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How can I set meshsize respectively for each parameter on patternsearch?

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Kei Manabe
Kei Manabe on 4 Jun 2020
Commented: Kei Manabe on 6 Jun 2020
I am trying to optimize 4 parameters of the Page test using patternsearch. However, the estimated orders of the 4 parameters are different. See the initial parameters "param0" in the code below. In particular, I would like to set the meshsize to 10 for the first parameter, 10 for the second parameter, 0.1 for the third parameter, and 0.001 for the fourth parameter. My question is that is it possible to set the different meshsize for each parameter? Thank you so much in advance.
rand1 = rand(1)*1000; rand2 = rand(1)*1000; rand3 = rand(1); rand4 = rand(1)/100;
param0 = [round(max(rand1,rand2)), round(min(rand1,rand2)), round(rand3, 2), round(rand4, 5)];
options = optimoptions('patternsearch', 'PlotFcn', 'psplotbestx', 'MeshTolerance', 1, 'ScaleMesh', false, 'InitialMeshSize',10);
A = [];
b = [];
Aeq = [];
beq = [];
nlcon = [];
lb = [1 1 0.1 1/500000];
ub = [100000 100000 10 1/25000];
fun = @do;
[param, RSS, exitflag, ~] = patternsearch(fun, param0, A, b, Aeq, beq, lb, ub, nlcon, options);

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Accepted Answer

Alan Weiss
Alan Weiss on 5 Jun 2020
Edited: Alan Weiss on 5 Jun 2020
Usually it is better to set the scale within your objective function so that the optimization parameters are all of the same order of magnitude. For example,
function f = myfun(x)
x(1) = x(1)/1000;
x(2) = x(2)/1000;
x(3) = x(3) + 1000;
x(4) = (x(4) - 1000)*1000;
% Now put your code here
end
Alan Weiss
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