if length(Chrom) == 1, option = 1; 
      else                   option = Chrom(2); end
      % Default dimension of objective function
      Dim = 10;
      % return text of title for graphic output
      if option == 2, 
         ObjVal = ['Four-Wings function'];
         if doDiscr == 1, ObjVal = [ObjVal, ' (discrete)']; end
      % return value of global minimum
      elseif option == 3, ObjVal = 0;
      % define size of boundary-matrix and values
      else   
         % lower and upper bound, identical for all n variables        
         ObjVal = repmat([-50; 50], [1 Dim]);
      end

  % compute values of function
   else 
      % Four-Wings : 
      %  f: R^n --> N, x -> f(x)
      %  let yi = round(xi); for i = 1:Nvar (Nvar = 30)  (round only for discrete variant)
      %  let z = 1 + sum of |yi| + prod of |yi|; for i = 1:Nvar (Nvar = 30)
      %  f = round(log(z))  (round only for discrete variant)
      %  n = Nvar, -50 <= xi <= 50
      %  global minimum at (xi) = (0) ; fmin = 0
      if doDiscr == 1, Chrom  = round(Chrom); end
      ObjVal =       log(1+(sum(abs(Chrom)')+prod(abs(Chrom)'))');
      if doDiscr == 1, ObjVal = round(ObjVal); end
   end


% End of function