When are genetic algorithms a good choice for optimization?

Genetic algorithms (GA) are a family of heuristics which are empirically good at providing a decent answer in many cases, although they are rarely the best option for a given domain. You mention derivative-based algorithms, but even in the absence of derivatives there are plenty of derivative-free optimization algorithms that perform way better than GAs. See this and this answer for some ideas. What many standard optimization algorithms have in common (even derivative-free methods) is the assumption that the underlying space is a smooth manifold (perhaps with a few discrete dimensions), and the function to optimize is somewhat well-behaved. However, not all functions are defined on a smooth manifold.