Conflict - based Statistics ∗

Value ordering heuristics play an important role in solving various problems. They allow to choose suitable values for particular variables to compute a complete and/or optimal solution. Usually, problem-specific heuristics are applied because problem-independent heuristics are computationally expensive. Here we propose an efficient problem-independent approach to value selection whose aim is to discover good and poor values. We have already applied this so called conflictbased statistics (CBS) in our iterative-forward search algorithm [7]. This combination helped us to solve a large-scale timetabling problem at Purdue University. Here we describe a general scheme for the conflict-based statistics and apply it to local search and iterative forward search methods. Methods similar to CBS were successfully applied in earlier works [2, 4]. In our approach, the conflict-based statistics works as an advice in the value selection criterion. It helps to avoid repetitive, unsuitable assignments of the same value to a variable. In particular, conflicts caused by this assignment in the past are memorized. In contrast to the weighting-conflict heuristics proposed in [4], conflict assignments are memorized together with the assignment which caused them. Also, we propose our statistics to be unlimited, to prevent short-term as well as long-term cycles.