ParetoRank_ordering

 [Index]=ParetoRank_ordering(Pop,FunVal)
 ParetoRank_ordering:        Individuals are firstly ordered according to the front they belong to. 
                             Then, in each front, they are ordered according to the average rank of
                             their fitness functions (see Pareto_ordering and fitness_ordering
                             for details)
                             The first front (non-dominated solutions) come first. Then individuals that are only
                             dominated by those in the first front and so on. 
 INPUTS 
 Pop:                 Population
 FunVal:              A matrix of function evaluations, one vector of m objectives for each individual
 OUTPUTS
 Index: Ordered index of the individuals in the population

 Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)

0001 function[Index]=ParetoRank_ordering(Pop,FunVal)
0002 % [Index]=ParetoRank_ordering(Pop,FunVal)
0003 % ParetoRank_ordering:        Individuals are firstly ordered according to the front they belong to.
0004 %                             Then, in each front, they are ordered according to the average rank of
0005 %                             their fitness functions (see Pareto_ordering and fitness_ordering
0006 %                             for details)
0007 %                             The first front (non-dominated solutions) come first. Then individuals that are only
0008 %                             dominated by those in the first front and so on.
0009 % INPUTS
0010 % Pop:                 Population
0011 % FunVal:              A matrix of function evaluations, one vector of m objectives for each individual
0012 % OUTPUTS
0013 % Index: Ordered index of the individuals in the population
0014 %
0015 % Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)
0016 
0017    PopSize = size(Pop,1);
0018    number_objectives = size(FunVal,2);
0019    Ind = [1:PopSize];
0020    nfronts = 0;
0021   % First, Pareto_ordering is applied to identify the fronts
0022   
0023   while ~isempty(Ind) 
0024    last = size(Ind,2);
0025    DomPop = zeros(1,last);
0026    for i=1:last-1
0027     for j=i+1:last,
0028       if(sum(FunVal(Ind(i),:)>=FunVal(Ind(j),:))==number_objectives)
0029         DomPop(j) = DomPop(j) + 1;
0030       elseif(sum(FunVal(Ind(j),:)>=FunVal(Ind(i),:))==number_objectives)      
0031         DomPop(i) = DomPop(i) + 1;  
0032       end,
0033     end
0034    end
0035    NonDom = Ind(find(DomPop==0));
0036    nfronts = nfronts + 1;
0037    Front{nfronts} = NonDom;
0038    Ind = setdiff(Ind,NonDom);
0039   end,
0040   
0041   % Solution in each front are ordered according to the rank
0042   Index = [];
0043   for i=1:nfronts
0044    [AuxIndex]=fitness_ordering(Pop(Front{i},:),FunVal(Front{i},:));
0045    Index = [Index,Front{i}(AuxIndex)];
0046   end
0047    
0048  return
0049  
0050    
0051    
0052