On-demand Bound Computation for Finding Leading Solutions to Soft Constraints

An important class of algorithms for constraint optimization searches for solutions guided by a heuristic evaluation function (bound) that can be computed using tree decomposition and dynamic programming. Recently, it has been shown that if only a few best solutions are needed, the cost of pre-processing can be avoided by interleaving dynamic programming with search. In this paper, we extend this hybrid method to the case of A* search for semiring-CSPs with a total order. A* is a specialization of branch-and-bound that finds best solutions in an optimal number of steps, but requires more space due to a larger search tree. To address this, we show how the hybridization can be understood as demand-driven heuristics computation. This allows to use techniques from heuristic search to significantly limit the number of search nodes expanded. The resulting approach uses lazy, best-first variants of constraint projection and combination operators to compute only those bounds specifically required to generate a next best solution. Experiments on randomly generated Max-CSPs indicate performance improvements over classical dynamic programming methods for best-first search.