Using GA can I put a condition on Population?

I am using GA, with nvars=32 and IntCon=1:32, so 32 integers

lb=[zeros(1,16),zeros(1,16)];

ub=[60*ones(1,16),4*ones(1,16)]

I want the first 16 elements be ascending and the last 16 elements no matter the order, and both of them respect the lb and ub.

Is there any way to obligate the population be between 0-60 with ascending order for the first 16 elements? (this 16 elements represent time so I can't have one value greater than the next value).

Answer 1

[Alan Weiss]

Sure, that is a simple linear inequality constraint. Probably easiest to represent using the problem-based formulation, but do what you like. In solver-based:

A = zeros(15,32);
for i = 1:15
    A(i,i) = 1;
    A(i,i+1) = -1; % means x(i) - x(i+1) <= 0
end
end
b = zeros(15,1);

You can use sparse matrices and MATLAB constructs to make this matrix, but this is fast enough.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Rim Abdallah]

First thank you Alan for your answer! Unfortunatetly, I used ur code but it doesn' work.

This is my main:

z=16;

first=sort(randi([0,60],1,z));

second=randi([0 4],1,z);

lb =[zeros(1,z),zeros(1,z)];

ub =[60*ones(1,z),4*ones(1,z)];

options = optimoptions('ga','Display','iter','PopulationSize',30,'FunctionTolerance',1e-5,'InitialPopulationMatrix',[first,second]);

nvars=2*z;

IntCon=1:(2*z);

funn = @(x)funct2(x,false); % handle to can cost

conss = @(x)nonlconfunct2(x,false); % handle to can constraints

A = zeros(z,2*z);

for i = 1:z-1

A(i,i) = 1;

A(i,i+1) = -1; % means x(i) - x(i+1) <= 0

end

B = zeros(z,1);

[x,fval,exitFlag,output,population,scores] = ga(funn,nvars,A,B,[],[],lb,ub,conss,IntCon,options);

Kindly check the attachement (result of the population), the population is not in an ascending order from column 1 to z=16.

(Row 12 for example:)

36 9 3 2 8 26 25 5 23 39 42 60 60 58 60 60 0 4 4 4 4 0 4 4 4 4 0 0 2 0 0 0

The first 16 elements: 36 9 3 2 8 26 25 5 23 39 42 60 60 58 60 60 are not in an ascending order.

[Alan Weiss]

Please check your answer against the linear constraint. What do you get when you run

A*x'

When I tried this against your reported x I get a vector whose first value is 27 (=36 - 9). A*x' should consist entirely of nonpositive numbers. So clearly the linear constraints are not being satisfied.

Did you get a positive exit flag from the optimization? I guess not. The solution is infeasible.

Alan Weiss

MATLAB mathematical toolbox documentation

[Rim Abdallah]

Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance

and constraint violation is less than options.ConstraintTolerance.

Exitflag=1

In fact my solution is correct because inside the functions I used command x1=sort(x(:,1:z),2), but I prefer to have a population with an ascending order for the first 16 elements instead of using sort and than I can reduce the time of running.