Graph Traversal

[lhoward]

This is more of a general computer science/graph traversal question than a perl question; but I'm coding in perl and I know that this is a very smart crowd so I thought I'd see what help you could offer.

I've recently started playing the online game CashWars (note: this post is not a troll to get people to play CashWars, but if you do want to try it out, use the following link CashWars and I will get some nominal credit for refering you).

The game is played on a 721x721 grid. Every day you get so many moves (I'm currently at 350 per day, but you can have as many as 600). Moving 1 square horizontally or vertically costs 1 movement point. Certain squares contain resources (Oil) that you can gather. You can only gather resources from a particular square once per day. I have a large list of the squares that contain oil. What I am trying to do is compute an "optimal or near optimal path" to visit as many oil squares as possible in a given number of moves from a particular starting location.

I've already tried out a few algorithms:

• weighting - I weigh each of the 4 squares adjacent to the current square based on some function of the distance from that square to nearby untapped squares with oil in them. I've tried a few diffrent weighting algorithms and this hueristic has worked ok.
• spanning tree - I read that a spanning-tree algorithm can be used to produce a close-to-optimal solution to the Travelling Salesman Problem so I decided to give it a try. It did slightly better than the weighting algorithm, but I feel I could do better (since my problem isn't the classic TSP "visit every node in the minimum # of moves" problem, it is "visit as many nodes as possible in N moves" which is slightly diffrent and would lead to diffrent optimizations).
• limited game tree - I store the 200 current best paths, then I add all possible moves to each one, and then rate the paths again; keeping only the 200 best out of that lot (best is determined by total path length to # of oil suqares ratio). This is the best algorithm so far, but I still feel that I can do better.

I'd like the other monk's thoughts about any other hueristics or algorithms that I could try that might give a good solution to this "visit as many X as possible in Y moves" problem.

I can post my code for any of those algorithms I've tried already if anyone is interested.