Hi everybody, i am looking for a solution for comparison of convergence time between two algorithms, two optimization problem actually. Is there any toolbox or sample code?

Calc convergence time of two algorithm and find out which one is better!

Answer 1

[Walter Roberson]

Niters = 5;

x = 1 : 50;
y = besselj(3, x) + randn(size(x))/20;

nvars = 2;
model1 = @(AB, x) AB(1).*x.^AB(2);        %a*x^b
model2 = @(AB, x) x.^3 + AB(1).*x.^2 + AB(2).*log(x);   %x^3 + a*x^2 + b*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);
algs = {alg1, alg2};
algnames = {'fminunc', 'ga'};
itercount_fminunc = @(info) info.funcCount;
itercount_ga = @(info) info.funccount;
itercount_funs = {itercount_fminunc, itercount_ga};

Nalgs = length(algs);

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);

for modidx = 1 : Nmodels
    thismodel = models{modidx};
    for algidx = 1 : Nalgs
        thisalg = algs{modidx};
        itercount_fun = itercount_funs{modidx};
        for iter = 1 : Niters
            tic;
            [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
    end
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'     }