Giving target function outputs to optimization algorithm

I have a multivariable function that I am trying to optimize the output of. The function is time-consuming so I am using surrogate optimization (through the global optimization toolbox). However, during the run of the function at a specific point, I am also obtaining knowledge of the function values at various additional points. (This is because I am using a continuation method when running the function, but that doesn'tmatter too much). This means that after a few times the optimization algorithm calls the function, I already have dozens of known function output values. My question is- Is there a way to inform the algorithm about these values? Either through the optimization options or through the code of the optimization code itself?

So far what I did is tabluate the obtained values, so that If the optimization algorithm calls the function with a value very near one of them, I can return the obtained value instead of running the function. However this is kind of a workaround and not an actual solution.

Would be thankfull for any assistance

Answer 1

[Alan Weiss]

While I haven't tried this before, it sounds to me as if you could change your objective function to use a data set of known points and objective function values, and the set of known points and values can grow over time. I'm not sure how you would best make use of this extra information, but that is something else.

For example, suppose M is the auxiliary matrix of known points, where each known point is one row in M. Suppose N is the vector of associated objective function values, so N(i) is the objective function value of row i of M. Maybe the easiest way to do things is to have M and N be persistent variables. Write the objective function like this:

function fval = myfun(x)
persistent M N
% Perform your computation here. You might want to check whether M and N
% are empty or not before using them.
%
% When you find a new point, say p with objective function value f, include
% them in the matrices:
M = [M;p(:)']; % ensure that p is in row form when appending
N = [N;f];
end

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathan Bblanc]

Thank you for your answer Alan. I am already doing something similar to this (Like I wrote I am tabluating the obtianed values), but so far it only helps me if the algorithm happens to call another point very near the ones I already obtained. What I would like is to use this information in a more intelligent way.

Thanks again

Nathan

[Alan Weiss]

I think that this depends very much on your function and requirements. In two or three dimensiions, one thing to try would be to make a scattered interpolant of the data points and attempt to interpolate the values. For higher dimensions I don't know of a good way (griddedInterpolant might work for 4 or 5 or even 6 dimensions, but it might not, either). The RBF that surrogateopt makes is not usually suitable as an interpolant, but you could try one to see.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathan Bblanc]

Thanks again Alan. I appreciate your help. however I do think that what you are suggesting is sort-of a workaround for what I am actually trying to do. My point is that the optimization algorithm, especially in surrogate optimization, makes use of known values during the optimization process. So if there was a way to "inform it" about the new values that I obtained maybe I could improve the optimization process.

Nathan

[Alan Weiss]

Oh, sorry for misunderstanding your request. Now I understand that you want to change the surrogateopt algorithm to accept extra data points and values in the middle of a run. That is indeed what you said in your original post, but I didn't understand it until now.

I don't know of any way of doing what you ask. I suppose that you could record the points and associated values, have a relatively short MaxFunctionEvaluations limit, and repeatedly restart surrogateopt with those points and values given in the InitialPoints option. But I doubt that this would really improve your optimization. So the short answer is no, I don't know of a way that would help.

Alan Weiss

MATLAB mathematical toolbox documentation

[Nathan Bblanc]

OK, thanks Alan. Maybe someone else might have a different answer.

Nathan