MATLAB: How to read symbolic varibales in a n optimization model

genetic algorithmsymbolic

I have a nonlinear discrete minimization problem, where x(j,k) is a binary variable (1 if the condition holds, 0 otherwise). I need to find x(j,k) for all j and k in a way that the objective value is minimized. I used symbolic variables to represent the x(j,k) by using a genetic algorithm. but after I run my code I get this error: _"Not enough input arguments.
Error in symengine>@(x11,x12,x21,x22)"_ Here is my code in the attached file:
 P = [24 6;8 8];
n = size(P,2);
x = cell(n, n);
for k = 1:n
    for j = 1:n
        x{k,j} = sprintf('x%d%d',j,k); % decision variable if job j is assigned to position k x(j,k) = 1
        % otherwise 0
    end
end
x = x(:); % now x is a n^2-by-1 vector
x = sym(x, 'integer');
J = 0;
for j = 1:n
    for k = 1:n
        W(j,k) = P(1,j) * x(J + k,1) ;% processing time of the job in position k
    end
    J = J + n;
end
W1 = sum(W);
C_1_k(1,1) = W1(1,1); % completion time of position 1 on machine 1
for k = 2:n
C_1_k(1,k) = W1(1,k) + (C_1_k(1,k-1)); % completion time of position k > 1 on machine 1
end
SumC1 = sum(C_1_k);
J = 0;
for j = 1:n
    WW(j,1) = (P(1,j) + P(2,j)) * x(J+j,1); % completion time of the first position on machine 2 %k=1
    J = J + n-1;
end
C_2_k(1,1) = sum(WW); %x(kj)
 for k = 2:n
    K = 0;
    MAX_function = 0.5*(C_1_k(1,k) + C_2_k(1,k-1) + abs(C_1_k(1,k) - C_2_k(1,k-1))); %max function does not work with symbolic variables I wrote simple equivalent
     for j = 1:n
       W_2_k(j,1)  =  (x(K+k,1) * P(2,j));
       K = K + n;
    end
    C_2_k(1,k) = MAX_function + sum(W_2_k,1); %Completion time job in position k on machine 2
 end
 Fun_C_2_k = matlabFunction(C_2_k);
SumC = sum(C_2_k);
Fun_SumC = matlabFunction(SumC);
 % to form optimization settings
 A = zeros(n,n^2);
 B = zeros(n,n^2);
 K = 0;
 for j = 1:n
    for k = 1:n
        A(j,K+k) = 1;
    end
    K = K+n; 
 end
 for j = 1:n
    K = j -1;
    for k = 1:n
       B(j,K+k) = 1;
        K = K+n-1;
    end
 end
 Aeq = [A;B]; %LHS of equality constriants
 beq = ones(2*n,1); %RHS of equality constriants
 %Aeq*x = beq EQUALITY constraints
 LB = zeros(n,n);%lower bonud for x, since x is a binary variable the lower bound is zero
 LB = LB(:);
 UB = ones(n,n); %Upper bonud for x, since x is a binary variable the upper bound is one
 UB = UB(:);
 nvars = n^2;
% for i = 1:nvars
% IntCon(i,1) = i;
% end
 [x, fval] = ga(Fun_SumC,nvars,[],[],Aeq,beq,LB,UB);

Best Answer

You need to use 'vars', {x} option for matlabFunction
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