The pathology of heuristic search in the 8-puzzle

In practice, an incomplete heuristic search nearly always finds better solutions if it is allowed to search deeper, i.e., expand and heuristically evaluate more nodes in the search tree. On the rare occasions when searching deeper is not beneficial, a curious phenomenon called “search pathology” occurs. In this paper we study the pathology and gain of a deeper search of the minimin algorithm in the 8-puzzle, a domain often used for evaluating single-agent search algorithms. We have analyzed the influence of various properties of the search tree and the heuristic evaluation function on the gain and the pathology. In order to investigate a broad range of the properties, the original 8-puzzle was extended with diagonal moves, yielding a larger variety of search trees. It turned out that in the 8-puzzle a substantial proportion of the solvable positions is pathological under various parameters. More importantly, the search parameters that enable the highest gains are quite consistent in pathological and non-pathological positions alike, thus pointing to potentially successful search strategies.