Nonsystematic backtracking search

Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Chronological backtracking can be applied to these problems, but it is unlikely to find a solution in the explored fraction of the space because of the order in which it examines nodes. A nonsystematic technique known as iterative sampling alleviates the problem by examining fringe nodes in a random order. Although nonsystematic techniques do not suffer from the problem of exploring nodes in a bad order, they do reconsider nodes they have already ruled out, a problem that is serious when the density of solutions is low. Unfortunately, for many practical problems, the order of examining nodes matters and the density of solutions is low. Consequently, neither chronological backtracking nor iterative sampling has good average case performance. We present a new search algorithm called bounded backtrack search that combines the merits of backtracking and iterative sampling. The algorithm backtracks chronologically until reaching a backtrack bound, whereupon it immediately backtracks to the root and restarts on a new random path. We show that the new algorithm does not suffer from the problems of the alternatives, and we derive theoretical conditions that guarantee better average case performance. Our analysis also shows that chronological backtracking does not use successor ordering heuristics effectively. The accuracy of the heuristics for early decisions is critical to the algorithm's efficiency, whereas the accuracy is relatively unimportant deep in the tree because the alternatives are considered quickly. Unfortunately, heuristics are typically least reliable for the early decisions--when they are most important. We present a second new algorithm called limited discrepancy search that examines nodes in increasing order of "discrepancies," or points of disagreement with a problem's heuristics. We show that the algorithm has exceptional average case performance when the heuristics are accurate and reasonable performance when the heuristics are bad. We present experimental results in job shop scheduling to show that the theoretical conditions and the expected performance hold for real problems.