So a few months ago I asked some help here for fitting a really complicated function and some really helpful people in this community helped me solve the problem using genetic algorithm. Now I just want to try to fit these use other algorithms (like pattern search, particle swarm etc.) and see how they perform too.
So for starters, here is the function with 9 parameters where V represents the voltage and a’s represent the fit parameters.
Theta= @(a,V) a(5).*V+a(6).*atan(a(7)+a(8).*V+a(9).*V.^2)
F= @(a,V) a(1).*(a(2) - a(3) - (a(2).*a(4))./(a(2).^2.*cos(Theta(a,V)).^2 + a(4).^2.*sin(Theta(a,V)).^2).^(1/2));
The code that used genetic algorithm to fit the data well was (Fitness value of 0.3):
V=volt(inistart:length(volt));
Phase=Phase(inistart:length(Phase))
ftns= @(a) norm(Phase-F(a,V))
optsAns = optimoptions('ga', 'PopulationSize',PopSz, 'MaxGenerations',5E3, 'FunctionTolerance',1E-10);
fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
[a_fit{i},fval,exitflag,output,population,scores]=ga(ftns,Parms, [],[],[],[],[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],[],[],optsAns);
fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval,output.generations)
fprintf(1,'\tRate Constants %d:\n',i)
for k1 = 1:numel(a_fit{i})
fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
plot(V, F(a_fit{i},V), '-r')
What does not work?
But just to see how the other algorithms do, I tried the following (For example the patternsolve algorithm):
optsAns = optimoptions('patternsearch','FunctionTolerance',1e-10,'MaxIterations',5e3);
fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
[a_fit{i},fval,exitflag,output]=patternsearch(ftns,[8e+04; 1.7;10000;1.7;10000;10000;10000;10000;10000],[],[],[],[],[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],[],optsAns);
fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval)
fprintf(1,'\tRate Constants %d:\n',i)
for k1 = 1:numel(a_fit{i})
fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
plot(V, F(a_fit{i},V), '-r')
I always get a fitness value as 25.7862 all the 20 times I loop this code. And the fit looks like this:
Particle swarm also gives bad results: 29.7108 30.8890 49.0237 30.8896 49.0237 49.0237 49.0237 49.0237 30.8896 49.0237 49.0237 30.8895 30.8894 49.0237 49.0237 30.4015 25.3389 30.8666 49.0237 30.8896 as the fitness values.
optsAns = optimoptions('particleswarm','FunctionTolerance',1e-10,'MaxIterations',5e3,'HybridFcn','fmincon');
fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
[a_fit{i},fval,exitflag,output]=particleswarm(ftns,Parms,[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],optsAns);
fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval)
fprintf(1,'\tRate Constants %d:\n',i)
for k1 = 1:numel(a_fit{i})
fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
plot(V, F(a_fit{i},V), '-r')
Can you help me understand why I get this?
Thanks in Advance!
