Learning while searching in constraint-satisfaction-problems (original) (raw)

Learning from Failure in Constraint Satisfaction Search

2006

Much work has been done on learning from failure in search to boost solving of combinatorial problems, such as clause-learning in boolean satisfiability (SAT), nogood and explanation-based learning, and constraint weighting in constraint satisfaction problems (CSPs), etc. Many of the top solvers in SAT use clause learning to good effect. A similar approach (nogood learning) has not had as large an impact in CSPs. Constraint weighting is a less fine grained approach where the information learnt gives an approximation as to which variables may be the sources of greatest contention. In this paper we present a method for learning from search using restarts, in order to identify these critical variables in a given constraint satisfaction problem, prior to solving. Our method is based on the conflict-directed heuristic (weighted-degree heuristic) introduced by Boussemart et al. and is aimed at producing a better-informed version of the heuristic by gathering information through restarting and probing of the search space prior to solving, while minimising the overhead of these restarts/probes. We show that random probing of the search space can boost the heuristics power by improving early decisions in search. We also provide an in-depth analysis of the effects of constraint weighting.

Dynamic Backtracking with Constraint Propagation

Recent w orks on constraint relaxation ] provided the decorum system (Deduction-based Constraint Relaxation Management). In this paper, we show h o w the ideas developed in that system can be used in order to integrate Constraint Propagation within the Dynamic Backtracking algorithm . Dynamic Backtracking replaces the backtracking process by a m uch less blind behavior that consists in local modi cations of the choices made up to the current situation. Thus the whole constraint programming community m a y derive bene ts from its integration with a constraint propagation algorithm.

The search efficiency of theorem proving strategies: an analytical comparison

1994

We analyze the search e ciency of a number of common refutational theorem proving strategies for rst-order logic. Search e ciency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We s h o w that most common strategies produce search spaces of exponential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to propositional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strategy which is of interest for term-rewriting based theorem proving is the A-ordering strategy, a n d we discuss it in some detail. We show some advantages of A-ordering over other strategies, which m a y help to explain its e ciency in practice. We also point out some of its combinatorial ine ciencies, especially in relation to goal-sensitivity and irrelevant clauses. In addition, SLD-resolution, which is of importance for Prolog implementation, has combinatorial ine ciencies this may suggest basing Prolog implementations on a di erent theorem proving strategy.

The search efficiency of theorem proving strategies

Springer eBooks, 1994

Backtracking Algorithms for Constraint Satisfaction Problems

1999

Over the past twenty five years many backtracking algorithms havebeen developed for constraint satisfaction problems. This survey describesthe basic backtrack search within the search space framework and thenpresents a number of improvements developed in the past two decades,including look-back methods such as backjumping, constraint recording,backmarking, and look-ahead methods such as forward checking and dynamicvariable ordering.1 IntroductionConstraint networks have proven...

Reasoning from last conflict(s) in constraint programming

Artificial Intelligence, 2009

Constraint programming is a popular paradigm to deal with combinatorial problems in artificial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but suffer from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classified into look-ahead (constraint propagation and search heuristics) and lookback (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conflicts and, as a side effect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conflict, the last assigned variable is selected in priority, so long as the constraint network cannot be made consistent. This allows us to find, following the current partial instantiation from the leaf to the root of the search tree, the culprit decision that prevents the last variable from being assigned. This way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing. Moreover, we show that this approach can be generalized so as to collect a (small) set of incompatible variables that are together responsible for the last conflict. Experiments over a wide range of benchmarks demonstrate the effectiveness of this approach in both constraint satisfaction and automated artificial intelligence planning.

Deduction Plans: A Basis for Intelligent Backtracking

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000

A proof procedure is described that relies on the construction of certain directed graphs called "deduction plans." Plans represent the structure of proofs in such a way that problem reduction may be used without imposing any ordering on the solution of subproblems, as required by other systems. The structure also allows access to all clauses deduced in the course of a proof, which may then be used as lemmas. Economy of representation is the maximum attainable, consistent with this unrestricted availability of lemmas. Restricted versions of this deduction system correspond to existing linear deduction procedures, but do not suffer from some of their shortcomings, such as redundant representation, strict ordering of subproblems, and explicit substitution. One of the rules for constructing plans, however, allows a subproblem to be factored to a previously solved one: this has no equivalent in existing system. A further economy is obtained by making it unnecessary to perform substitutions and calculate most general unifiers. The source of unification failure can be located when a subproblem is found to be unsolvable, so that exact backtracking can be performed rather than the blind backtracking performed by existing systems. Therefore, a deduction system based on the construction of plans can avoid the wasteful search of irrelevant areas of the search space that results from the usual backtracking methods. Furthermore, because of the graphical structure, it is necessary to remove only the offending parts of the proof when a plan is pruned after backtracking, rather than the entire proof constructed after the cutting point.

Towards a framework to integrate proof search paradigms

2003

Research on automated and interactive theorem proving aims at the mechanization of logical reasoning. Aside from the development of logic calculi it became rapidly apparent that the organization of proof search on top of the calculi is an essential task in the design of powerful theorem proving systems. Different paradigms of how to organize proof search have emerged in that area of research, the most prominent representatives are generally described by the buzzwords: automated theorem proving, tactical theorem proving and ...

Learning while searching in constraint-satisfaction-problems (original) (raw)

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