The definition of Schwefel function seems inconsistent with the implementation

[NDManh]

If we respect to the implementation :

1. The x_opt in the formula z = 100(Lambda^10(z^hat - x_opt) + x_opt) should be 2*abs(x_opt).
2. The formula - frac{1}{D} sum(...) should be - frac{1}{100D} sum(...).

(Thanks Niko, I've updated some expressions such that the context is more clear)

[nikohansen]

Thanks for spotting these! There is a third mistake in the description: x_i^opt in the second bullet point must be 2 * abs(x_i^opt) as well. It's the same problem as with 1), it's a confusion of what x_opt is supposed to mean in the given context (\hat x_opt seems asked for). Re 2), I guess this might also cancel the 100 in front of the penalty term, not sure though...

[nikohansen]

Also: in f23 and f24 "+ f_opt" is missing and for f21/22 we should add the reference M. Gallagher and B. Yuan. A General-Purpose Tunable Landscape Generator. IEEE Transactions on Evolutionary Computation 10(5):590-603, 2006.

[brockho]

I started to have a look at the above as well as at #1266.

The only unclear thing was whether the 100 should appear in front of the penalty term or not. It is not obvious to see that the implementation follows the LaTeX definition here but after checking the code carefully, I am convinced that @NDManh was correct in the sense that the 100 should stay in the LaTeX definition in front of the penalty term to coincide with the implementation.

The coco svn repository has now the updated LaTeX code (in coco/BBOB/doc/latexFunctions/) and it will be nice if somebody can check (with me) whether everything is actually correct now in the pdf. We then have to update the HAL version and the links from the web pages.

[nikohansen]

It seems I spotted another mistake: Section 2.7, Step-Ellipsoid function, if \hat z_i > 0.5 must read if |\hat z_i| > 0.5, as correctly implemented here.

[brockho]

Nice catch!

[nikohansen]

There is another small glitch in the definition of the Rosenbrock function f8: x_opt is chosen in [-3, 3]^n. This should have been mentioned explicitly in the definition.

[nikohansen]

All above errors are now addressed in the source file.

[nikohansen]

The fixed document were uploaded to HAL and to http://coco.gforge.inria.fr/downloads/download16.00 and are used at the COCO gforge home and in the links at the latest old release.