Evaluating symbolic expression and handing them to optimisation problem: How should I introduce symbolic variables to ga function?

I have a problem understanding how symbolic functions should be handled when first manipulating them and then sending to optimisation. I have symbols in matrices which I manipulate and try to send the final result to ga optimisation function.

For example:

>> fun = @(q) q(1)^2 + q(2)^2 + q(3)^2 + q(4)^2;
>> [x,fval,exitflag,output,population,scores] = ga(fun,4,[],[],[],[],zeros(4,1),ones(4,1),[],[1:1:4]);

Works OK, but leads to errors:

>> B=q(1)^2 + q(2)^2 + q(3)^2 + q(4)^2;
>> fun = @(q) B;
>> [x,fval,exitflag,output,population,scores] = ga(fun,4,[],[],[],[],zeros(4,1),ones(4,1),[],[1:1:4]);

The errors are:

xxxxx

The following error occurred converting from sym to double:
DOUBLE cannot convert the input expression into a double array.

Error in fcnvectorizer (line 13)
            y(i,:) = feval(fun,(pop(i,:)));

Error in gaminlppenaltyfcn

Error in gapenalty

Error in makeState (line 64)
            Score = FitnessFcn(state.Population(initScoreProvided+1:end,:));

Error in galincon (line 17)
state = makeState(GenomeLength,FitnessFcn,Iterate,output.problemtype,options);

Error in gapenalty

Error in gaminlp

Error in ga (line 366)
    [x,fval,exitFlag,output,population,scores] = gaminlp(FitnessFcn,nvars, ...

Caused by:
    Failure in user-supplied fitness function evaluation. GA cannot continue.
    Failure in initial user-supplied fitness function evaluation. GA cannot continue.
xxxxx

What I understood B becomes evaluated and q1, q2, q3, q4 are no longer understood as q(:).

Question: I have a matrix manipulated and having symbolic values q1...q75. How should I introduce them to ga function?

Answer 1

[Alan Weiss]

You should convert your symbolic variables to a MATLAB function before trying to pass them to a solver such as ga. See Using Symbolic Mathematics with Optimization Toolbox and Symbolic Math Toolbox Calculates Gradients and Hessians for examples.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kari Tammi]

Thanks, I've read those few times. It seems I repeat the same error whether I use a function file or not. I believe the essence is that I don't really understand the difference between the examples I give above in my question. The first example works, but the second does not. I only can repeat the same error by putting the B in a function file.

[Alan Weiss]

The first example:

fun = @(q) q(1)^2 + q(2)^2 + q(3)^2 + q(4)^2;

This function accepts a row vector of double-precision variables, which is what ga passes by default, and returns a double-precision scalar, which is what a solver expects.

The second example:

B = q(1)^2 + q(2)^2 + q(3)^2 + q(4)^2;
fun = @(q) B;

If q is a symbolic expression, say

syms a b c d
q = [a b c d]

then what do you think that fun([1 2 3 4]) gives?

fun([1 2 3 4])

ans =

a^2 + b^2 + c^2 + d^2

You see, you made the function incorrectly. If, instead, you make

fun2 = matlabFunction(B,'vars',{q});
fun2([1 2 3 4])

ans =

      30

I hope that this helps you understand the difference.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kari Tammi]

Thanks again! This clarified the issue quite a bit.

[Walter Roberson]

fun = @(q) subs(B);