How can I get binary output instead of fraction from gamultiobj 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

Answer 1

[Walter Roberson]

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.

[Md Enamul Haque]

Thank you for the reply. Could you please give a simple example? I have been trying to do that but can not get any reference in the documentation.

[Md Enamul Haque]

Hi I have the current code attached, but I am getting the following error.

 Error using checkbounds
 Too many input arguments.

 Error in linprog (line 238)
 [x0,lb,ub,msg] = checkbounds(x0,lb,ub,nvars);

 Error in preProcessLinearConstr (line 135)
    [XOUT,~,success] = linprog([],Aineq,Bineq,Aeq,Beq,LB,UB,[], ...

 Error in gacommon (line 97)
 [Iterate.x,Aineq,bineq,Aeq,beq,lb,ub,msg,exitFlag] = 
 preProcessLinearConstr( ...

 Error in gamultiobj (line 262)
    ~,options] = 
 gacommon(nvars,fun,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,
 [],options,user_options);

 Error in main (line 56)
 [x, f, exitflag, output, population, score] = 
 gamultiobj(fitnessFunction,...

[Walter Roberson]

The checkbounds.m that you have provided is interfering with the Mathworks function of the same name.

[Md Enamul Haque]

I changed the name and still the same error. However sometimes it runs and gives the following message.

 Infeasible individuals are present in the final population.
Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.
Constraints are not satisfied within constraint tolerance.

[Walter Roberson]

The initial population that you provide through the int_pop function must satisfy the linear constraints (I would need to dig deeper to see if it had to satisfy the nonlinear constraints.)

Your int_pop function, given that lb and ub, has a 50% chance of returning a matrix of all 0, and a 50% chance of returning a matrix of all 1, with all of the population members being that same 0 or 1.

Inside the int_pop it will find that the span between the 0 lowerbound and 1 upperbound is 1. It will multiply the span by rand() and add that to the lowerbound of 0, getting you a matrix of values that turn out to be the values of rand() unchanged. Then the code generates a single random number, and 50% chance takes the floor() of the entire matrix, and 50% chance takes the ceil() of the entire matrix. Well, rand() is not able to generate either 0 or 1 exactly, so the range of data that has been generated is (0, 1) open-open interval -- none of the values as large as 1, none of the values as small as 0. floor() of such a matrix would be all 0, and ceil() of such a matrix would be all 1.

This is not a situation in which you need to generalize. You can construct a function:

function Population = int_pop(GenomeLength, ~, options)

    A = options.LinearConstr.Aineq;
    b = options.LinearConstr.bineq;

    curpop = zeros(0, GenomeLength);
    popsize = options.PopulationSize;

    while size(curpop,1) < popsize
      more_needed = popsize - size(curpop,1);
      thisbatch = round(rand(more_needed, GenomeLength));
      passfail = all(A * thisbatch.' <= b, 1);
      goodones = thisbatch(passfail,:);
      curpop = [curpop; goodones];
    end

    Population = curpop;