Learning general constraints in CSP

We present a new learning scheme for solvers of the Constraint Satisfaction Problem (CSP), which is based on learning (general) constraints rather than the generalized no-goods or signed-clauses that were used in the past. The new scheme is integrated in a conflict-analysis algorithm reminiscent of a modern systematic propositional satisfiability (SAT) solver: it traverses the conflict graph backwards and gradually builds an asserting conflict constraint. This construction is based on new inference rules that are tailored for various pairs of constraints types, e.g., x≤y1+k1x≤y1+k1 and x≥y2+k2x≥y2+k2, or y1≤xy1≤x and [x,y2]⊈[a,b][x,y2]⊈[a,b]. The learned constraint is stronger than what can be learned via signed resolution. Our experiments show that our solver HCSP backtracks orders of magnitude less than other state-of-the-art solvers, and is overall on par with the winner of this year's MiniZinc challenge.