Prediction-Based Adaptive Variable Ordering Heuristics for Constraint Satisfaction Problems

Jitao Xu, Yaling Wu, Hongbo Li, Minghao Yin

Abstract: Variable ordering heuristics (VOH) play a central role in solving Constraint Satisfaction Problems (CSP). The performance of different VOHs may vary greatly when solving the same CSP instance, so identifying an efficient candidate VOH for a given CSP has been a key issue in the community. In this study, we propose a prediction-based approach to adaptively select efficient VOHs for different CSPs from a set of candidates. Our work demonstrates that efficient candidate VOHs can be identified by learning from the topology of search trees. Specifically, we propose to represent the topology of a binary search tree by the sequence of the Numbers of Positive Decisions (NPD) made before each failure occurs. Based on the representation, we predict the total failure number of a search tree from its beginning part. When solving a CSP, we run a probing procedure to obtain the NPD sequences generated by candidate VOHs and select an efficient one for the resolution according to the prediction results. Our experiments show that the Long Short Term Memory model and Gradient Boosting Decision Tree models trained with the search trees sampled from easy instances are effective in identifying efficient VOHs for hard instances. The models capture some common structure properties hidden in the search trees of different problems. Our approach outperforms the state-of-the-art adaptive VOHs in terms of the number of solved instances and the PAR2 score of runtime.