GA function changing an input array

I am trying to optimize 12 coefficients that describe a surface equation. The coefficients are normally in a 3X4 matrix. I use C = reshape(C',1,[]) to reshape the coefficients into an array but when that 1x12 array passes into the GA function the values randomly change. I can tell the values change by having Matlab spit out the C matrix before and after the GA function is called.

(code calling the ga and the function holding the cost function)

    C = reshape(C',1,[])
    [C,J_Cmax] = ga(@(C) C_Opt_Normalized(C,ThetaH_norm,Dim,L,D,lam0,lb,ub),[],[],[],[],[],[],[],ga_options);

(function being optimized)

    function [J_Cmax] = C_Opt_Normalized(C,ThetaH_norm,Dim,L,D,lam0,lb,ub)
    C

Between the first C spit out and the second the values change. I need my cost function to use:

C = [.02 .01 0 0 5 2 1.5 0 6 4 4.5 3]

but the ga changes it to:

C = [-6.6700 -7.4019 -7.9294 1.3010 -9.8413 -7.0841 -3.7203 -2.3271 -1.9639 5.1746 6.8477 -5.1248]

Answer 1

[Walter Roberson]

The C that you create with C = reshape(C',1,[]) is not being passed into C_Opt_Normalized .

Your call

    [C,J_Cmax] = ga(@(C) C_Opt_Normalized(C,ThetaH_norm,Dim,L,D,lam0,lb,ub),[],[],[],[],[],[],[],ga_options);

creates an anonymous function with dummy parameter name C; until the end of the expression that defines the anonymous function, C refers to a vector of values that ga randomly creates and passes in to the anonymous function. The expression

@(C) C_Opt_Normalized(C,ThetaH_norm,Dim,L,D,lam0,lb,ub)

has exactly the same effect as

@(VectorToBeEvaluated) C_Opt_Normalized(VectorToBeEvaluated,ThetaH_norm,Dim,L,D,lam0,lb,ub)

Furthermore, you have

    [C,J_Cmax] = ga(@(C) C_Opt_Normalized(C,ThetaH_norm,Dim,L,D,lam0,lb,ub),[],[],[],[],[],[],[],ga_options);

which assigns the result of the ga() call to C, so after ga() finishes, you overwrite C with the best solution that ga() found. That is very unlikely to be the same as the C = reshape(C',1,[]) that you had before that line.

[Stuart Belcke]

I am trying to use the C as an initial guess for the ga to run C_Opt_Normalized with. So you are saying the ga populates my C matrix regardless of an initial guess?

The second value in my original post is the value of C without running the cost function. It is simply what is on the other side of what I passed into the ga().

[Walter Roberson]

The only way to give an initial guess to ga() is to pass in an options structure created by optimoptions() passing in InitialPopulationMatrix

Question for you: why are you passing in what looks like lower bound (lb) and upper bound (ub) to C_Opt_Normalized, but not passing those to ga itself? If you have a restricted range it would seem to make sense to tell ga what the ranges are ?

[Stuart Belcke]

I got the initial guess into the ga. However, the initial guess I am feeding into the GA is the correct answer (i.e. the optimum C to minimize the cost function) and the program continues to change the C matrix. So I must have something wrong in my code otherwise the program would stop immediately.

I am attempting to complete parameter uncertainty analysis and the ub and lb are for the bounds on the surface plane and not for the bounds of the C matrix (describing the surface) that the ga is searching for.

[Walter Roberson]

ga has no way of knowing that a particular proposed value is the location of the minima: it has to try a number of locations and see what happens.

As far as ga is concerned, if there is a different vector of values that returns a value that is 1e-17 smaller just because of mathematical round-off error, then ga thinks that is a "better" solution. ga is not concerned with any kind of mathematical proof of minima: ga cares only about what numeric value is actually returned from the cost function.