I am trying to find the minimum of some unexplored "staircase like" surface - image many Rastrigin functions side by side (some with a higher center and some with a lower center) but with flat parts instead of smooth bumps. The slope at any point is either undefined or $0$.
The best solutions I have found so far are "pattern search" and "genetic algorithms". I was also thinking that "coordinate descent" with "simulated annealing" might work as well.
Does anyone have suggestions or thoughts?