Choice of algorithm for mixed-integer-continuous variables optimization problem

I need to find optimum set of variables (K, M) which minimize cost function

c(x, y) = [z(x, y) - z*(x, y)].^2

Here, z(x, y) = N x N target matrix and z*(x, y) = f(x, y; K, M) : function of K and M

Also the constraints are given as follows

• K: integer = [2, 3 .... 200]
• M: H by V matrix, 0 <=M(h, v) <= 250, all elements of M(h, v) are continuous variables (double)

In this problem, what kind of algorithm would be the best choice for this problem??

Answer 1

[Torsten]

I'd call fmincon 199 times for k=2,3,4,...,200 and choose the result for K which gives a minimum for the cost function.

[Matt J]

Or perhaps lsqcurvefit instead of fmincon.

[Yunhyeok Ko]

Your suggestion seems to be simple but iterative approach to find optimal choice of both K and M.

I wanted to find them simultaneously.

Thanks Torsten :)

[Walter Roberson]

Then you will need to use ga with a cost function that is the sum of the c values (so, sum of squares), and using as input a vector that your cost function then splits up between K and M. Number of inputs is numel(K)+numel(M) and the ones that represent K should be marked as integer. Use upper and lower bound to constrain K and M.

You might prefer to write this using Problem Based Optimization

[Torsten]

@Yunhyeok Ko

Why do you call the approach "iterative" ?

You independently run the solver 199 times and choose the run with the minimum value for the objective function as optimum.