It is well known that modeling with constraints networks require a fair expertise. Thus tools able to automatically generate such networks have gained a major interest. The major contribution of this paper is to set a new framework based on Inductive Logic Programming able to build a constraint model from solutions and non-solutions of related problems. The model is expressed in a middle-level modeling language. On this particular relational learning problem, traditional topdown search methods fall into blind search and bottom-up search methods produce too expensive coverage tests. Recent works in Inductive Logic Programming about phase transition and crossing plateau shows that no general solution can face all these difficulties. In this context, we have designed an algorithm combining the major qualities of these two types of search techniques. We present experimental results on some benchmarks ranging from puzzles to scheduling problems.
Abstract. Minimax Weighted Constraint Satisfaction Problems (formerly called Quantified Weighted CSPs) are a framework for modeling soft constrained problems with adversarial conditions. In this paper, we describe novel definitions and implementations of node, arc and full directional arc consistency notions to help reduce search space on top of the basic tree search with alpha-beta pruning for solving ultra-weak solutions. In particular, these consistencies approximate the lower and upper bounds of the cost of a problem by exploiting the semantics of the quantifiers and reusing techniques from both Weighted and Quantified CSPs. Lower bound computation employs standard estimation of costs in the sub-problems used in alpha-beta search. In estimating upper bounds, we propose two approaches based on the Duality Principle: duality of quantifiers and duality of constraints. The first duality amounts to changing quantifiers from min to max, while the second duality re-uses the lower bound approximation functions on dual constraints to generate upper bounds. Experiments on three benchmarks comparing basic alpha-beta pruning and the six consistencies from the two dualities are performed to confirm the feasibility and efficiency of our proposal.
A constraint is a relation with an active behavior. For a given relation, we propose to learn a representation adapted to this active behavior. It yields two contributions. The first is a generic metatechnique for classifier improvement showing performances comparable to boosting. The second lies in the ability of using the learned concept in constraint-based decision or optimization problems. It opens a new way of integrating Machine Learning in Decision Support Systems.
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