MakeConfObjectivesFormulas

 [Formulas]=MakeConfObjectivesFormulas(n,m,c,cfixed) 
 MakeConfObjectivesFormulas: Creates a set of formulas (one correspond to each objective). 
                            The first cfixed formulas are uniformly randomly selected. 
                            The rest of formulas are constructed by
                            randomly picked a previous generated formula
                            and replacing some of the variables by other
                            variables that are not in the formula. 
                            The idea is to generate conditionally independent objectives given the variables
 INPUT
 n: Number of variables
 m: Number of formulas (objectives)
 c: Number of clauses in each formula 
 cfixed: Number of fixed formulas (the first clauses generated)
 OUTPUT
 Formulas{i,j}: Contains the clause j in the formula i. A clause is six
                component vector. The first three components are the numbers of the
                variables in the clause. The rest three component indicate whether the
                literal is negated (0) or not (1).

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

0001 function[Formulas]=MakeConfObjectivesFormulas(n,m,c,cfixed) 
0002 % [Formulas]=MakeConfObjectivesFormulas(n,m,c,cfixed)
0003 % MakeConfObjectivesFormulas: Creates a set of formulas (one correspond to each objective).
0004 %                            The first cfixed formulas are uniformly randomly selected.
0005 %                            The rest of formulas are constructed by
0006 %                            randomly picked a previous generated formula
0007 %                            and replacing some of the variables by other
0008 %                            variables that are not in the formula.
0009 %                            The idea is to generate conditionally independent objectives given the variables
0010 % INPUT
0011 % n: Number of variables
0012 % m: Number of formulas (objectives)
0013 % c: Number of clauses in each formula
0014 % cfixed: Number of fixed formulas (the first clauses generated)
0015 % OUTPUT
0016 % Formulas{i,j}: Contains the clause j in the formula i. A clause is six
0017 %                component vector. The first three components are the numbers of the
0018 %                variables in the clause. The rest three component indicate whether the
0019 %                literal is negated (0) or not (1).
0020 %
0021 % Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)
0022 
0023 clear Formulas
0024 triples = nchoosek([1:n],3);
0025 ntriples = size(triples,1);
0026 
0027  val = ones(ntriples,1);
0028 
0029  matrix = zeros(n,n);
0030  val = cumsum(val/sum(val));
0031 
0032 
0033  
0034  for i=1:cfixed  % The initial formulas are randomly selected from the [1:fixedvars];
0035     Index = sus(c,val);  
0036    for j=1:c
0037      Formulas{i,j} = [triples(Index(j),:),fix(2*rand(1,3))];
0038    end 
0039  end
0040  
0041  
0042   for i=cfixed+1:m,           % The rest of formulas are found by replacing some the literals in some of the previously generated formulas
0043     prev = fix((i-1)*rand) + 1;  % Previous clause that will be used to construct the new one
0044     auxvect = zeros(1,n);
0045     for j=1:c,
0046      auxvect(Formulas{prev,j}(1:3)) = 1;
0047     end 
0048     VarsIn = find(auxvect==1);
0049     totIn = size(VarsIn,2);
0050     
0051     InPerm = randperm(totIn);
0052     tochange = fix((totIn)*rand)+1;   % Number of variables that will change their literals
0053     VarsToChange = VarsIn(InPerm(1:tochange));
0054 
0055     for j=1:c
0056       for k=1:3
0057         found = find(VarsToChange==Formulas{prev,j}(k));
0058         if isempty(found)
0059           Formulas{i,j}(k+3) = Formulas{prev,j}(k+3);
0060         else 
0061           Formulas{i,j}(k+3) = 1-Formulas{prev,j}(k+3);
0062         end         
0063       end  
0064       Formulas{i,j}(1:3) = Formulas{prev,j}(1:3);
0065     end      
0066   end
0067   
0068    
0069  
0070  
0071    
0072  
0073  %matrix
0074  %sum(matrix(1:10,1:10))
0075  %sum(matrix(11:20,11:20))