Conﬂict Ordering Search for Scheduling Problems Steven Gay 1 , Renaud Hartert 1 , Christophe Lecoutre 2 , Pierre Schaus 1 1 UCLouvain, ICTEAM, Place Sainte Barbe 2, 1348 Louvain-la-Neuve, Belgium, {firstname.lastname}@uclouvain.be 2 CRIL-CNRS UMR 8188, Universit´ e d’Artois, F-62307 Lens, France lecoutre@cril.fr Abstract. We introduce a new generic scheme to guide backtrack search, called Conﬂict Ordering Search (COS), that reorders variables on the ba- sis of conﬂicts that happen during search. Similarly to generalized Last Conﬂict (LC), our approach remembers the last variables on which search decisions failed. Importantly, the initial ordering behind COS is given by a speciﬁed variable ordering heuristic, but contrary to LC, once con- sumed, this ﬁrst ordering is forgotten, which makes COS conﬂict-driven. Our preliminary experiments show that COS – although simple to im- plement and parameter-free – is competitive with specialized searches on scheduling problems. We also show that our approach ﬁts well within a restart framework, and can be enhanced with a value ordering heuristic that selects in priority the last assigned values. 1 Introduction Backtracking search is a central complete algorithm used to solve combinatorial constrained problems. Unfortunately, it suﬀers from thrashing – repeatedly ex- ploring the same fruitless subtrees – during search. Restarts, adaptive heuristics, and strong consistency algorithms are typical Constraint Programming (CP) techniques used to cope with thrashing. Last Conﬂicts (LC) [9] has been shown to be highly proﬁtable to complete search algorithms, both in constraint satisfaction and in automated artiﬁcial intelligence planning. The principle behind LC is to select in priority the last conﬂicting variables as long as they cannot be instantiated without leading to a failure. Interestingly enough, last conﬂict search can be combined with any underlying variable ordering heuristic. In normal mode, the underlying heuristic selects the variables to branch on, whereas in conﬂict mode, variables are directly selected in a conﬂict set built by last conﬂict. While last conﬂict uses conﬂicts to repair the search heuristic, we show in this paper that conﬂicts can also be used to drive the search process by progressively replacing the initial variable heuristic. Basically, the idea behind our approach – namely, Conﬂict Ordering Search – is to reorder variables according to the most recent conﬂict they were involved in. Our experiments highlight that this simple reordering scheme, while being generic, can outperform domain speciﬁc heuristics for scheduling problems.