Defining objective function using nested functions (Genetic Algorithm Solver)

Hello everyone,

I am trying to do a maximization problem using optimization toolbox genetic algorithm solver. My objective function has parameters so I need to write a nested function(Since i have extra parameters besides from my variables) But i am having a trouble writing it. Here is what my objective function looks like and i wrote so far;

function z = objectivefunc(x,r,aii)

z= sum(x.*r.*aii, 'all');

end

(I reshaped my matrixes to be a row vector.)

X is my decsision variable and its dimensions are 1*1296 and r and aii are my parameters with dimensions 1*1296. I have looked through the documentation matlab provides and found this one;

https://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

I am very new to MATLAB so i really do not know how to write it correctly. So, any ideas or suggestions on how to implement nested functions to my problem?

[Torsten]

a must have dimension of I, r and x must have dimension of IxJ. So if I has 12 elements and J has 6 elements, a must have dimension 1x12, r and x must have dimension 1x72.

So 1x1296 for all three cannot be correct.

[Azime Beyza Ari]

originally, matrixes had 36x36 dimensions but for some reason i reshaped them(x and r) to be 1x1296 and originally a is 1x36 matrix. When i used 1x1296 for x and r and 1x36 for a i get an error saying index in this position exceeds array bounds etc. So i figured that the reason is a does not have same dimensions with the other two so it may be the reason. So i repeated a (lets say a is [1 2 3 4....] i repeated this matrix for 36 times ) to be 1x1296. Now it says not enough input.

So, what you are telling me might cause a error again since i am using optimization toolbox and i understand that this toolbox is not very flexible with the dimensions.

As a solution, i was recommended to use nested functions etc. But failed to write the nested function.

[Torsten]

This problem has nothing to do with nested functions. You pass r and a to objectivefunc - so the two matrices can be accessed there. Maybe in a former version of your code, you did not include r and a in the list of parameters passed to objectivefunc and so someone suggested that you should use nested functions (because r and a are then also visible in objectivefunc although you don't pass them).

If you define the array of initial values for the unknowns x0 for "ga" as a 36x36 matrix, you will find them in objectivefunc also as a 36x36 matrix and you can use Matt's answer to calculate z if r is 36x36 and a is 36x1.

Answer 1

[Matt J]

I suspect that the r and x are both in fact 36x36 matrices while a is a 36x1 vector. If so, then, the correct implementation is,

function z = objectivefunc(x,r,a)
   
       z= sum(x.*r.*a, 'all');
       
end 

[Azime Beyza Ari]

First of all, thank you for your answer. I actually reshaped all 3 of them to be 1x1296 matrixes. In the workspace they are 1x1296 matrixes and when i hoover my mouse onto them i can still see that they are 1x1296 matrixes.

But still since r and a are parameters i need to pass them to the function using some functions but could not figured out the right form to write a nested function.

[Torsten]

The length of all three arrays cannot be the same unless the set J contains only one element.

I = I*J -> J = 1.

If they have equal length, you did something wrong when initializing them.

[Matt J]

First of all, thank you for your answer. I actually reshaped all 3 of them to be 1x1296 matrixes.

Is that relevant? Restore them to their original 36x36 shape (36x1 in the case of a) and my proposal will work.

[Azime Beyza Ari]

I restored them. x now 36x36 , r 36x36 and a 36x1.

Error is now saying 'Arrays have incompatible sizes for this operation'

[Matt J]

Nope, the following simple example, which you can run yourself, proves that this will not happen if the variables have the sizes that you say.

r=rand(36); x=rand(36); a=rand(36,1);

z=sum(x.*r.*a,'all');

whos r x a z

  Name       Size            Bytes  Class     Attributes

  a         36x1               288  double              
  r         36x36            10368  double              
  x         36x36            10368  double              
  z          1x1                 8  double              

[Azime Beyza Ari]

Here i will attach the file, if can have a look i will be very happy. Because I do not see any difference between what you wrote and i write for objective function. But i am sure there is something i did wrong.

[Matt J]

Ah, yes. It's because it's ga().

 function z = objectivefunc(xij,rij,ai)
   
                 xij=reshape(xij,size(rij));
                      
                 z= sum(xij.*rij.*ai, 'all');
           
 end 

[Azime Beyza Ari]

Yes thank you, it worked. But still gives not enough input argument. For this line;

xij=reshape(xij,size(rij));

[Matt J]

Not for me. I ran your script with my proposed change and it worked fine.

[Azime Beyza Ari]

Okey thank you!!