This question refers to the Google-sponsored AI Challenge, a contest that happens every few months and in which the contenders need to submit a bot able to autonomously play a g
Tricky indeed. You may find some hints in Bee algorithms. This is a set of algorithms to use swarm cooperation and 'reasonable computation time'. Bee algorithms can for instance be used to roughly (!) solve the traveling salesman problem. I expect that these algorithms can provide you with the best solution given computing time.
Of course, the problem can be simplified using geometry: relative positions of ants in a neighbourhood are more important than absolute positions. And also light_303's solution is complementatry to the search pattern I propose.