% RANKING.M      (RANK-based fitness assignment)%% This function performs ranking of individuals.%% Syntax:  FitnV = ranking(ObjV, RFun, SUBPOP)%% This function ranks individuals represented by their associated% cost, to be *minimized*, and returns a column vector FitnV% containing the corresponding individual fitnesses. For multiple% subpopulations the ranking is performed separately for each% subpopulation.%% Input parameters:%    ObjV      - Column vector containing the objective values of the%                individuals in the current population (cost values).%    RFun      - (optional) If RFun is a scalar in [1, 2] linear ranking is%                assumed and the scalar indicates the selective pressure.%                If RFun is a 2 element vector:%                RFun(1): SP - scalar indicating the selective pressure%                RFun(2): RM - ranking method%                         RM = 0: linear ranking%                         RM = 1: non-linear ranking%                If RFun is a vector with length(Rfun) > 2 it contains%                the fitness to be assigned to each rank. It should have%                the same length as ObjV. Usually RFun is monotonously%                increasing.%                If RFun is omitted or NaN, linear ranking%                and a selective pressure of 2 are assumed.%    SUBPOP    - (optional) Number of subpopulations%                if omitted or NaN, 1 subpopulation is assumed%% Output parameters:%    FitnV     - Column vector containing the fitness values of the%                individuals in the current population.%                % Author:     Hartmut Pohlheim (Carlos Fonseca)% History:    01.03.94     non-linear ranking%             10.03.94     multiple populationsfunction FitnV = ranking(ObjV, RFun, SUBPOP);% Identify the vector size (Nind)   [Nind,ans] = size(ObjV);   if nargin < 2, RFun = []; end   if nargin > 1, if isnan(RFun), RFun = []; end, end   if prod(size(RFun)) == 2,      if RFun(2) == 1, NonLin = 1;      elseif RFun(2) == 0, NonLin = 0;      else error('Parameter for ranking method must be 0 or 1'); end      RFun = RFun(1);      if isnan(RFun), RFun = 2; end   elseif prod(size(RFun)) > 2,      if prod(size(RFun)) ~= Nind, error('ObjV and RFun disagree'); end   end   if nargin < 3, SUBPOP = 1; end   if nargin > 2,      if isempty(SUBPOP), SUBPOP = 1;      elseif isnan(SUBPOP), SUBPOP = 1;      elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end   end   if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('ObjV and SUBPOP disagree'); end   Nind = Nind/SUBPOP;  % Compute number of individuals per subpopulation   % Check ranking function and use default values if necessary   if isempty(RFun),      % linear ranking with selective pressure 2         RFun = 2*[0:Nind-1]'/(Nind-1);   elseif prod(size(RFun)) == 1      if NonLin == 1,         % non-linear ranking         if RFun(1) < 1, error('Selective pressure must be greater than 1');         elseif RFun(1) > Nind-2, error('Selective pressure too big'); end         Root1 = roots([RFun(1)-Nind [RFun(1)*ones(1,Nind-1)]]);         RFun = (abs(Root1(1)) * ones(Nind,1)) .^ [(0:Nind-1)'];         RFun = RFun / sum(RFun) * Nind;      else         % linear ranking with SP between 1 and 2         if (RFun(1) < 1 | RFun(1) > 2),            error('Selective pressure for linear ranking must be between 1 and 2');         end         RFun = 2-RFun + 2*(RFun-1)*[0:Nind-1]'/(Nind-1);      end   end;   FitnV = [];% loop over all subpopulationsfor irun = 1:SUBPOP,   % Copy objective values of actual subpopulation      ObjVSub = ObjV((irun-1)*Nind+1:irun*Nind);   % Sort does not handle NaN values as required. So, find those...      NaNix = isnan(ObjVSub);      Validix = find(~NaNix);   % ... and sort only numeric values (smaller is better).      [ans,ix] = sort(-ObjVSub(Validix));   % Now build indexing vector assuming NaN are worse than numbers,   % (including Inf!)...      ix = [find(NaNix) ; Validix(ix)];   % ... and obtain a sorted version of ObjV      Sorted = ObjVSub(ix);   % Assign fitness according to RFun.      i = 1;      FitnVSub = zeros(Nind,1);      for j = [find(Sorted(1:Nind-1) ~= Sorted(2:Nind)); Nind]',         FitnVSub(i:j) = sum(RFun(i:j)) * ones(j-i+1,1) / (j-i+1);         i =j+1;      end   % Finally, return unsorted vector.      [ans,uix] = sort(ix);      FitnVSub = FitnVSub(uix);   % Add FitnVSub to FitnV      FitnV = [FitnV; FitnVSub];end% End of function