Disjoint pattern database heuristics

We describe a new technique for designing more accurate admis sible heuristic evaluation functions based on pattern databases While many heuristics such as Manhattan distance compute the cost of solving individual subgoals independently pattern databases consider the cost of solving multiple subgoals simultaneously Exist ing work on pattern databases allows combining values from di erent pattern databases by taking their maximum If the subgoals can be divided into disjoint subsets so that each operator only a ects sub goals in one subset then we can add the pattern database values for each subset resulting in a more accurate admissible heuristic function We used this technique to improve performance on the Fifteen Puzzle by a factor of over and to nd optimal solutions to random instances of the Twenty Four Puzzle Introduction and Oveview The sliding tile puzzles are a classic challenge for search algorithms in AI The key to nding optimal solutions to these problems is an accurate admissible heuristic function We describe a generalization of the Manhattan distance heuristic that considers the interactions among multiple tiles while allowing the moves of di erent groups of tiles to be added together without violating admissibility This results in a much more accurate admissible heuristic Sliding Tile Puzzles The Fifteen and Twenty Four Puzzles are shown in Figure A square frame is lled with tiles except for one empty or blank position Any tile horizontally or vertically adjacent to the blank can be slid into that position The task is to rearrange the tiles from a given initial con guration into a particular goal con guration ideally or optimally in a minimum num ber of moves The state space for the Fifteen Puzzle space contains about states and the Twenty Four Puzzle contains almost states