YIELDS: A Yet Improved Limited Discrepancy Search for CSPs

Abstract

Abstract. In this paper, we introduce a Yet ImprovEd Limited Discrepancy Search (YIELDS), a complete algorithm for solving Constraint Satisfaction Problems. As indicated in its name, YIELDS is an improved version of Limited Discrepancy Search (LDS). It integrates constraint propagation and variable order learning. The learning scheme, which is the main contribution of this paper, takes benefit from failures encountered during search in order to enhance the efficiency of variable ordering heuristic. As a result, we obtain a search which needs less discrepancies than LDS to find a solution or to state a problem is intractable. This method is then less redundant than LDS. The efficiency of YIELDS is experimentally validated, comparing it with several solving algorithms: Depth-bounded Discrepancy Search, Forward Checking, and Maintaining Arc-Consistency. Experiments carried out on randomly generated binary CSPs and real problems clearly indicate that YIELDS often outperforms the algorithms with which it is compared, especially for tractable problems.

Weight-based Heuristics for Constraint Satisfaction and Combinatorial Optimization Problems

“…In the following of this section, the heuristic is integrated into the YIELDS method proposed in [20] with a binary counting of discrepancies. In the YIELDS method, the Wvar_YIELDS_Probe algorithm (see Algorithm 1) is iterated either until a solution is found or until CurrentM axDiscr reached the maximum number of allowed discrepancies or until an inconsistency is detected.…”

“…Depth-bounded Discrepancy Search (DDS) [33] first favors discrepancies at the top of the search tree authorizing the discrepancies only in the 4 first levels of a given depth; it is non-redundant. Another variant is the method YIELDS [20], which is based on LDS and includes a mechanism to limit the exploration when the problem is inconsistent, even if the total number of discrepancies has not been used. The proposed heuristic Wvar consists in associating a weight with each variable.…”

Parallel machine scheduling with precedence constraints and setup times

“…DBDFS consists in a classical DFS where the nodes explored are limited by the discrepancies. Recently, in the YIELDS method (Karoui et al, 2007), learning process notions are integrated. In what follows, we propose several versions of LDS adapted to the considered parallel machine scheduling context.…”

Limited discrepancy search revisited

“…We put this to the test by replicating Korf 's experiments, using ILDS over number partitioning problems, taking discrepancies late and early. We then repeat Harvey and Ginsberg's [1995] experiments over job shop scheduling problems, and the job shop experiments in Karoui et al [2007], again taking discrepancies late and early. Finally, we examine randomly generated independent set decision problem.…”

“…This is due to the search process performing redundant probes. In Karoui et al [2007], an early stopping condition was proposed in the YIELDS algorithm. We present this stopping condition in isolation, prove that it is sound, and show how it can be easily incorporated into ILDS.…”