GA fitness function with variables in a summation

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Nima 2022-11-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1846143-ga-fitness-function-with-variables-in-a-summation

评论： Star Strider 2022-11-10

采纳的回答： Star Strider

What is the best way to define the following fitness function for GA optimization?

where

are the variables to be found with GA-toolbox. N can be a positive integer.

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Star Strider 2022-11-8

What is y?

How large is N and how is it defined?

Nima 2022-11-8

I just made a change in the formula! So

ist frequency dependent impedance and

as an example.

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Answer 1

Star Strider 2022-11-8

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https://ww2.mathworks.cn/matlabcentral/answers/1846143-ga-fitness-function-with-variables-in-a-summation#answer_1094133

编辑：Star Strider 2022-11-8

在 MATLAB Online 中打开

I still do not completely understand what you want to do.

Perhaps this —

Z = randn(16,1) + 1j*randn(16,1); % Creeate Data

omega = (0:15).'; % Creeate Data

objfcn = @(b,x) b(1) + 1i.*x.*b(2) + 1./(b(3) + 1j.*x.*b(4)); % Objective Function

Parms = 4; % Number Of Parameters To Be Estimated

ftnsfcn = @(b) norm(Z - objfcn(b,omega)); % Fitness Function

[B,fval,exitflag,output,population,scores] = ga(ftnsfcn, Parms, [],[],[],[], zeros(1,Parms)); % Genetic Algorithm Call

Optimization terminated: average change in the fitness value less than options.FunctionTolerance.

fprintf('\nR\t= %15.3f\nL\t= %15.3f\nG\t= %15.3f\nC\t= %15.3f\n',B)

R = 0.000 L = 0.007 G = 1.275 C = 0.760

fprintf('\nFinal Fitness Value = %15.6f\n',fval)

Final Fitness Value = 6.843630

fprintf('\nGenerations = %6d\n', output.generations)

Generations = 157

fprintf('\nMessage: %s\n',output.message)

Message: Optimization terminated: average change in the fitness value less than options.FunctionTolerance.

figure

plot(omega, real(Z), 'pm', 'DisplayName','Re(Z)')

hold on

plot(omega, imag(Z), 'pc', 'DisplayName','Im(Z)')

plot(omega, real(objfcn(B,omega)), '-m', 'DisplayName','Re(Z_{est})')

plot(omega, imag(objfcn(B,omega)), '-c', 'DisplayName','Im(Z_{est})')

hold off

grid

legend('Location','best')

I do not understand the reason for the summation in the objective funciton, so I do not use it here.

It may be necessary to run ga a few times to get the best fit (save the results each time), however it should be possible to get a decent fit to your data.

EDIT — Corrected typographical errors.

.

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Star Strider 2022-11-8

在 MATLAB Online 中打开

This runs without error, however it has become something of a moving target, so I leave it to you to correct any differences between the objective function I wrote and the one you want. See the documentation on the norm function for details.

The ‘objfcn’ function reshapes the matrix so that the columns are the values of R, L, G and C in order, and the rows are each circuit. It then iterates through all 16 rows and sums the results at the end, then transposes that to fit the data.

It may be necessary for you to use an 'InitialPopulationMatrix' to create the correct ranges for the variables. For example is R is in

, L in

, and C in

(I have no idea what G woiuld be), it could be something like this:

format shortE
IPM = randi(1E+4, 5, 4) .* [1 1E-9 1E-3 1E-15]
IPM = 5×4
1.0e+00 *

   5.1210e+03   6.5960e-06   9.4080e+00   8.4710e-12
   5.9620e+03   6.8550e-06   4.2310e+00   5.7960e-12
   9.3860e+03   4.1560e-06   9.0080e+00   5.3650e-12
   4.1920e+03   9.8970e-06   3.9130e+00   4.1800e-12
   2.0940e+03   7.5560e-06   5.1570e+00   4.6060e-12
format shortG

This scales the matrix appropriately, making convergence more likely.

I limited the number of generations to 5 so it would run here. Change that (and any other options you want to use) to do what you want.

Try this —

Ndata = 11;

Z = randn(Ndata,1) + 1j*randn(Ndata,1); % Creeate Data

omega = (0:Ndata-1).'; % Creeate Data

% objfcn = @(b,x) b(1) + 1i.*x.*b(2) + 1./(b(3) + 1j.*x.*b(4)); % Objective Function

opts = optimoptions('ga', 'MaxGenerations',5); % Change This

Parms = 64; % Number Of Parameters To Be Estimated

ftnsfcn = @(b) norm(Z - objfcn(b,omega)/Ndata); % Fitness Function

[B,fval,exitflag,output,population,scores] = ga(ftnsfcn, Parms, [],[],[],[], zeros(1,Parms),[],[],[],opts); % Genetic Algorithm Call

Optimization terminated: maximum number of generations exceeded.

fprintf('\nR\t= %15.3f\nL\t= %15.3f\nG\t= %15.3f\nC\t= %15.3f\n',B)

R = 18.198 L = 4.352 G = 16.301 C = 19.328 R = 7.640 L = 0.963 G = 13.551 C = 12.728 R = 3.636 L = 9.410 G = 3.550 C = 14.360 R = 4.090 L = 0.113 G = 1.689 C = 0.301 R = 19.972 L = 6.039 G = 11.053 C = 6.713 R = 16.999 L = 0.693 G = 11.361 C = 1.642 R = 3.259 L = 2.534 G = 3.123 C = 8.141 R = 17.178 L = 0.965 G = 19.393 C = 10.615 R = 4.370 L = 5.042 G = 8.982 C = 17.368 R = 18.659 L = 1.798 G = 1.602 C = 0.663 R = 16.729 L = 2.769 G = 11.482 C = 16.732 R = 4.066 L = 0.756 G = 19.334 C = 6.838 R = 0.998 L = 2.161 G = 1.286 C = 17.267 R = 11.470 L = 6.461 G = 4.122 C = 15.188 R = 15.062 L = 0.271 G = 15.560 C = 2.741 R = 5.511 L = 4.545 G = 12.820 C = 17.735

fprintf('\nFinal Fitness Value = %15.6f\n',fval)

Final Fitness Value = 101.409210

fprintf('\nGenerations = %6d\n', output.generations)

Generations = 5

fprintf('\nMessage: %s\n',output.message)

Message: Optimization terminated: maximum number of generations exceeded.

figure

plot(omega, real(Z), 'pm', 'DisplayName','Re(Z)')

hold on

plot(omega, imag(Z), 'pc', 'DisplayName','Im(Z)')

plot(omega, real(objfcn(B,omega)), '-m', 'DisplayName','Re(Z_{est})')

plot(omega, imag(objfcn(B,omega)), '-c', 'DisplayName','Im(Z_{est})')

hold off

grid

legend('Location','best')

function zv = objfcn(b,x)

mb = reshape(b, 4, []).';

for k = 1:16

z(k,:) = mb(k,1) + 1i.*x.*mb(k,2) + 1./(mb(k,3) + 1j.*x.*mb(k,4));

end

zv = sum(z).';

% Qzzv = size(zv)

end

.

Nima 2022-11-10

Thank you so much!

Star Strider 2022-11-10

As always, my pleasure!

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