Example: - Find the geographical point of minimum distance between multiple points (Useful for location-based application) ...
The following was added as further clarification:
The scoring function is probably mostly "continuous"-ish. Small changes in the coordinates probably lead to small changes in the score, although there will be areas (hyper-volumes) where this isn't entirely true. It is possible to use non-integer coordinates for exploration, and the evaluation/scroing function is probably reasonably well behaved when doing this.
Hill-climbing/descending techniques give moderate results, but there are lots of local minima. Some local minima have wide catchment areas (hyper-volumes) but are not particularly extreme. Local gradients are mostly present - there aren't likely to be huge swathes that are effectively "flat".
You can keep a list of several local minima, maybe even see to it so that they are not "close" to each other (or equal to each other) when the algorithm goes through the area, so that it avoids already known local minima and tries to just seek more.