Optimization of random matrix

Hello, I have a matrix 'MC' of 6 x 6 random complex numbers. My problem is how to define my fitness function to optimize the matrix elements using GA ? Can any one help

Here is the code I'm using,

function costFunction = FACGFSEM(MC)

FF(:,:,t)=F(:,:,t)*MC;

costFunction = sum(sum(FF))

[Image Analyst]

Either read this and fix the formatting, or attach via the paper clip icon so people can help you. Right now we can't read it.

Also, it looks like you've stripped all of the comments out of the code, or, just as bad, never put in any. Please put the comments back in to the code so people can follow and understand what you're doing.

[Walter Roberson]

Your F and FF are three dimensional. Your sum(sum()) will reduce by 2 dimensions, leaving you a vector. You cannot use a vector as the cost in GA unless you are using the multiobjective ga.

[abdelelah alzahed]

I tried to do another sum to get a single number and it's still not working. in the GA it always defines the MC as a single number instead of a matrix. My question is how to define the MC as a matrix of 6 x 6 numbers

[Walter Roberson]

Wait, these are complex numbers in MC, so the sum would generally be complex. None of the optimizers are going to work on complex objectives. Optimizers depend upon being able to order results, but you cannot order complex numbers.

[abdelelah alzahed]

So, I guess I have to make them real. In this case how to define the matrix?

[Walter Roberson]

Use 36 input variables. reshape() the x vector to be 6 x 6 to do the calculation.

[abdelelah alzahed]

I tried that but It didn't work.

I'm using the optimization tool in MATLAB and made the number of variables to be 36, still not working !!

[Walter Roberson]

What happens when it fails to work? Are you getting an error message? Please show your code and any associated error message.

[abdelelah alzahed]

Optimization running.

Error running optimization.

Not enough input arguments.

function costFunction = FACGFSEM(MC1,MC2,MC3,MC4,MC5,MC6,MC7,MC8,MC9,MC10,MC11,MC12,MC13,MC14,MC15,MC16,MC17,MC18,MC19,MC20,... MC21,MC22,MC23,MC24,MC25,MC26,MC27,MC28,MC29,MC30,MC31,MC32,MC33,MC34,MC35,MC36)

MC=[MC1,MC2,MC3,MC4,MC5,MC6;MC7,MC8,MC9,MC10,MC11,MC12;MC13,MC14,MC15,MC16,MC17,MC18;MC19,MC20,... MC21,MC22,MC23,MC24;MC25,MC26,MC27,MC28,MC29,MC30;MC31,MC32,MC33,MC34,MC35,MC36];

FF(:,:,t)=F(:,:,t)*MC;

costFunction=(1/N)*(sum(sum(sum(FF))));

[Walter Roberson]

function costFunction = FACGFSEM(x)
  MC = reshape(x, 6, 6).';  %transpose so that the values go across rows

    %presumably some other code here that defines FF and t and N
    FF(:,:,t)=F(:,:,t)*MC;

    costFunction = sum(FF(:))/N;

[abdelelah alzahed]

Will that make the MC matrix only with one variable repeated ? or should I change the number of variables in the optimization tool to 36 ?

Anyway, Thanks It's working but it's taking too long

[Walter Roberson]

That will make the MC matrix out of a vector of 36 values, which is what your tool should be set to expect.

When I try with a randomly populated F, I find that the mathematics favours driving the coefficients arbitrarily large, with wilder and wilder differences between the positive and negative contributions, with the objective function going more and more infinitely negative.

I could see the benefit of a closely related objective if the layers of F were all positive definite (or semi-definite) matrices, but I cannot see the benefit of optimizing this present calculation -- not unless there are bounds on the inputs.