Seed-in-Bayesian-Optimization

As Eugene pointed out the WL Help system explains "Seed" as follows:
Seed of random number generator
Well, this is both: True and only part of the truth.

Let ma add some background explanations:
Modern optimizer algorithms are not completely deterministic but contain some random elements. The Bayesian Optimizer for example "samples new promising parameter candidates" (explanation form Help).
Such sampling is done in a random way, the software uses a random number generator in its decision for new parameter values.

If done naively, such a random component makes the comparison of two optimization runs difficult:
Is one run better than the next because we changed some interesting parameter or is it due to fluctuations which stem form the randomness of internal samplings?

To stop the algorithm from walking different paths each time it is run there is a "Seed" value. This is used to initialize the random number generator before each run with the effect that it generates the same sequence of random numbers again and again.

This adds the benefits of both worlds: The optimizer uses some random sampling internally (the best it can do without further knowledge) and this randomness is completely repeatable and therefore deterministic.

So a more complete user manual would state:

Use the same Seed value whenever you are comparing various optimizer runs for the effect of parameter/condition/strategy changes.

Use different Seed values if you run the same optimization over the same strategy to find the intrinsic variability of your results (e.g. error margins of your results)