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Discussing the article: "Role of random number generator quality in the efficiency of optimization algorithms" - page 9

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Andrey Dik #:

on the example of this FF what vertices (or areas) are required to be obtained?

Only vertices are needed, some of which are marked in the figure. I.e. for each rectangle you need only one vertex.

If FF has exactly 50 vertices, then AO should return no more than 50 points. 51 is the wrong job.

fxsaber #:

Only vertices are needed, some of which are marked in the figure. I.e. for each rectangle you need only one vertex.

If FF has exactly 50 vertices, then AO should return 50 points. 51 is the wrong job.

For example, there are 51 vertices in total, one of them is global, and that one needs to get 50 vertices?
Andrey Dik #:
For example, there are 51 vertices in total, one of them is global, so you need to get 50 vertices?

50+1 vertices to get.

fxsaber #:

Only vertices are needed, some of which are marked in the figure. I.e. for each rectangle we need only one vertex.

If FF has exactly 50 vertices, then AO should return no more than 50 points. 51 is the wrong job.

At a vertex, if it is smooth, the derivative is zero.
in the neighbourhood is negative.

Vladimir Suslov #:

At the vertex, if it is smooth, the derivative is zero.
in the neighbourhood is negative.

I don't know how this can help.

fxsaber #:

Not sure how that would help.

look not for the maximum, but for the zero of the derivative.
if the derivative is positive in the neighbourhood, it is a trough.
if it is negative, it is a peak.

Vladimir Suslov #:

you're not looking for the maximum, you're looking for the zero of the derivative.

Go ahead and calculate derivatives OnTester.
fxsaber #:
Go ahead and calculate OnTester derivatives.

What's the problem?

Smooth functions are unlikely to occur in practical problems (to be able to correctly determine the derivative at points), but to run into fractality is quite possible:


Derivative is a good option, if the space is well enough probed, it can be smoothed as a post-processing by some kind of spline, and then you can get a derivative. But then the number of FF runs increases, which smoothly nullifies the effect of using AO.

In general, it is a bad let in the general case, but in the particular case it can be useful.

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