How can I use the Genetic Algorithm (GA) to minimize a cost function of two variables C(T,K) where T is a real an K an integer.

Answer 1

[John D'Errico]

Trivial.

1. Write your function as an objective function. I won't do that for you, but just start at the beginning and write it.
2. Set up any constraints.
3. Call GA.

And while you may think of it as a 2 variable problem, you have only ONE variable, a vector of length 2. One of those variables is constrained to be integer.

For example:

a = 1.25;
b = 100;
obj = @(xy) (a - xy(1)).^2 + b*(-1/8 + xy(1)-(xy(2)/10).^2).^2;

This is just effectively the Rosenbrock function, with a tweak or two in there. I'll constrain y to be an integer.

intcon = 2 % So only y is constrained to be integer

intcon = 2

lb = [-20,-20];
ub = [20 20];
[xysol,fval,exitflag] = ga(obj,2,[],[],[],[],lb,ub,[],intcon)

Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance
and constraint violation is less than options.ConstraintTolerance.

xysol = 1×2

1.1262 10.0000

fval = 0.0155

exitflag = 1

fsurf(@(x,y) obj([x,y]),[0 2 8 13])

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.