Your fitness function must return a scalar value.

i am currently working on Genetic Algorithm. and i am getting this error everytime i try to execute. 'Your fitness function must return a scalar value.' i am new to optimization and matlab. could someone please fix this and help me out. thank you. ps: i have attached code.

[Birdman]

solarandwind.xlsx?

[mohammad hodaei]

Dear Friends,

I am also currently facing with the same problem. Your objective function must return a scalar value.

My fucntion is a long function as I call it with another fuicntion. I put the name of second function, reader, on the ga or fmincon or others, but I still get the same response.

A COPY OF MY FUNCTIONS ARE ATTAHCED

Thanks and a dvice

M.H.

[Walter Roberson]

load('Z.mat')

We do not have Z.mat to test with.

Omega=10:10000:4e6;
% % % % x=0.1;
for i=1:1:400
    finalresp(i)=abs((TransOpt(x,Omega(i))-Z(i))^2);
end

You should be pre-allocating finalresp.

It would be better not to assume that Omega is exactly length 400, and to loop to length(Omega) instead of to 400.

y=(finalresp);

Well, that is obviously going to be a vector result, of length 400. ga() cannot process a vector result. gamultiobj() can process a vector result -- but do you really want to optimize for the pareto fronts of finalresp, or do you instead want to optimize some property of finalresp() as a whole, such as sum(finalresp) ?

If you are going for minimum residue, then I recommend that you switch to

finalresp = zeros(size(Omega));
for i = 1 : length(Omega) 
  finalresp(i)=(TransOpt(x,Omega(i))-Z(i))^2;
end
y = sum(finalresp);   %no need to take sqrt() for optimization purposes

because abs() is not differentiable .

Exception: if Z can be complex valued, then

finalresp = zeros(size(Omega));
for i = 1 : length(Omega) 
  temp = (TransOpt(x,Omega(i))-Z(i))^2;
  finalresp(i) = temp .* conj(temp);
end
y = sum(finalresp);   %no need to take sqrt() for optimization purposes

[Walter Roberson]

Note that

Z=inv(T)*Y;

would be better written as

Z = T\Y;

inv() is not as numerically stable as using the \ operator.

Answer 1

[Stephen23]

The error message refers to the fast that ga requires the objective function to return a scalar, as the help clearly states "The fitness function should accept a row vector of length nvars and return a scalar value.". Instead of returning a scalar value your objective function returns a vector f which has length(pvy) elements:

for i=1:length(pvy)
    f(i)=pvy(i)+pwy(i)-pdy(i)
end

Your code has other bugs, such as that the filenames differ from the function names. The objective function calls xlsread multiple times: this is going to be very inefficient because the objective function gets called many times and reading from file is slow. You would be much better off parameterizing your function using either an anonymous function or nested functions:

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Plotting inside the objective function will also waste a lot of time: it would be better to wait until after the GA algorithm has returned a result, or if you want to follow the results as the ga algorithm progresses then use one of the inbuilt ga plotting functions:

https://www.mathworks.com/help/gads/genetic-algorithm-options.html#f14474

You have a lot of code and its purpose is not clear so I would not hazard any guesses how to fix it. I recommend that you should start small before jumping into such a complex task as this one (with file reading, etc.): copy one of the examples from the help and make sure that it works for you. Understand how it works, before starting to make small changes to incrementally turn it into the solver that you require. Your current approach of writing lots of code without testing it nor knowing what it is doing is a total waste of your time.

[anu vru]

How can I make the ga function return a vector? Because I need the vector output...I need all the values

[Walter Roberson]

ga() does return a vector -- it returns the entire x vector at which the objective function was best.

However, you objective function cannot return a vector for ga(). Returning a vector from your objective function would correspond to trying to minimize multiple functions at the same time, which would be termed a "multi-objective" problem. You would use gamultiobj() for multi-objective problems; it will return one of the pareto fronts.

[anu vru]

I am giving 3 variables...each of size 11×1....I need to optimise each of the values to its minimum...and it has bound constraints.and I need 11×1 output... Which optimization can I use for this.....

[Walter Roberson]

Are you trying to optimize 11 different functions simultaneously? If so then is it just a coincidence that you have three 11x1 variables and 11 functions to be optimized? Or do you have 11 functions to be optimized each of which has three scalar inputs? Or something else?

When you say that you need an 11 x 1 output, that sounds to me as if you have a problem with 11 different parameters and that you are trying to find the combination of parameters that optimizes one particular function -- a function that might happen to have three vectors of 11 x 1 data as (effective) constants.

If you have an objective function that has 11 parameters but which calculates one scalar, and the value of the scalar is to be minimized (or maximized) then ga() or other optimizers might be good. The one scalar calculated could, for this purpose, be a residue from fitting, just like you can optimize

@(P) sum((f(x,P)-y).^2)

for parameter vector P and inputs vector x and vector y in order to try to find the parameter vector that best fits the model f(x,P) . ga() is an acceptable routine for this kind of fitting (though it probably will not find the closest representation of the global minima.)

The problem comes when you have a function producing multiple outputs that are not comparable somehow. If you are given two functions f(x) and g(x) and asked to minimize them simultaneously, but you are not doing fitting, then you do not have any least-squares expression that can be minimized. Minimizing one might be contradictory to minimizing the other -- for example for a scalar, the functions could be f(x) = x and g(x) = -x, and although you can find that those two happen to intersect at x = 0, you might not be given any weights as to how important it is to minimize f(x) compared to minimizing g(x). The functions often do not even intersect, so you cannot generally use intersection as your goal.

For that kind of situation, where you are given vague instructions about minimizing multiple functions that might be antagonistic, then ga() and fmincon() and the others are not suitable: you need gamultiobj() or fgoalobtain() for those kinds of problems... together with a bunch of thought about how relatively important it is to minimize the various results.

[anu vru]

I have F=a+b-c Each a b and c have size of 11×1. I need 11x1 f...which is f(1) to f(11) each of them optimized... How do I give this as a input to my gamultiobj()?

[Walter Roberson]

Are you trying to find the a, b, and c values that optimize, and then for further calculations after the ga(), you need the vector F evaluated with those parameters?

If so then you would be doing an optimization on 11*3 = 33 parameters, and ga() would give back a 33 x 1 vector, that you would then use to evaluate F giving you an 11 x 1 F result based upon the 33 optimal parameters.

[anu vru]

I need minimised f values...hence values at which a b and c are optimal... But my ga() does give a vector output..so how do I proceed?

[Walter Roberson]

You are missing a basic structure:

function [a, b, c, Fvals] = drive_ga
  ...
  bestx = ga(@func, 33, ....);  %find best values
  a = bestx(1:11).';            %break the vector into variables
  b = bestx(12:22).';
  c = bestx(23:33).';
  Fvals = F(a, b, c);           %calculate F at that optimal position

function r = func(x)            %called by ga
  a = x(1:11);                  %break the vector into variables
  b = x(12:22);
  c = x(23:33);
  r = cost(a, b, c);            %call routine that determines cost for that configuration

function r = cost(a, b, c)
  ... something that might possibly call F(a,b,c)

In this construction, the cost() function does not need to be the same as F, but could be. For example, "cost" might be the norm of the outputs of F, if what you were looking for was the inputs that give the F value that is closest to the origin -- but the output you might be looking for might be the actual position vector implied by inputs a, b, and c.

[anu vru]

could you show the above code you have given with an example please.

[Walter Roberson]

function [a, b, c, Fvals] = drive_ga
  bestx = ga(@func, 33, ....);  %find best values
  a = bestx(1:11).';            %break the vector into variables
  b = bestx(12:22).';
  c = bestx(23:33).';
  Fvals = F(a, b, c);           %calculate F at that optimal position

function r = func(x)            %called by ga
  a = x(1:11);                  %break the vector into variables
  b = x(12:22);
  c = x(23:33);
  r = cost(a, b, c);            %call routine that determines cost for that configuration

function r = cost(a, b, c)
  r = norm( F(a, b, c) );

function r = F(a, b, c)
  r = a.^2 - b.^c;

[Jafar Nur Arafah]

Hi Walter Roberson,

I got the same problem as anu vru, where I want to do an optimization for objective function with scalar values. What are the suitable optimization method should I use?

In my objective function, the output (y) consists of 28x1 matrix (28 refer to 28 samples and each sample have 1 output). Each output made up of combination of inputs (x(1), x(2), x(3) and x(4)). Where, each sample have different combination of inputs.

I want to use all the data that I have in the optimation process (however, i dont want to combine the output by using sum(y)). I have tried multiobj, but that method give me list of optimized x's (for each sample available). However, I only want a set of optimized input (x(1), x(2), x(3) and x(4)) that able to give optimized output (y=1).

Kindly, please help me.

Thank you in advance.

Regards,

Nur Arafah

[Walter Roberson]

Do I understand correctly that although you have an objective function that returns a vector of length 28, that what you want to optimize is just the first of those outputs, and the values of the other 27 do not contribute to the optimization?

If so then make your objective for optimization

First = @(vec) vec(1);
obj_to_optimize = @(vec) First(YourExistingObjective(vec));

[Jafar Nur Arafah]

Hi Walter Roberson,

No, I want to optimize all those outputs together (with one time optimization). Because all of the contributes to the optimization process.

Thank you.

Regards,

Nur Arafah.

[Walter Roberson]

If I have two vectors of length 28, how should I calculate which one is "better" than the other? Is [1 2 3] better or worse than [3 2 1] ? How does [2 2 2] compare to them? How about [3 0 3] ? Is [2 2 4] better or worse than [2.5 3 3.5] ?

[Walter Roberson]

You appear to have asked this in https://www.mathworks.com/matlabcentral/answers/567282-how-to-do-optimization-for-result-calculated-by-using-experimental-data . It is recommended that you do not have two different questions going at the same time on the same topic, as it makes the discussion more difficult to track, and some people might not see all of the discussion.

[Jafar Nur Arafah]

Hi Walter Roberson,

I'm sorry what do you mean by two vectors of length 28?

FYI, I have attached the files for your reference.

Thank you.

Regards,

Nur Arafah

[Jafar Nur Arafah]

Hi,

Yes, I had ask this question in the link above. The discussion in the link really help me alot in improving my code. However, the discussion comes to an end as we did not came out with the good solution for optimization with non-scalar objective function. Then, I came across to this Q&A and found out the previous researcher have a quite similar problem with me. That is why I ask in this Q&A session, hoping that I can get a good solution to my problem.

Came back to your reply above, what do you mean by two vectors of length 28? Because if you run the Fifth_edit.m file you can found out that the output in a matrix 28x1. So, I think it is one vector of length 28?

Thank you.

Regards,

Nur Arafah