Documentation of objfun11

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Function Synopsis

ObjVal = objfun11(Chrom, option);

Help text

 OBJective function for langermann's function 11

 This function implements the LANGERMANN function 11.

 Syntax:  ObjVal = objfun11(Chrom, option)

 Input parameters:
    Chrom     - Matrix containing the chromosomes of the current
                population. Each row corresponds to one individual's
                string representation.
                if Chrom == [], then special values will be returned
    option    - if Chrom == [] and
                option == 1 (or []) return boundaries
                option == 2 return title
                option == 3 return value of global minimum
                if Chrom is not empty, option can optionally contain
                the number of sum steps, that means m in the algorithm

 Output parameters:
    ObjVal    - Column vector containing the objective values of the
                individuals in the current population.
                if called with Chrom == [], then ObjVal contains
                option == 1, matrix with the boundaries of the function
                option == 2, text for the title of the graphic output
                option == 3, value of global minimum
                
 See also: objfun1a, objfun1b, objfun2, objfun6, objfun7, objfun8, objfun9, objfun10,

 Examples:
    ObjVal = objfun11(Chrom);
    ObjVal = objfun11(Chrom, 10);    % use 10 sum steps

 Reference:
      

Cross-Reference Information

Listing of function objfun11

% Author:   Hartmut Pohlheim
% History:  30.08.95    file created
%           05.10.95    function creation finished
%           10.10.97    small change for Matlab5 compliance


function ObjVal = objfun11(Chrom, option);

a = [	9.681, 0.667, 4.783, 9.095, 3.517, 9.325, 6.544, 0.211, 5.122, 2.020;
	9.400, 2.041, 3.788, 7.931, 2.882, 2.672, 3.568, 1.284, 7.033, 7.374;
	8.025, 9.152, 5.114, 7.621, 4.564, 4.711, 2.996, 6.126, 0.734, 4.982;
	2.196, 0.415, 5.649, 6.979, 9.510, 9.166, 6.304, 6.054, 9.377, 1.426;
	8.074, 8.777, 3.467, 1.863, 6.708, 6.349, 4.534, 0.276, 7.633, 1.567;
	7.650, 5.658, 0.720, 2.764, 3.278, 5.283, 7.474, 6.274, 1.409, 8.208;
	1.256, 3.605, 8.623, 6.905, 0.584, 8.133, 6.071, 6.888, 4.187, 5.448;
	8.314, 2.261, 4.224, 1.781, 4.124, 0.932, 8.129, 8.658, 1.208, 5.762;
	0.226, 8.858, 1.420, 0.945, 1.622, 4.698, 6.228, 9.096, 0.972, 7.637;
	7.305, 2.228, 1.242, 5.928, 9.133, 1.826, 4.060, 5.204, 8.713, 8.247;
	0.652, 7.027, 0.508, 4.876, 8.807, 4.632, 5.808, 6.937, 3.291, 7.016;
	2.699, 3.516, 5.874, 4.119, 4.461, 7.496, 8.817, 0.690, 6.593, 9.789;
	8.327, 3.897, 2.017, 9.570, 9.825, 1.150, 1.395, 3.885, 6.354, 0.109;
	2.132, 7.006, 7.136, 2.641, 1.882, 5.943, 7.273, 7.691, 2.880, 0.564;
	4.707, 5.579, 4.080, 0.581, 9.698, 8.542, 8.077, 8.515, 9.231, 4.670;
	8.304, 7.559, 8.567, 0.322, 7.128, 8.392, 1.472, 8.524, 2.277, 7.826;
	8.632, 4.409, 4.832, 5.768, 7.050, 6.715, 1.711, 4.323, 4.405, 4.591;
	4.887, 9.112, 0.170, 8.967, 9.693, 9.867, 7.508, 7.770, 8.382, 6.740;
	2.440, 6.686, 4.299, 1.007, 7.008, 1.427, 9.398, 8.480, 9.950, 1.675;
	6.306, 8.583, 6.084, 1.138, 4.350, 3.134, 7.853, 6.061, 7.457, 2.258;
	0.652, 2.343, 1.370, 0.821, 1.310, 1.063, 0.689, 8.819, 8.833, 9.070;
	5.558, 1.272, 5.756, 9.857, 2.279, 2.764, 1.284, 1.677, 1.244, 1.234;
	3.352, 7.549, 9.817, 9.437, 8.687, 4.167, 2.570, 6.540, 0.228, 0.027;
	8.798, 0.880, 2.370, 0.168, 1.701, 3.680, 1.231, 2.390, 2.499, 0.064;
	1.460, 8.057, 1.336, 7.217, 7.914, 3.615, 9.981, 9.198, 5.292, 1.224;
	0.432, 8.645, 8.774, 0.249, 8.081, 7.461, 4.416, 0.652, 4.002, 4.644;
	0.679, 2.800, 5.523, 3.049, 2.968, 7.225, 6.730, 4.199, 9.614, 9.229;
	4.263, 1.074, 7.286, 5.599, 8.291, 5.200, 9.214, 8.272, 4.398, 4.506;
	9.496, 4.830, 3.150, 8.270, 5.079, 1.231, 5.731, 9.494, 1.883, 9.732;
	4.138, 2.562, 2.532, 9.661, 5.611, 5.500, 6.886, 2.341, 9.699, 6.500
    ];

c = [	0.806,	0.517,	1.5,	0.908,	0.965,	0.669,	0.524,	0.902, ...
	0.531,	0.876,	0.462,	0.491,	0.463,	0.714,	0.352,	0.869, ...
	0.813,	0.811,	0.828,	0.964,	0.789,	0.360,	0.369,	0.992, ...
	0.332,	0.817,	0.632,	0.883,	0.608,	0.326];

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

% Check size of Chrom and do the appropriate thing
   % Default dimension of objective function
   Dim = 10;
   % if Chrom is [], then define size of boundary-matrix and values
   if Nind == 0
      % return text of title for graphic output
      if option == 2
         ObjVal = ['LANGERMANNs function 11'];
      % return value of global minimum
      elseif option == 3
         ObjVal = -1.4;
      % define size of boundary-matrix and values
      else   
         % lower and upper bound, identical for all n variables        
         ObjVal = repmat([ 0; 10], [1 Dim]);
      end
   % compute values of function
   else
      % function langermann
      %    -sum of c(i)*(exp(-1/pi*sumnorm)*cos(pi*sumnorm)) for i = 1:m
      %       sumnorm = sum((Chrom -a(i))^2)
      % 0 <= xi <= 10, m = 5
      % global minimum at (xi) = (???) ; fmin = -1.4 (for m = 5)
      % check input parameter and set default value
      if Nvar > size(a, 2),
         error(sprintf('Number of variables per individual too big. Maximum is %g', size(a,2)));
      end
      if nargin < 2, m = []; else m = option; end
      if isempty(m), m = Dim; end
      if m > size(a, 1),
         error(sprintf('Number of sum steps too big. Maximum is %g', size(a,1)));
      end
      % get the matrices of function parameters depending on size of problem
      ce = c(1:m); ce = ce(:); aa = a(1:m,1:Nvar);
      % compute the norm between Chrom and the 'a' matrix
      sumnorm = sum(((expandm(Chrom,[m,1]) - repmat(aa,[Nind,1]))').^2)';
      sumnorm = reshape(sumnorm', m, Nind)';
      % compute the sum as defined in function description
      ObjVal = -((exp(-(sumnorm/pi)) .* cos(pi * sumnorm)) * ce);
   end   


% End of function