MATLAB: How to get binary output instead of fraction from gamultiobj optimization

gamultiobjmulti-objective optimization

I am using the below code to get a binary decision output. Instead I am getting fractions. How can I fix this?
    D = [1,2,3,1,2,3,4,1,2,2,1,2,3,4,4,1,2,3,4,3];
    F = [4,3,2,4,4,3,2,4,2,2,4,4,4,2,2,5,4,2,2,2];
    T = 21;
    %H = round(rand(20,20));
    H = zeros(20,20);
    H(1,2) = 1;
    H(1,3) = 1;
    H(2,3) = 1;
    H(4,5) = 1;
    H(4,6) = 1;
    H(4,7) = 1;
    H(5,6) = 1;
    H(5,7) = 1;
    H(6,7) = 1;
    H(8,9) = 1;
    H(8,10) = 1;
    H(11,12) = 1;
    H(11,13) = 1;
    H(12,13) = 1;
    H(13,14) = 1;
    H(13,15) = 1;
    H(16,17) = 1;
    H(17,18) = 1;
    H(17,19) = 1;
    H(17,20) = 1;
    fitnessfcn = @(x)[sum(x), -sum(D.*x)];
    nvars = 20;
    A = -F;
    b = -T;
    Aeq = [];
    Beq = [];
    lb = zeros(20,1);
    ub = ones(20,1);
    [x, fval] = gamultiobj(fitnessfcn, nvars, A, b, Aeq, Beq, lb, ub, @(x) mycon(x, H));
    function xsum= constraint2(x,H)
        xsum = 0;
        for i = 1:length(H)
            for j = i+1:length(H)
                xsum = xsum + H(i,j) * x(i) * x(j);
            end
        end    
    end
    function [c,ceq] = mycon(x,H)
        c = [];
        ceq = constraint2(x,H);
    end

Best Answer

gamultiobj() does not do integer constraints explicitly. You have constrained that the values must be at least 0 and no greater than 1, but you have not constrained that they must be exactly 0 or exactly 1.
In order to implement integer constraints in gamultiobj, you need to use a custom initial population and custom mutation function and custom cross-over function that just happen to only return binary values.
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