Multistart parameter space and fval return

Hi everyone,

In the link below, please see section under Multistart -> Create GlobalOptimSolution Object.

http://www.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html?refresh=true

It says that after Multistart reaches a stopping condition, it "creates a vector of GlobalOptimSolution". I am using multistart using the below syntax to solve a lsqnonlin problem to fit 6 parameters.

[x fval] = run(ms,problem,k)

But after multistart finishes going through all of the 'k' points, it returns just one value , the minimum value of fval that that found from 'k' different initial points and does not return a vector called 'GlobalOptimSolution' where all the values of fval are stored.

My questions are:

a)How can I get multistart to return a vector of all fvals as described in the section in the link above.

b) Is there a way I can see the kind of initial values matlab uses for the 'k' points ? I know that there are ways to give random OR custom start points but is there a way to know the initial values being used if I just specify 'k', i.e. number of initial points within given bounds to be sampled. Does MATLAB use some special code to generate 'k' values so that I can know that it is sampling the entire parameter space.

Thank you

Answer 1

[Walter Roberson]

The solution vector you are looking for is the 5th output returned by run(), but you are only saving the first 2 outputs.

[Alan Weiss]

To expand on what Walter said, take a look at the last listed syntax for MultiStart run:

 [x,fval,exitflag,output,solutions] = run(...) returns a vector of solutions containing the distinct local minima found during the run.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Abdelmoumen Bacetti]

Actually I didn't know that Matlab allows automatically running optim problems with different start points. This is why I wrote my own multistart by generating random vectors and applying the upper and lower bounds.

I save everything (random start points, their respective solutions and performance indicators) in matrices.

lb = [ 50, 1e-4, 1e-4, 1e-4, 1e-4, 1e-4];
ub = [ 10000, 1, 1, 1, 1, 1];
nvars = 6;
nr = 100;
r = rand(nvars,nr);
x0 = zeros(nvars,nr);
xlsq = zeros(nvars,nr);
resnorm = zeros(nr);
for i=1:nr
    x0(:,i) = (ub - lb) .* r(:,i)' + lb;
    [xlsq(:,i),resnorm(i)] = lsqnonlin(@(x)ObjFcn(x, Additional_param), x0(:,i),lb,ub,lsqoptions);
end
best = find(resnorm==min(resnorm));
best_xlsq = xlsq(:,best);