Consistencies for ultra-weak solutions in minimax weighted CSPs using the duality principle
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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Soft constraints are functions returning costs, and are essential in modeling over-constrained and optimization problems. We are interested in tackling soft constrained problems with adversarial conditions. Aiming at generalizing the weighted and quantified constraint satisfaction frameworks, a Quantified Weighted Constraint Satisfaction Problem (QWCSP) consists of a set of finite domain variables, a set of soft constraints, and a min or max quantifier associated with each of these variables. We formally define QWCSP, and propose a complete solver which is based on alpha-beta pruning. QWCSPs are useful special cases of QCOP/QCOP+, and can be solved as a QCOP/QCOP+. Restricting our attention to only QWCSPs, we show empirically that our proposed solving techniques can better exploit problem characteristics than those developed for QCOP/QCOP+. Experimental results confirm the feasibility and efficiency of our proposals.