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Re: Which optimization method to use?
Posted:
Nov 28, 2013 12:00 PM


Alan_Weiss <aweiss@mathworks.com> wrote in message <kj1pj5$178$1@newscl01ah.mathworks.com>... > On 3/28/2013 11:23 AM, Aino wrote: > > Alan_Weiss <aweiss@mathworks.com> wrote in message > > <kj1dck$hh5$1@newscl01ah.mathworks.com>... > >> On 3/27/2013 1:09 PM, Aino wrote: > >> > Hello all. > >> > > >> > I have a function that includes a simulation. The input of the > > >> simulation is seven parameters. I need to vary five of the seven > > >> parameters to find the combination that would minimize the final > > >> output (error that is calculated between a measured signal and the > > >> simulated signal). I have somewhat a good initial guess for the five > >> > parameters and I know that they should all be positive. I need to > >> do > this optimization several times, so computational cost is an > >> issue too. > >> > > >> > I tried the optimization with "fminsearch". It worked quite ok, but > >> > two problems still occurred. First, one of the five parameters had > >> > negative values. This particular parameter is possible to just > >> leave > out. Second, it would seem that there are several local > >> minimum that > are all feasible when considering the parameter values > >> :( and > "fminsearch" didn't always find the global minimum. Also, I > >> think that > the output error includes "noise", or maybe one/several > >> parameters are > not always relevant. > >> > I am now trying out "fminsearchbnd" (File Exchange) without the > >> fifth > parameter and with lower bounds [0,0,0,0]. However, I was > >> wondering if > "fmincon" would be more appropriate for me? I am not > >> sure how to > implement it, though. Is there possibly even better > >> (more robust, not > too timeconsuming) optimization method for me? > >> > > >> > Thanks, > >> > Aino > >> > >> You might be interested in the documentation on optimizing simulations: > >> http://www.mathworks.com/help/optim/ug/optimizingasimulationorordinarydifferentialequation.html > >> > >> > >> fmincon is indeed an appropriate solver for your problem. It is part > >> of Optimization Toolbox. You should use the interiorpoint or sqp > >> algorithms; see > >> http://www.mathworks.com/help/optim/ug/writingconstraints.html#br9p_ry > >> > >> Alan Weiss > >> MATLAB mathematical toolbox documentation > > > > Thank you for your answer! > > > > I am now testing the "fmincon" with "sqp". I still have some questions > > about the optimization.. First, I don't know exactly the whole > > parameter space (therefore I use only the "0" lower bounds and "Inf" > > higher bounds) and with bad parameters the simulation stops and gives > > something rather arbitrary for the error. I tried to put "NaN" as the > > error when the simulation stops, but "sqp" algorithm doesn't seem to > > know how to deal with the "NaN". Did I misunderstand the last part of > > your first link, about returning "NaN"? I get the following error > > statement: > > > > "Objective function is undefined at initial point. Fmincon cannot > > continue." > > > > Also, I would be happy with an error smaller than 0.05, is that what > > "TolFun" is for? I didn't see any difference between TolFun=0.1 and > > TolFun=0.05. Also, to speed the optimization, I would like to have a > > minimum step size for the input parameters. "DiffMinChange"? Setting > > DiffMinChange=0.01 lead to slower computing but also smaller error. > > Also, the parameters have a very different magnitude, is it possible > > to tweak the step size separately for each parameter? I have to say > > I'm a bit lost with this optimization. > > > > Aino > > If the simulation fails at the initial point x0, then fmincon fails, and > there is nothing you can do about it except ensure that the initial > point leads to a sensible result. > > To find out what the various tolerances such as TolFun mean, see > http://www.mathworks.com/help/optim/ug/tolerancesandstoppingcriteria.html > > To see what the DiffMinChange option means, read carefully the section > http://www.mathworks.com/help/optim/ug/optimizingasimulationorordinarydifferentialequation.html > > You might also want to look at the options description: > http://www.mathworks.com/help/optim/ug/optimizationoptionsreference.html > > The "step size" might not mean what you think it means. You seem to > think it is the change in parameters that fmincon takes. But it is, in > fact, the size of a step for estimating gradients by finite differences. > > Good luck, > > Alan Weiss > MATLAB mathematical toolbox documentation
Hello again. :)
I'm still working with this optimization problem, though the simulation is updated a bit. I realized another possible problem. Changing the input parameters e.g. by 0.05 (5%), some parameters have larger effect to the outcome measure (the variable that is being minimized) than others. Could this have an effect to my results (optimized parameters)?
Aino



