>> shotgun stochastic ballistic hill-climbing
  >> works at least as well

  > This is the method that I'd like a lot of these
  > stochastic optimization algorithms compared to,
  > especially genetic algorithms.

  > At least brute force sampling of the entire space ...

Not sure you meant it to do so, but this sounds like you think that "shotgun stochastic ballistic hill-climbing" is a brute force sampling of the entire space. It's not, it's a stochastic optimization algorithm. Brute force sampling of the entire space, or even reasonable portions of it, is completely infeasible for the problems I deal with, so I'm not sure what you're saying here. You might like to explain a little more.

Now I've read your other comment with the terminology, I think "shotgun hill-climbing" is the appropriate phrase for the sort of materials science thing I'm talking about - you start atoms in random configurations, with minimal bias, and then minimise using the forces (available analytically) on those atoms using gradient descent/whatever optimiser (usually BFGS) until you find local minima. There's no momentum involved, and the gradient is available, but you still start in random positions and minimise to local minima. That sort of method is in competition with other structure finding algorithms that use GAs, SAs or some other fudged hybrids.

My reference to "brute force" was that, as far as I understand, in the limit of lots of attempts, "shotgun" will approach "brute force" -- imagine a really nasty landscape with lots of tiny basins. I understand "stochastic ballistic" modifies things slightly.

Yes to all - thanks for the clarification. The only comment is that in large dimension cases shotgun might theoretically approach brute force, but it never does so because there are just too many places to start.

If gradient is available then it makes little sense to say you want people to compare that method to GAs. GAs are for black box search.

Discrete gradients are always available - you can step in random directions and re-evaluate giving an approximation. If your space is smooth(ish) (and usually it's "smooth enough") then you can use the local approximations.

Yes, sometimes it's not possible, but usually local random search gives enough to use the concept of "gradient" to help. Mostly I find that people doing the optimisation/search don't know enough about the techniques they're using to adapt them and transform their problem to get the best out of things.

Yes, but it still makes no sense to compare GA performance with a gradient-based method on the problem GP is talking about, because an explicit gradient is available.