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Good afternoon,

I have an objective function for which no gradient is available.
So I am currently testing three derivative-free, local optimizers
available in the nlopt-package:
COBYLA
BOBYQA
Sbplex
via the c++-Wrapper.

All three work quite well only with small differences on my function, so
everything is great.

But: After a code refactoring, COBYLA computes a different final result
from before. The other two algorithms work fine again.
To be precise:
The input consists of e.g x=11 values (11 dimensions), each of them
constrained by lower and upper bonds. When I observe the development of
these 11 values over the course of the optimization, I can observe the
same consecutive changes in x until step 97. Based on the same score for
the same x, nlopt-COBYLA chooses diverging changes in step 98 for x in
the fifth etc. digit after the dot. (See example below.)

Thus, I checked through the pseudo-random step in nlopt-COBYLA and nlopt
seems to compute a fully deterministic seed for this step.
 * n         : number of variables (>=0)
 * m         : number of constraints (>=0)
.. and both have a fixed size
- -> seed = n+m = 11 + 22 (or sth. similar)
in both tries. Recompiling nlopt with a seed of 12345 resulted in the
same behavior. I was not able to determine another random choice in
COBYLA by Powell.

Did I misunderstand how choices in COBYLA are made in general or how
this algorithm was tweaked in nlopt? I would be grateful if somebody
on this list could enlighten me.

Thanks & greets
Agnes

Example:
Software V1:
X 0.0749661 0.0192328 -0.053719 -0.0263031 0.0175889 0.00720839
0.0183608 0.0284882 0.0251937 -0.00431795 -0.00957517
Scores: -66.2673 -80.9919 14.7247 97 (#steps)
X 0.0745738 0.0192303 -0.053562 -0.0264908 0.0176959 0.00696263
0.0183886 0.0286858 0.0253243 -0.00428986 -0.00971649
Scores -66.2706 -80.9935 14.7229 98 (#steps)

Software V2:
X 0.0749661 0.0192328 -0.053719 -0.0263031 0.0175889 0.00720839
0.0183608 0.0284882 0.0251937 -0.00431795 -0.00957517
Scores -66.2673 -80.9919 14.7247 97 (#steps)
X 0.0745132 0.0192907 -0.0535049 -0.0260577 0.017551 0.00691121
0.0182708 0.028576 0.0253385 -0.00429313 -0.00966163
Scores -66.2697 -80.9926 14.7229 98 (#steps)


- -- 
Dipl.-Inform. (Bioinf.) Agnes Meyder
040-42838-7324 -- [email protected]
Research Group for Computational Molecular Design
Center for Bioinformatics Hamburg -- http://www.zbh.uni-hamburg.de
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