The most likely winning approaches will be a blend of randomness with hill-climbing. You might start by trying purely random coordinates for a while. Then, with time ticking on, you pick the highest you’ve hit so far and try some more random coordinates within a few kilometers of that point—hopefully, by now, you’re fishing in a mountain range. Finally, you pick the highest point so far and switch to a pure hill-climbing algorithm until time runs out.
This is like Bayesian Inference
