Anytime Hybrid Best-First Search with Tree Decomposition for Weighted CSP

We propose Hybrid Best First Search (HBFS), a search strategy for optimization problems that combines Best First Search (BFS) and Depth First Search (DFS). Like BFS, HBFS provides an anytime global lower bound on the optimum, while also providing anytime upper bounds, like DFS. Hence, it provides feedback on the progress of search and solution quality in the form of an optimality gap. In addition, it exhibits highly dynamic behavior that allows it to perform on par with methods like limited discrepancy search and frequent restarting in terms of quickly finding good solutions. We also use the lower bounds reported by HBFS in problems with small treewidth, by integrating it into Backtracking with Tree Decomposition (BTD). BTD-HBFS exploits the lower bounds reported by HBFS in individual clusters to improve the anytime behavior and global pruning lower bound of BTD. In an extensive empirical evaluation on optimization problems from a variety of application domains, we show that both HBFS and BTD-HBFS improve both anytime and overall performance compared to their counterparts.