[scilab-Users] optimization : general question
Michaël Baudin
michael.baudin at scilab.org
Fri Dec 3 10:58:43 CET 2010
Hi,
Thanks for your report : you just found a bug. In the tests which were
done, the objective function was always defined, whatever x. I just
created a bug report for this:
http://bugzilla.scilab.org/show_bug.cgi?id=8546
As a workaround, we may use the following method.
* Use the -simplex0method = "randbounds" initial simplex so that the
initial simplex is inside the bounds, by design.
* Penalize the objective function, so that the objective function is
always defined, but equal to infinity if the point is outside the bounds.
Notice how the additionnal input argument data is used to pass the
bounds to the function.
function [ f , index , data ] = myquad ( x , index , data )
mprintf("index=%d, x=[%.2f %.2f]\n",index,x(1),x(2))
xmin = data(1)'
xmax = data(2)'
if ( or(x < xmin) | or(x > xmax) ) then
f = %inf
else
f = x(1)^2 + x(2)^2
end
endfunction
rand("seed" , 0)
x0 = [1.2 1.9].';
xmin = [1 1];
xmax = [2 2];
data = list(xmin,xmax);
nm = nmplot_new ();
nm = nmplot_configure(nm,"-numberofvariables",2);
nm = nmplot_configure(nm,"-function",myquad);
nm = nmplot_configure(nm,"-costfargument",data);
nm = nmplot_configure(nm,"-x0",x0);
nm = nmplot_configure(nm,"-method","box");
nm = nmplot_configure(nm,"-boundsmin",xmin);
nm = nmplot_configure(nm,"-boundsmax",xmax);
nm = nmplot_configure(nm,"-simplex0method","randbounds");
nm = nmplot_search(nm);
xcomp = nmplot_get(nm,"-xopt") // Should be [1 1]
fcomp = nmplot_get(nm,"-fopt") // Should be 2
nm = nmplot_destroy(nm);
But this is a workaround: as the algorithm is designed to manage bounds,
defining the function outside the bounds is unacceptable.
A complete update of neldermead/fminsearch is planned in a future
release: I will fix these issues there.
Best regards,
Michaël Baudin
PS
By the way, I discovered a similar issue for the management of nonlinear
constraints:
http://bugzilla.scilab.org/show_bug.cgi?id=8547<http://bugzilla.scilab.org/show_bug.cgi?id=8549>
As I was using the function, I discovered various minor flaws:
<http://bugzilla.scilab.org/show_bug.cgi?id=8549>http://bugzilla.scilab.org/show_bug.cgi?id=8542
http://bugzilla.scilab.org/show_bug.cgi?id=8543
http://bugzilla.scilab.org/show_bug.cgi?id=8544
http://bugzilla.scilab.org/show_bug.cgi?id=8545
http://bugzilla.scilab.org/show_bug.cgi?id=8549
Le 30/11/2010 21:39, Paul CARRICO a écrit :
>
> Michaël,
>
> The calculations run with the code herebelllow ... nevertheless the
> parameters do not remain in the range defined by the brackets nay it
> leads to FEA failure !
>
> I suppose consequently they are too far from the optimized value isn't
> it (or there's a problem in my code) ècould you confirm ?
>
> Regards
>
> Paul
>
> ##################################################################
>
> initial_parameters = [C10 C01]'; // BE CAREFUL : [C10 C01]' =
> transposed matrix
>
> nm = nmplot_new ();
>
> nm = nmplot_configure(nm,"-numberofvariables",2); // Number of
> variables => C10 & C01
>
> nm = nmplot_configure(nm,"-function",optimization2);
>
> nm = nmplot_configure(nm,"-x0",initial_parameters); // BE CAREFUL :
> [C10 C01]' = transposed matrix
>
> nm = nmplot_configure(nm,"-method","box"); // box =>
> brackets are taken into account
>
> nm = nmplot_configure(nm,"-boundsmin",[0 0]);
>
> nm = nmplot_configure(nm,"-boundsmax",[1 1]);
>
> [nm,SSE] = nmplot_function(nm,initial_parameters);
>
> nm = nmplot_configure(nm,"-simplexfn","history.simplex.dat");
>
> #################################################################
>
> The inital value of the C10 parameters are :
>
> - C10 = 0.0623844
>
> - C01 = 0.01
>
> #########################################################
>
> * C10 = 0.0623844
>
> * C01 = 0.01
>
> * SSE = 0.640828
>
> Optimization in progress (please wait) ...
>
> #########################################################
>
> * C10 = 0.0623844
>
> * C01 = 0.01
>
> -->mode(0);
>
> -->mode(0);
>
> * SSE = 0.640828
>
> #########################################################
>
> * C10 = 0.0623844
>
> * C01 = 0.01
>
> -->mode(0);
>
> -->mode(0);
>
> * SSE = 0.640828
>
> #########################################################
>
> * C10 = 0.0623844
>
> * C01 = 0.01
>
> * SSE = 0.640828
>
> #########################################################
>
> * C10 = 1.06238
>
> * C01 = 0.01
>
> * SSE = 3097.29
>
> #########################################################
>
> * C10 = 0.0623844
>
> * C01 = 1.01
>
> * SSE = 1390.08
>
> #########################################################
>
> * C10 = -1.23762
>
> * C01 = 1.16
>
> * SSE = 0.218768
>
> #########################################################
>
> * C10 = 1e-006
>
> * C01 = 1.16
>
> * SSE = 1525.15
>
> #########################################################
>
> * C10 = 0.143483
>
> * C01 = -0.335
>
> * SSE = 42.4482
>
> #########################################################
>
> * C10 = 0.143483
>
> * C01 = 1e-006
>
> * SSE = 23.5783
>
> #########################################################
>
> * C10 = 0.155648
>
> * C01 = -1.3015
>
> * SSE = 1807.92
>
> #########################################################
>
> * C10 = 0.129291
>
> * C01 = -0.648249
>
> * SSE = 356.971
>
> #########################################################
>
> * C10 = 0.129291
>
> * C01 = 1e-006
>
> * SSE = 16.6268
>
> #########################################################
>
> * C10 = 0.0338986
>
> * C01 = 0.0114998
>
> * SSE = 0.56774
>
> #########################################################
>
> * C10 = -0.0573523
>
> * C01 = 0.0247235
>
> * SSE = 18.4969
>
> #########################################################
>
> * C10 = -0.00460543
>
> * C01 = 0.0177367
>
> * SSE = 4.48301
>
> #########################################################
>
> * C10 = 1e-006
>
> * C01 = 0.0177367
>
> * SSE = 5.72026
>
> #########################################################
>
> * C10 = 0.110724
>
> * C01 = 0.00166708
>
> * SSE = 9.75208
>
> #########################################################
>
> * C10 = 0.0794328
>
> * C01 = 0.0062085
>
> * SSE = 2.50334
>
> #########################################################
>
> * C10 = 0.00746278
>
> * C01 = 0.0166538
>
> * SSE = 4.02474
>
> #########################################################
>
> * C10 = 0.0278021
>
> * C01 = 0.0137018
>
> * SSE = 1.00242
>
> #########################################################
>
> * C10 = 0.0745827
>
> * C01 = 0.00691242
>
> * SSE = 1.80759
>
> #########################################################
>
> * C10 = 0.0613621
>
> * C01 = 0.00883117
>
> * SSE = 0.494514
>
> #########################################################
>
> * C10 = 0.02845
>
> * C01 = 0.0103807
>
> * SSE = 1.18104
>
> #########################################################
>
> * C10 = 0.0380402
>
> * C01 = 0.0102731
>
> The .dat file is empty - The calculation stops
>
> !--error 4
>
> Variable non définie: displacement_
>
> at line 90 of function ccx_dat_file called by :
>
> at line 51 of function called by :
>
> at line 57 of function optimbase_function called by :
>
> at line 23 of function _boxlinesearch called by :
>
> at line 106 of function neldermead_box called by :
>
> at line 8 of function neldermead_algo called by :
>
> at line 15 of function neldermead_search called by :
>
> at line 5 of function nmplot_search called by :
>
> nm = nmplot_search(nm); // start
>
> at line 33 of exec file called by :
>
> exec('C:\ETUDE_CALCULIX\ccx_scilab\fitting_procedure2.sce', -1)
>
> -->exec('SCI/etc/scilab.quit','errcatch',-1);quit;
>
> *De :*Michaël Baudin [mailto:michael.baudin at scilab.org]
> <mailto:[mailto:michael.baudin at scilab.org]>
> *Envoyé :* mardi 30 novembre 2010 14:00
> *À :* users at lists.scilab.org <mailto:users at lists.scilab.org>
> *Cc :* Carrico, Paul
> *Objet :* Re: [scilab-Users] optimization : general question
>
> Hi,
>
> There is no way to apply bounds to the parameters from the fminsearch
> function. This is because the algorithm was mainly designed for
> unconstrained optimization. Nevertheless, it is possible to apply them
> with the lower level component that the fminsearch function uses, the
> neldermead component. This is possible by projecting the parameters on
> the bounds. This makes the simple degenerate on the bounds and, if not
> far away from the optimum, let the simplex converge on the optimum.
>
> In order to find an example, please look, in Scilab v5.2.2, in the
> demonstrations:
>
> ? > Scilab Demonstrations > Optimization and simulation > neldermead Box B
>
> This example is based on the problem B from the Box' paper. It is a
> problem with 2 bounded parameters (see in attachment).
>
> In Scilab v5.3, I added some other examples. This includes a simple
> problem with bounds and Rosenbrock's post office problem, an
> optimization with 3 parameters and linear constraints (see in
> attachement). The simplest problem is the following:
>
> function [ f , index ] = myquad ( x , index )
> f = x(1)^2 + x(2)^2
> endfunction
> rand("seed" , 0)
> x0 = [1.2 1.9].';
> nm = nmplot_new ();
> nm = nmplot_configure(nm,"-numberofvariables",2);
> nm = nmplot_configure(nm,"-function",myquad);
> nm = nmplot_configure(nm,"-x0",x0);
> nm = nmplot_configure(nm,"-method","box");
> nm = nmplot_configure(nm,"-boundsmin",[1 1]);
> nm = nmplot_configure(nm,"-boundsmax",[2 2]);
> nm = nmplot_search(nm);
> xcomp = nmplot_get(nm,"-xopt") // Should be [1 1]
> fcomp = nmplot_get(nm,"-fopt") // Should be 2
> nm = nmplot_destroy(nm);
>
> This example is not provided in the help of neldermead (see bug
> #7164): I will fix this in the next release.
>
> Best regards,
>
> Michaël
>
> PS
> http://bugzilla.scilab.org/show_bug.cgi?id=7164
>
> Le 30/11/2010 11:58, Carrico, Paul a écrit :
>
> Dear all,
>
> The purpose of this mail is to benefit from user feedback of Scilab
> community ... even if my experience on optimization item is currently
> rather limited, this study will significantly increase my own expertise.
>
> I'm currently working in linking a FEA code with Scilab to fit
> parameters from tests (see attached fig - in red the steps realized in
> Scilab ) :
>
> - On a single parameter I used with success the *_fminsearch_*
> function (based on the simplex theory),
>
> - with 2 parameters, the calculated ran ... nevertheless the final
> result is physically non applicable (need to bracket one of the values
> for examples)
>
> Does somebody be experienced on such item ? what is the best Scilab
> function ? Some advices in reading ?
>
> Thanks in advance
>
> Regards
>
> Paul
>
> imap://michael%2Ebaudin@imap.scilab.org:993/fetch%3EUID%3E.INBOX.Users%3E3068?header=quotebody&part=1.2&filename=image001.jpg
>
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>
> --
> Michaël Baudin
> Ingénieur de développement
> michael.baudin at scilab.org <mailto:michael.baudin at scilab.org>
> -------------------------
> Consortium Scilab - Digiteo
> Domaine de Voluceau - Rocquencourt
> B.P. 105 - 78153 Le Chesnay Cedex
> Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
>
--
Michaël Baudin
Ingénieur de développement
michael.baudin at scilab.org
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
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