Using results from genetic algorithm as initial values in least square non-linear fitting

I have tried to take the initial values from genetic algorithm and use them in the least square nonlinear fit but every time I try to run the script,an error message appears.I have attached the data file.There are 4 variables Nu=f(Re,Theta,Beta).

clc
clear all
% Create an anonymous function that describes the expected relationship
% between X and Y
f=@(c,x) c(1).*(x(:,1).^c(2)).*exp((x(:,3)*c(4))+(x(:,2)*c(3)));
% data set 
% Specify x variables from data file,Re,Theta and Beta columns.
x=xlsread('all data for fitting');
% Specify y variable from data file ,(Nu)column.
y=x(:,4);
% objective function 
ff=@(c)(f(c,x)-y)./y;
% maximum of objective function
ffmax=@(c)norm(ff(c));
% Identifying population size and number of parameters for genetic
% algorithm
PopSz = 500;
Parms = 4;
% Modifying the options of genetic algotithm optimization function
options = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-4, 'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf, 'PlotInterval',1);
% Genetic algorithm application
[theta,fval,exitflag,output] = ga(ffmax, Parms, [],[],[],[],-Inf(Parms,1),Inf(Parms,1),[],[],options);
% Specify a vector of starting conditions for the solvers(Least squre
% nnonlinear fit)
c0=[theta(1) ;theta(2);theta(3); theta(4)];
% Perform a nonlinear regression
c=lsqnonlin(ff,c0);
y1=f(c,x);
diff_Nu=y-y1;
Abs_diff_Nu=abs(diff_Nu);
perc_error=(Abs_diff_Nu./y);
x_line45=0:max(y);y_line45=0:max(y);
[max_error,I_max]=max(perc_error);
[min_error,I_min]=min(perc_error);
x_line_high=0:max(y); y_line_high=(max_error+1)*(0:max(y));
x_line_low=0:max(y); y_line_low=(1-max_error)*(0:max(y));
figure
plot(x_line45,y_line45,'k')
hold on
scatter(y,y1)
hold on
plot(x_line_high,y_line_high,'r')
hold on
plot(x_line_low,y_line_low,'r')
N=[y,y1];
header=['Nuact','Nufit'];
disp(header)
disp(N)

Here is the error:

Error using optimoptions (line 114)
Invalid solver specified. Provide a solver name or handle
(such as 'fmincon' or @fminunc).
Type DOC OPTIMOPTIONS for a list of solvers.
Error in bestfitever (line 20)
options = optimoptions('ga', 'PopulationSize',PopSz,
'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-4,
'MaxGenerations',2E3, 'PlotFcn',@gaplotbestf,
'PlotInterval',1);

Answer 1

[Dev]

Hi @MOHAMED ABDULAZIM,

The error mentioned in the question arises comes from the following line of code-

options = optimoptions('ga', 'PopulationSize', ...
    PopSz, 'InitialPopulationMatrix', ...
    randi(1E+4,PopSz,Parms)*1E-4, ...
    'MaxGenerations',2E3, ...
    'PlotFcn',@gaplotbestf, 'PlotInterval',1);

The main issue is that "ga" belongs to the "Global Optimization Toolbox", but "optimoptions" only supports solvers from the "Optimization Toolbox" (like "fmincon", "lsqnonlin", etc.). In case we aim to use "ga", we need to use "gaoptimset" function instead of "optimoptions". I have attached a reference code snippet for the same below-

options = gaoptimset('PopulationSize', PopSz, ...
    'InitialPopulation', randi(1E+4,PopSz,Parms)*1E-4, ...
    'Generations', 2E3, 'PlotFcns', ...
    @gaplotbestf, 'PlotInterval', 1);

We can then call the "ga" function and the script executes successfully, resulting in the following graph-

For more information regarding the usage of toolboxes and function mentioned above, please refer to the links below-

"Global Optimization Toolbox"- https://www.mathworks.com/products/global-optimization.html

"Optimization Toolbox"- https://www.mathworks.com/products/optimization.html

"optimoptions"- https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationproblem.optimoptions.html

"ga"- https://www.mathworks.com/help/gads/ga.html

"gaoptimset"- https://www.mathworks.com/help/gads/gaoptimset.html

I hope the above explanation helps to solve your question.