GA fitness function with variables in a summation

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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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Nima
Nima on 8 Nov 2022
I just made a change in the formula! So ist frequency dependent impedance and as an example.

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Accepted Answer

Star Strider
Star Strider on 8 Nov 2022
Edited: Star Strider on 8 Nov 2022
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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