Speeding up weighted constraint satisfaction using redundant modeling

In classical constraint satisfaction, combining mutually redundant models using channeling constraints is effective in increasing constraint propagation and reducing search space for many problems. In this paper, we investigate how to benefit the same for weighted constraint satisfaction problems (WCSPs), a common soft constraint framework for modeling optimization and over-constrained problems. First, we show how to generate a redundant WCSP model from an existing WCSP using generalized model induction. We then uncover why naively combining two WCSPs by posting channeling constraints as hard constraints and relying on the standard NC* and AC* propagation algorithms does not work well. Based on these observations, we propose m-NCc* and m-AC(c)(*) and their associated algorithms for effectively enforcing node and arc consistencies on a combined model with m sub-models. The two notions are strictly stronger than NC* and AC* respectively. Experimental results confirm that applying the 2-NCc* and 2-AC(c)(*) algorithms on combined models reduces more search space and runtime than applying the state-of-the-art AC*, FDAC*, and EDAC* algorithms on single models.