Drescher and Walsh, to satisfiability modulo theories, the key idea is to incorporate 2010). Then, constraint answer sets of the resulting program theory-specific predicates into propositional formulas, can be characterized via Boolean assignments over and extending an ASP solver's decision engine for a atom(Π) body(Π) that do not violate a set of nogoods more high-level proof procedure. A promising approach to imposed by Π. Formally, a Boolean assignment A is a sequence constraint answer set programming (CASP) has been presented (σ

In many real-life optimization problems involving multiple agents, the rewards are not necessarily known exactly in advance, but rather depend on sources of exogenous uncertainty. For instance, delivery companies might have to coordinate to choose who should serve which foreseen customer, under uncertainty in the locations of the customers. The framework of Distributed Constraint Optimization under Stochastic Uncertainty was proposed to model such problems; in this paper, we generalize this formalism by introducing the concept of evaluation functions that model various optimization criteria. We take the example of three such evaluation functions, expectation , consensus , and robustness , and we adapt and generalize two previous algorithms accordingly. Our experimental results on a class of Vehicle Routing Problems show that incomplete algorithms are not only cheaper than complete ones (in terms of simulated time , Non-Concurrent Constraint Checks , and information exchange) , but they are also often able to find the optimal solution. We also show that exchanging more information about the dependencies of their respective cost functions on the sources of uncertainty can help the agents discover higher-quality solutions.

This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constraint propagation is actually equivalent to solving a Lyapunov matrix equation, which is widely used in Control Theory as a standard continuous-time equation. Different from most previous constraint propagation methods that suffer from severe limitations, our method can directly be applied to multi-class problem and also can effectively exploit both must-link and cannot-link constraints. The propagated constraints are further used to adjust the similarity between data points so that they can be incorporated into subsequent clustering. The proposed method has been tested in clustering tasks on six real-life data sets and then shown to achieve significant improvements with respect to the state of the arts.

Web Service (WS) domains constitute an application field where automated planning can significantly contribute towards achieving customisable and adaptable compositions. Following the vision of using domain-independent planning and declarative complex goals to generate compositions based on atomic service descriptions, we apply a planning framework based on Constraint Satisfaction techniques to a domain consisting of WSs with diverse functionalities. One of the key requirements of such domains is the ability to address the incomplete knowledge problem, as well as recovering from failures that may occur during execution. We propose an algorithm for interleaving planning, monitoring and execution, where continual planning via altering the CSP is performed, under the light of the feedback acquired at runtime. The system is evaluated against a number of scenarios including real WSs, demonstrating the leverage of situations that can be effectively tackled with respect to previous approaches.

In this paper, we investigate the hybrid tractability of binary Quantified Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of binary QCSPs is identified by using the broken-triangle property. In this class, the variable ordering for the broken-triangle property must be same as that in the prefix of the QCSP. Second, we break this restriction to allow that existentially quantified variables can be shifted within or out of their blocks, and thus identify some novel tractable classes by introducing the broken-angle property. Finally, we identify a more generalized tractable class, i.e., the min-of-max extendable class for QCSPs.

We formulate a general framework for pseudo-Boolean multi-valued nogood-learning, generalizing conflict analysis performed by modern SAT solvers and its recent extension for disjunctions of multi-valued variables. This framework can handle more general constraints as well as different domain representations, such as interval domains which are commonly used for bounds consistency in constraint programming (CP), and even set variables. Our empirical evaluation shows that our solver, built upon this framework, works robustly across a number of challenging domains.

Several MaxSAT algorithms based on iterative SAT solving have been proposed in recent years. These algorithms are in general the most efficient for real-world applications. Existing data indicates that, among MaxSAT algorithms based on iterative SAT solving, the most efficient ones are core-guided, i.e. algorithms which guide the search by iteratively computing unsatisfiable subformulas (or cores). For weighted MaxSAT, core-guided algorithms exhibit a number of important drawbacks, including a possibly exponential number of iterations and the use of a large number of auxiliary variables. This paper develops two new algorithms for (weighted) MaxSAT that address these two drawbacks. The first MaxSAT algorithm implements core-guided iterative SAT solving with binary search. The second algorithm extends the first one by exploiting disjoint cores. The empirical evaluation shows that core-guided binary search is competitive with current MaxSAT solvers.

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a complexity theoretic assumption, none of the considered problems can be reduced by polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, such as induced width or backdoor size. Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems.

In constraint solving, a critical bottleneck is the formulation of aneffective constraint model of an input problem. The Conjure system describedin this paper, a substantial step forward over prototype versions of Conjurepreviously reported, makes a valuable contribution to the automation ofconstraint modelling by automatically producing constraint models from theirspecifications in the abstract constraint specification language Essence. Aset of rules is used to refine an abstract specification into a concreteconstraint model. We demonstrate that this set of rules is readily extensibleto increase the space of possible constraint models Conjure can produce. Ourempirical results confirm that Conjure can reproduce successfully the kernelsof the constraint models of 32 benchmark problems found in the literature.