y = besselj(3, x) + randn(size(x))/20;
model1 = @(AB, x) AB(1).*x.^AB(2);
model2 = @(AB, x) x.^3 + AB(1).*x.^2 + AB(2).*log(x);
residue1 = @(AB) sum((model1(AB, x) - y).^2);
residue2 = @(AB) sum((model2(AB, x) - y).^2);
models = {residue1, residue2};
modnames = {'a*x^b', 'x^3 + a*x^2 + b*log(x)'};
Nmodels = length(models);
x0 = randn(1,nvars) * 10;
fminunc_options = optimoptions(@fminunc, 'MaxIterations', 1e5);
ga_options = optimoptions(@ga, 'MaxGenerations', 1e5);
A = []; b = []; Aeq = []; beq = []; lb = []; ub = []; nlcon = [];
alg1 = @(FUN) fminunc( FUN, x0, fminunc_options );
alg2 = @(FUN) ga(FUN, nvars, A, b, Aeq, beq, lb, ub, nlcon, ga_options);
algnames = {'fminunc', 'ga'};
itercount_fminunc = @(info) info.funcCount;
itercount_ga = @(info) info.funccount;
itercount_funs = {itercount_fminunc, itercount_ga};
timings = zeros(Niters, Nalgs, Nmodels);
fvals = zeros(Niters, Nalgs, Nmodels);
infos = cell(Niters, Nalgs, Nmodels);
bestAB = cell(Niters, Nalgs, Nmodels);
itercounts = zeros(Niters, Nalgs, Nmodels);
thismodel = models{modidx};
itercount_fun = itercount_funs{modidx};
[bestAB{iter, algidx, modidx}, fvals(iter, algidx, modidx), ~, infos{iter, algidx, modidx}] = thisalg(thismodel);
timings(iter, algidx, modidx) = toc;
itercounts(iter, algidx, modidx) = itercount_fun(infos{iter, algidx, modidx});
end
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Local minimum found.
Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
meantimes = permute(mean(timings), [2 3 1]);
meaniters = permute(mean(itercounts), [2 3 1]);
t = table(meaniters(:), meantimes(:), repmat(modnames(:), Nalgs, 1), repelem(algnames(:), Nmodels, 1));
t.Properties.VariableNames = {'iterations', 'time [s]', 'model', 'algorithm'};
disp(t)
iterations time [s] model algorithm
__________ _________ __________________________ ___________
42 0.093775 {'a*x^b' } {'fminunc'}
42 0.0073104 {'x^3 + a*x^2 + b*log(x)'} {'fminunc'}
39900 0.84803 {'a*x^b' } {'ga' }
40915 0.56368 {'x^3 + a*x^2 + b*log(x)'} {'ga' }
