Automatic Generation of Memory Based Search Heuristics

Abstract

Our goal is to automatically generate heuristics to guide state space search. The heuristic values are distances computed in an abstract space which is automatically derived from the original space. The search space is described in a production system. Simple syntactic transformations of this description give rise to another search space. The distances of abstract states from the abstract goal state are stored in a look-up table and provide admissible and monotonic heuristics for search algorithms such as IDA*. The size of the abstract space is the size of the look-up table and different transformations on the description of the space give rise to abstract spaces of different size. We are interested in the relationship between the memory required to store the heuristic and the speed of search. We are also interested in ranking abstractions which generate abstract spaces of the same cardinality with respect to their predicted performance without actually performing searches in the original space. We also plan to use our technique to search for macro operators to find suboptimal paths very quickly. A macro operator is a sequence of operators which immediately reaches a subgoal state applied to a state without performing search. Culberson and Schaeffer (Culberson & Schaeffer 1996) developed a technique (pattern database) to represent heuristic look-up tables and effectively used it on the 15Puzzle. Korf used pattern databases to find optimal paths for random instances of the Rubik's Cube for the first time. In his paper he conjectured that the size of the pattern database and the speed of search can be linearly traded for each other. We verified his conjecture in a large scale experiment and reported it in (Holte & Hernadvolgyi 1999). Korf and Reid in (Korf & Reid 1998) gave a more formal derivation of the expected number of states generated by the search algorithm based on the distribution of heuristic values. We used their ideas to select the best heuristics in a large pool of heuristics with equal memory requirements. We devised a simple vector notation for representing state spaces and a method for automatically creating abstractions based on this notation. Our technique based on mapping labels (domain abstraction) is guaranteed to create abstract spaces where the distances provide admissible and monotonic heuristic values. Some abstractions are non-surjective; there are states in the abstract space which have no pre-image in the original