1,086 research outputs found
Propagators and Solvers for the Algebra of Modular Systems
To appear in the proceedings of LPAR 21.
Solving complex problems can involve non-trivial combinations of distinct
knowledge bases and problem solvers. The Algebra of Modular Systems is a
knowledge representation framework that provides a method for formally
specifying such systems in purely semantic terms. Formally, an expression of
the algebra defines a class of structures. Many expressive formalism used in
practice solve the model expansion task, where a structure is given on the
input and an expansion of this structure in the defined class of structures is
searched (this practice overcomes the common undecidability problem for
expressive logics). In this paper, we construct a solver for the model
expansion task for a complex modular systems from an expression in the algebra
and black-box propagators or solvers for the primitive modules. To this end, we
define a general notion of propagators equipped with an explanation mechanism,
an extension of the alge- bra to propagators, and a lazy conflict-driven
learning algorithm. The result is a framework for seamlessly combining solving
technology from different domains to produce a solver for a combined system.Comment: To appear in the proceedings of LPAR 2
Generalizing backdoors
Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.
A Multi-Engine Approach to Answer Set Programming
Answer Set Programming (ASP) is a truly-declarative programming paradigm
proposed in the area of non-monotonic reasoning and logic programming, that has
been recently employed in many applications. The development of efficient ASP
systems is, thus, crucial. Having in mind the task of improving the solving
methods for ASP, there are two usual ways to reach this goal: extending
state-of-the-art techniques and ASP solvers, or designing a new ASP
solver from scratch. An alternative to these trends is to build on top of
state-of-the-art solvers, and to apply machine learning techniques for choosing
automatically the "best" available solver on a per-instance basis.
In this paper we pursue this latter direction. We first define a set of
cheap-to-compute syntactic features that characterize several aspects of ASP
programs. Then, we apply classification methods that, given the features of the
instances in a {\sl training} set and the solvers' performance on these
instances, inductively learn algorithm selection strategies to be applied to a
{\sl test} set. We report the results of a number of experiments considering
solvers and different training and test sets of instances taken from the ones
submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows
that, by applying machine learning techniques to ASP solving, it is possible to
obtain very robust performance: our approach can solve more instances compared
with any solver that entered the 3rd ASP Competition. (To appear in Theory and
Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure
Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning
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 under structural
restrictions. All these problems involve two tasks: (i) identifying the
structure in the input as required by the restriction, and (ii) using the
identified structure to solve the reasoning task efficiently. We show that for
most of the considered problems, task (i) admits a polynomial-time
preprocessing to a problem kernel whose size is polynomial in a structural
problem parameter of the input, in contrast to task (ii) which does not admit
such a reduction to a problem kernel of polynomial size, subject to a
complexity theoretic assumption. As a notable exception we show that the
consistency problem for the AtMost-NValue constraint admits a polynomial kernel
consisting of a quadratic number of variables and domain values. Our results
provide a firm worst-case guarantees and theoretical boundaries for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541,
arXiv:1104.556
Cost-based domain filtering for stochastic constraint programming
Cost-based filtering is a novel approach that combines techniques from Operations Research and Constraint Programming to filter from decision variable domains values that do not lead to better solutions [7]. Stochastic Constraint Programming is a framework for modeling combinatorial optimization problems that involve uncertainty [9]. In this work, we show how to perform cost-based filtering for certain classes of stochastic constraint programs. Our approach is based on a set of known inequalities borrowed from Stochastic Programming ¿ a branch of OR concerned with modeling and solving problems involving uncertainty. We discuss bound generation and cost-based domain filtering procedures for a well-known problem in the Stochastic Programming literature, the static stochastic knapsack problem. We also apply our technique to a stochastic sequencing problem. Our results clearly show the value of the proposed approach over a pure scenario-based Stochastic Constraint Programming formulation both in terms of explored nodes and run time
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