Documentation of asknondom

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Function Synopsis

ObjVal = asknondom(Chrom, MObjFun, varargin)

Help text

 Ask for the percentage of non-dominated individuals in a population

 This function implements the answer to the question:
 How many individuals of a given population are non-dominated (and
 the remainder is dominated)?
 Depending on the size of the population and the number of ojectives 
 this number changes dramatically (from only a few non-dominated to 
 nearly all individuals are non-dominated).
 The function is implemented as an objective function. Thus, it can be 
 used throughout the GEATbx (but especially for plotmesh).
 The parameters of the "individuals" are the size of the population
 and the number of objectives (optional). An additional parameter 
 to the function defines the multi-objective objective function to 
 use. Any of the many examples of the GEATbx an be used.

 The results of this experiment are published in:
 Bagot, Benoit and Pohlheim, Hartmut: Complementary Selection and 
 Variation for an Efficient Multiobjective Optimization of Complex 
 Systems. CEC2005, 2005.
 The paper can also be found at: http://pohlheim.com/publications.html

 Syntax:  ObjVal = asknondom(Chrom, MObjFun)
 

 Input parameters:
    Chrom     - Matrix containing the variables of the problem formulation.
                Each line constitutes one population with the given size and
                the given number of objectives.
                Chrom(:,1): number of individuals in the population
                Chrom(:,2): number of objectives of the used MO function
    MObjFun   - (optional) String containing the name of the MO function to use
                if omitted or NaN 'mobjfonseca2' is used

 Output parameters:
    ObjVal    - Column vector containing the percentage of non-dominated 
                individuals in the given populations.
                
 See also: plotmesh, mobjfonseca2, objfun1, objfunoptset

Cross-Reference Information

Listing of function asknondom

% Author:   Hartmut Pohlheim
% History:  15.01.2005  file created


function ObjVal = asknondom(Chrom, MObjFun, varargin)

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

   % Check input parameters
   if nargin < 1, Chrom = []; end
   if isnan(Chrom), Chrom = []; end
   if isempty(Chrom), Chrom = [NaN, NaN, 1]; end
   ObjVal = [];
   
   if nargin < 2, MObjFun = []; end
   if isnan(MObjFun), MObjFun = []; end
   if isempty(MObjFun), MObjFun = 'mobjfonseca2'; end

   % Create option-structure
   if isnan(Chrom(1,1)), 
      if isnan(Chrom(1,2)),
         if Chrom(1,3) <= 10,
           ObjVal = objfunoptset( 'FunctionName', 'Non-Dominated Individuals 1' ...
                                , 'VarBoundMin', 1, 'VarBoundMax', Inf ...
                                , 'NumVarDefault', 2, 'NumVarMin', 1, 'NumVarMax', 3 ...
                                , 'NumObjDefault', 2, 'NumObjMin', 1, 'NumObjMax', 2 ...
                                );
         end
      end

   % Calculate objective values
   else
      ParaNumInd = round(Chrom(:,1));
      % Check if number of objectives is given
      if Nvar > 1, ParaNumMObj = round(Chrom(:,2)); else ParaNumMObj = []; end
      % Check if number of variables is given
      if Nvar > 2, ParaNumVar = round(Chrom(:,3)); else ParaNumVar = repmat(NaN, [Nind,1]); end
      % For statistical reasons multiple runs are performed and we use only the mean value
      NumofStats = 1;
      % Loop through all the given configurations/individuals
      for irun = 1:Nind,
         if irun == 1, fprintf(1, ' %s [%s] point: ', mfilename, MObjFun);
         elseif irun > 1, fprintf(1, '\b\b\b\b\b\b\b\b\b\b\b'); end
         fprintf(1, '%5g/%5g', irun, Nind);
         % Set the number of objectives to use for the current configuration
         if ~(isempty(ParaNumMObj(irun))),
            StateNObj = geaobjpara(MObjFun, [11 ParaNumMObj(irun)]);
         end
         
         for istat = 1:NumofStats,
            % Get VLUB of MO function
            VLUB = geaobjpara(MObjFun, [1 ParaNumVar(irun)]);
            % Get number of individuals of current population
            CurNumInd = ParaNumInd(irun,1);
            % Generate population of given size
            CurPop = initrp(CurNumInd, VLUB);
            % Calculate the objective values for the current population
            CurObjV = feval(MObjFun, CurPop, varargin{:});
            % Rank the current population objective values
            % Put all the ranking options into one array for later use
            % GEAOpt.Selection.Pressure; GEAOpt.Selection.RankingMethod; GEAOpt.Selection.RankingMultiobj
            RankOpt = [2; 0; 1]';
            [CurFitnV, CurRankV] = ranking(CurObjV, RankOpt, 1);
            % Get all rank values of 0 and calculate percentage
            CurRankNonDom(istat,1) = sum(CurRankV < 1);
         end
         ObjVal(irun,1) = 100 .* mean(CurRankNonDom) ./ CurNumInd;
         ObjVal(irun,2) = 100 .*  std(CurRankNonDom) ./ CurNumInd;
      end
   end


% End of function


% plotmesh('asknondom', [40, 3, 20; 230, 18, 30], [10, 25;NaN,NaN;0 100], 'mobjdtlz1')

      % plotmesh(PF{imesh,1}, PF{imesh,2}, PF{imesh,3}); 
      % eval(['print ' ' -d' PrintStyle ' ' PrintExt ' ',  ResPathMesh, PF{imesh,4} FileSuffix ';'])
      % disp([sprintf('%2d: ', imesh) 'Grafic saved as  ', ResPathMesh, PF{imesh,4} FileSuffix '   ' ]);