FindParetoSet

 [Index]=FindParetoSet(Pop,FunVal)
 FindParetoSet:       Identify the set of non-dominated solutions 
 INPUTS 
 Pop:                 Population
 FunVal:              A matrix of function evaluations, one vector of m objectives for each individual
 OUTPUTS
 Index: Index of non-dominated solutions in Pop

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

0001 function[Index]=FindParetoSet(Pop,FunVal)
0002 % [Index]=FindParetoSet(Pop,FunVal)
0003 % FindParetoSet:       Identify the set of non-dominated solutions
0004 % INPUTS
0005 % Pop:                 Population
0006 % FunVal:              A matrix of function evaluations, one vector of m objectives for each individual
0007 % OUTPUTS
0008 % Index: Index of non-dominated solutions in Pop
0009 %
0010 % Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)
0011 
0012    PopSize = size(Pop,1);
0013    number_objectives = size(FunVal,2);
0014   
0015    last = size(FunVal,1);  % Number of individuals in the population
0016    DomPop = zeros(1,last); % Indicator of dominated individuals
0017    
0018    i = 1;
0019  while i<last,    
0020    while DomPop(i)>0 && i<last  % Find the first non-dominated individual
0021      i = i + 1;
0022    end,  
0023    j = i + 1;
0024    while j<=last 
0025     while DomPop(j)>0 && j<last  % Find the second non dominated individual
0026      j = j + 1;
0027     end,
0028       if(sum(FunVal(i,:)>=FunVal(j,:))==number_objectives) % j is dominated by i (they could be equal)
0029         DomPop(j) = DomPop(j) + 1;   % j is marked as dominated
0030       elseif(sum(FunVal(j,:)>=FunVal(i,:))==number_objectives) % i is dominated by j
0031         DomPop(i) = DomPop(i) + 1;  % i is marked as dominated
0032         j = last;     
0033       end,
0034     j = j + 1;
0035    end
0036    i = i + 1; 
0037  end
0038 
0039 
0040  Index = find(DomPop==0); %Non dominated solutions
0041    
0042  return
0043  
0044    last = size(FunVal,1);
0045    DomPop = zeros(1,last);
0046    for i=1:last-1
0047     for j=i+1:last
0048       if(sum(FunVal(i,:)>=FunVal(j,:))==number_objectives)
0049         DomPop(j) = DomPop(j) + 1;
0050       elseif(sum(FunVal(j,:)>=FunVal(i,:))==number_objectives)      
0051         DomPop(i) = DomPop(i) + 1;  
0052       end,
0053     end
0054    end
0055    Index = find(DomPop==0); %Non dominated solutions
0056    
0057    
0058