Genetic algorithm problem with integer variables

I have created an optimization algorithm using ga.

The problem has 32 real variables (plant production) and 32 integer variables (binary: open/closed plant).

        N=4;
        T=8;
        nvars=N*T*2;
        IntCon=[N*T+1:N*T*2];
        [x,fval,exitflag,output,population,score] = ga(@objective,nvars,A,b,[],[],lb,ub,@constraint,IntCon,options);

These are the linear constraints where I constraint the integer variables to be between lb(J)=0 and ub(J)=1 (because they are binary):

for t=1:T
    for i=1:N
        I=index(i,t,1);
        lb(I)=0;
        ub(I)=G(i,1);
        J=index(i,t,2);
        lb(J)=0;
        ub(J)=1;
        A(t,index(i,t,1))=-1;
        A(t,index(i,t,2))=0;
    end
    b(t)=-D(t);
end

This is the fitness function:

function f = objective(x)
global G
global N
global T
f=0;
for i=1:N
    for t=1:T
        I=index(i,t,1);
        J=index(i,t,2);
        %if the plant is open then it has costs
        if x(J)==1
        f = f+G(i,3)*(x(I))^2+G(i,4)*x(I)+G(i,5);
        end
    end
end

When I run the program it immediately stops and says:

Subscripted assignment dimension mismatch.
...
Error in ga (line 351)
...
Caused by:
    Failure in initial user-supplied fitness function evaluation. GA cannot continue.

These are the ga lines 350:365:

if ~isempty(intcon)   
    [x,fval,exitFlag,output,population,scores] = gaminlp(FitnessFcn,nvars, ...
        Aineq,bineq,Aeq,beq,lb,ub,NonconFcn,intcon,options,output,Iterate);
else    
    switch (output.problemtype)
        case 'unconstrained'
            [x,fval,exitFlag,output,population,scores] = gaunc(FitnessFcn,nvars, ...
                options,output,Iterate);
        case {'boundconstraints', 'linearconstraints'}
            [x,fval,exitFlag,output,population,scores] = galincon(FitnessFcn,nvars, ...
                Aineq,bineq,Aeq,beq,lb,ub,options,output,Iterate);
        case 'nonlinearconstr'
            [x,fval,exitFlag,output,population,scores] = gacon(FitnessFcn,nvars, ...
                Aineq,bineq,Aeq,beq,lb,ub,NonconFcn,options,output,Iterate,type);
    end
end

The algorithm runs if all integer variables are set to 1:

          lb(J)=1;
          ub(J)=1;

However, in that case, the integer variables appear in the results as real: 1.000

Does the algorithm understand that these variables are integers?

[Walter Roberson]

What is "index" in this context?

[Stefanos Mavropoulos]

Thanks for the answer.

i:refers to the plant i

t:refers to time period t

j: j=1 refers to production variables, while j=2 refers to on/off state for the plant i the period t

Hence, I use index to number the variables in one-dimension since the variable matrix x needs to be one-dimensional.

So the on/off state of the plant 2 the period 3 would be f(2,3,2)=42

 function f = index(i,t,j)
  global N
  global T
  f=i+(t-1)*N+(j-1)*N*T;

Update: I transferred all the linear constraints to the non-linear constraint and now the script runs but matlab refuses to recognize the integer variables as integer! I made another question about that:

https://uk.mathworks.com/matlabcentral/answers/229645-binary-integer-variables-in-genetic-algorithm

[Walter Roberson]

You could recode your index function in terms of sub2ind()

[Stefanos Mavropoulos]

Is the only way to define binary variables in matlab, if you define them as integer and then constraint them [0,1]?

It always gives me as a solution values close to 0 for all binary variables. (0.0142, -0.02312, ...).

[Matt J]

You haven't shown us your nonlinear constraints.

[Stefanos Mavropoulos]

function [c,ceq] = constraint(x)
%%Global variables
global N
global T
global G
global D
%%Nonlinear Constraints (Max,min production, ramp rates)
m=1;%nonlinear constraint m
for t=1:T
    C=0;
    for i=1:N
        I=index(i,t,1);
        J=index(i,t,2);
        J1=index(i,t+1,2);
        %Max,min power generation
        %x(i,t)<=MAX*u(i,t)
        c(m)=x(I)-x(J)*G(i,1);
        %MIN*u(i,t)<=x(i,t)
        c(m+1)=-x(I)+x(J)*G(i,2);
        %The integer values are binary to represent on/off for plants
        c(m+2)=x(J)-1;
        c(m+3)=-x(J);
        m=m+4;
        %Ramp rates
        if t<T & x(J)==1 & x(J1)==1
            I1=index(i,t+1,1);
            %x(i,t)*RD?x(i,t+1)
            c(m)=x(I)*G(i,10)-x(I1);
            %x(i,t+1)?x(i,t)*RU
            c(m+1)=x(I1)-x(I)*G(i,9);
            m=m+2;
        end
        %If a power plant is closed, it shall remain closed for some hours
        if t<T & x(J)==1 & x(J1)==0
            tt=t+2;
            while tt<T & tt<t+G(i,8)+1
                c(m)=x(index(i,tt,2));
                m=m+1;
                tt=tt+1;
            end
        end
        %Total supply in period t calculation
        C=C+x(I);
    end
    %Total supply in period t has to match demand
    c(m)=D(t)-C;
    m=m+1;
end
%%Ceq nonlinear equalities
ceq=[];

Is it possible that the ga can't solve it because of the number of integer variables. Each one of them can have 2 states (on/off:1/0). Hence, there are 2^32 combinations=4bn. That's why I have included a loop "If a power plant is closed, it shall remain closed for some hours" to keep a power plant closed for a few hours (G(i,8)) and drastically reduce the number of combinations.

[Ghada Saleh]

What are 'G' and 'D' in your code?