Discrepancy-Bounded Depth First Search J. Christopher Beck and Laurent Perron ILOG SA 9, rue de Verdun, BP85, 94253 Gentilly Cedex, France cbeck,lperron @ilog.fr Abstract. In this paper, we present a novel discrepancy-based search technique implemented as an instance of the generic search procedures framework intro- duced in [10]. Our empirical results indicate that the Discrepancy-Bounded Depth First Search (DBDFS) procedure exhibits a number of good properties. As a dis- crepancy based search technique, it is able to quickly find solution with low de- viation from the optimal solution. In addition, it revisits fewer nodes than other discrepancy-based techniques (e.g., Limited Discrepancy Search), making it a good candidate for proving optimal solutions. 1 Introduction Discrepancy-based search techniques such as Limited Discrepancy Search (LDS) [6] and Depth-bounded Discrepancy Search (DDS) [14] have been empirically shown to outperform traditional Depth First Search (DFS) in a number of problem contexts and theoretically in a simple model of search [6, 3, 14, 15]. The foundation for discrepancy- based search is the assumption that in any path from the root node to a solution node, a good heuristic is likely to make only a few mistakes. Therefore, paths with one ”discrep- ancy” from the heuristic path should be searched before paths with two discrepancies, etc. The evaluation of discrepancy-based techniques has tended to focus either on their ability to find satisfying solutions or on their ability to find solutions close to the optimal solution. When the goal of problem solving is to find and prove the optimal solution, DFS is often the favored search technique as it implements the optimal, worst-case behavior: DFS visits every node in the search space only once. In contrast, the usual implementations of discrepancy-based techniques incur an overhead due to the need to revisit internal nodes and, in some cases, leaf nodes [7, 14]. In this paper, we introduce and explore Discrepancy-Bounded Depth First Search (DBDFS), a novel discrepancy-based search technique motivated by the goal of finding and proving optimal solutions. DBDFS is designed to minimize the number of search states which are revisited while, at the same time, to preserve, as much as possible, the discrepancy-based order in which potential solutions are visited. In the following section, we review generic search procedures and then describe DBDFS. Our empirical investigation, then, compares the performance of DBDFS with LDS, DDS, and DFS on two sets of job shop scheduling problems.