How do I use global solver to estimate parameters in SimBiology R2021A

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I am looking for some information on how to properly use the SimBiology global solver, as I have never used it before. I am trying it for the first time, and the progress plots show my fits all failed to converge with criterion due to max iterations. However, the actual fitting results are quite excellent.
Can anyone help interpret this and indicate how to refine the solver settings? I am using scattersearch function with lsqnonlin as the local solver. Currently estimating 2 parameters related to saturable kinetics (Km & Vmax).

Accepted Answer

Arthur Goldsipe
Arthur Goldsipe on 9 Dec 2021
I would not read too much into this message. It simply explains why the optimization stopped when it did. In and of itself that it not inherently good or bad. You need to use your knowledge of the specific problem to decide whether the reported optimum is good enough and whether you have explored parameter space sufficiently well. If you decide that you want to run another optimization that runs longer then the message suggests that you might want to increase the value of the MaxIterations option. Note however that scattersearch is a stochastic algorithm, so the results will vary from one run to the next unless you take care to reset the random number generator to the same state before each run.
Hope that helps.
-Arthur
  2 Comments
Arthur Goldsipe
Arthur Goldsipe on 9 Dec 2021
Hmm... What kind of information are you looking for? I wrote the implementation for scattersearch based on the information in this paper. But the paper is definitely not an easy read for a lay audience. If you want to learn more about global optimization in general, I suggest this documentation from Global Optimization Toolbox. Even though scattersearch is not part of that toolbox, many of the same principles apply.
The options for scattersearch are documented here. If you're estimating 2 parameters, the default of "auto" corresponds to 40 iterations, so you'd want to set it to something larger than that.
Regarding the random number generator, that's part of the global state of MATLAB. You can read more about it here. But a common approach is to execute rng('default') between runs to make the results reproducible.
Finally, if you're not already using it, I suggest enabling progress plots. That can give you some sense of the progress being made. It also allows you to stop the optimization early (by clicking on a stop button) in the progress plot window.

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