I am working on an AI bot for the game Defcon. The game has cities, with varying populations, and defensive structures with limited range. I’m trying to work out a good algorithm for placing defence towers.
- Cities with higher populations are more important to defend
- Losing a defence tower is a blow, so towers should be placed reasonably close together
- Towers and cities can only be placed on land
So, with these three rules, we see that the best kind of placement is towers being placed in a ring around the largest population areas (although I don’t want an algorithm just to blindly place a ring around the highest area of population, sometime there might be 2 sets of cities far apart, in which case the algorithm should make 2 circles, each one half my total towers).
I’m wondering what kind of algorithms might be used for determining placement of towers?
I don’t know the game but from your description it seems that you need an algorithm similar to the one for solving the (weighted) k-centers problem. Well, unfortunately, this is an NP hard problem so in the best case you’ll get an approximation upper bounded by some factor.
Take a look here: http://algo2.iti.kit.edu/vanstee/courses/kcenter.pdf