Combat strategy for ants

Question

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

Answer 1

I think your problem can be solved by turning the problem around. Instead of calculating the best moves - per ant - you could caclulate the best move candidates per discrete position on your playing board.

• +1 for a save place
• +2 for a place that results in an enemy dying
• -1 point for a position of certain death

That would scale in a linear way - but have some trade off in not providing best individual movement.

Maybe worth a try :)

Answer 2

My question is substantially about complexity. I thought to this problem extensively, but I still couldn't come up with an acceptable way to calculate the optimal set of moves in a reasonable time.

Exactly!

It's an AI competition. AI deals with problems which are too complex to be solved with optimal algorithms.

So you have to try "stuff", like your idea about centers of gravity. Even better would be some genetic algorithms where better strategies are found through natural selection (but it's hard to set up some evolving "framework" for that).

BTW: you can see the blog of the current leader and his strategy is surprisingly simple.

Answer 3

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.

Answer 4

EDIT FROM THE OP:

I'm selecting this answer as accepted as the winner of the contest published a post-mortem analysis of his code, and indeed he followed the approach suggested by the author of this answer. You can read the winner's blog entry here.

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For these kind of problems, MinMax algorithm with alpha beta pruning is usually used. (*) [simple explanation for minmax and alpa beta prunning is at the end, but for more details, the wikipedia page should also be read].

In order to overcome the problem you have mentioned about extremely large number of possible moves, a common improvement is doing the minmax algorithm iteratively. At first you explore all nodes until depth 1, and find the best solution. If you still have some time: explore all nodes until depth 2, and now chose a new more informed best solution, and so on...
When out of time: gives the best solution you could find, at the last level you explored.

To further improve your solution, you might want to reorder the nodes you develop: for iteration i, sort the nodes in iteration (i-1) [by their heuristical value for each vertex] and explore each possibility according the order. The idea behind it is that you are more likely to prun more vertices, if you first investigate the "best" solutions.

The problem here remains finding a good heuristical function, which evaluates "how good a state is"

(*)The MinMax algorithm is simple: You explore the game tree, and decide what will you do for each state, and what is your oponent is most likely to do for each action. This is done until depth k, where k is given to the algorithm.

The alpha beta prunning is an addition to minmax, which tells you "which nodes should not be explored anymore, since any way I am not going to chose them, because I have a better solution"