Genetic algorithm problem with integer variables

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Stefanos Mavropoulos
评论： Ghada Saleh 2015-7-16
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?
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Stefanos Mavropoulos
Stefanos Mavropoulos 2015-7-14
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.

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