Good question about whether it's sparse searching. To me the point of using markov chains seemed to be to converge more quickly, not to increase coverage (where you'd actually want to introduce more variation).
Annealing is always worth mentioning because a lot of the time, it's a better performer. GAs and GPs carry a lot of systemic overhead.
Annealing is hit or miss. I often have to sample a distribution on a domain that approximates an infinite dimensional space and annealing doesn't cut it for me. There are just far too many modes. Personally, I'd like to see what GAs and GPs have to offer in this regard.
From a mathematical perspective, it looks as though your statement could imply that GA may potentially be viewed as a finite dimensional analogue of GP. Interesting.
Annealing is always worth mentioning because a lot of the time, it's a better performer. GAs and GPs carry a lot of systemic overhead.