Fuzzified tree search in real domain games

1. Fuzzified tree search in real domain games DmitrijsRutko, Faculty of Computing, University of Latvia dim_rut@inbox.lv max 8 max ≥5 min 2 8 min <5 ≥5 max 2 7 8 9 max <5 ? ≥5 ≥5 1 2 7 4 3 6 8 9 5 4 √ √ √ Χ Χ √ √ √ Χ Χ 1 2 7 4 3 6 8 9 5 4 √ √ Χ Χ Χ √ Χ √ Χ Χ α β 2 8 X1 X3 X2 ALGORITHM GAME TREE SEARCH RESULTS • We present a new game tree search algorithm which is based on the idea that the exact game tree evaluation is not required to find the best move. • Experimental results in real domain games demonstrated 10 percent performance increase over existing algorithms Algorithm Performance Fig. 3. Geometric interpretation of the fuzzified game tree search function BNS(node, α, β) subtreeCount := numberofchildrenofnode do test := NextGuess(α, β, subtreeCount) betterCount := 0 foreachchildofnode bestVal := -AlphaBeta(child, -test, -(test - 1)) ifbestVal ≥ test betterCount := betterCount + 1 bestNode := child updatenumberofsub-treesthatexceedsseparationtestvalue updatealpha-betarange whilenot((β - α < 2) or (betterCount = 1)) returnbestNode Fig 5. Number of positions searched Fig 6. Relative number of positions • Better results than the existing algorithms in real domain • Iterative Deepening gives additional improvement FUZZIFIED APPROACH Conclusions HEY! THAT'S MY FISH! • In current experiments BNS demonstrated itself to be more efficient comparing scanned leaf node count. BNS gives a 10 percent performance improvement over MTDF algorithm • Comparable with expected results achieved in experiments in abstract domain • BNS demonstrates good potential and could be used as a general purpose game tree search algorithm • 2-4 player board game. • Collect as many fish as you can with your penguins. Future Work Fig. 1. Traditional Alpha-Beta Fig. 2. Fuzzified approach • The implementation and analysis of transposition tables • The usage of different knowledge based or heuristic based evaluation functions. • The future experiments should also consider analyzing algorithm performance in other games, but we believe that the proposed approach could be successfully applied for any type of game as well • Take a look at game tree from a relative perspective like “is this move better or worse than some value X” (Fig. 2). At each level we identify if a sub-tree satisfies “greater or equal” criteria. Fig 4. “Hey! That's My Fish!” game board • Simple but with some subtle strategy behind • Fair amount of tactical content in the game. The moves are not entirely obvious This research is supported by the European Social Fund project No. 2009/0138/1DP/1.1.2.1.2/09/IPIA/VIAA/004.