Intelligent search strategies based on adaptive Constraint Handling Rules

The most advanced implementation of adaptive constraint processing with Constraint Handling Rules (CHR) allows the application of intelligent search strategies to solve Constraint Satisfaction Problems (CSP). This presentation compares an improved version of conflict-directed backjumping and two variants of dynamic backtracking with respect to chronological backtracking on some of the AIM instances which are a benchmark set of random 3-SAT problems. A CHR implementation of a Boolean constraint solver combined with these different search strategies in Java is thus being compared with a CHR implementation of the same Boolean constraint solver combined with chronological backtracking in SICStus Prolog. This comparison shows that the addition of ``intelligence'' to the search process may reduce the number of search steps dramatically. Furthermore, the runtime of their Java implementations is in most cases faster than the implementations of chronological backtracking. More specifically, conflict-directed backjumping is even faster than the SICStus Prolog implementation of chronological backtracking, although our Java implementation of CHR lacks the optimisations made in the SICStus Prolog system. To appear in Theory and Practice of Logic Programming (TPLP).Comment: Number of pages: 27 Number of figures: 14 Number of Tables:

Reasoning from Last Conflict(s) in Constraint Programming

International audienceConstraint programming is a popular paradigm to deal with combinatorial problems in arti cial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but su er from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classi ed into look-ahead (constraint propagation and search heuristics) and look-back (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conicts and, as a side e ect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conict, 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 conict. Experiments over a wide range of benchmarks demonstrate the e ectiveness of this approach in both constraint satisfaction and automated arti cial intelligence planning

Maintaining Soft Arc Consistency in BnB-ADOPT+ During Search

Gutierrez and Meseguer show how to enforce consistency in BnB-ADOPT + for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforcing consistency in these subproblems can cause further search space reduction. We introduce efficient methods to maintain soft arc consistencies in every subproblem during search, a non trivial task due to asynchronicity and induced overheads. Experimental results show substantial benefits on three different benchmarks. © 2013 Springer-Verlag.The work of Gutierrez and Meseguer was partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya 2009-SGR-1434.Peer Reviewe

Lazy Repairing Backtracking for Dynamic Constraint Satisfaction Problems

Extended Partial Dynamic Backtracking (EPDB) is a repair algorithm based on PDB. It deals with Dynamic CSPs based on ordering heuristics and retroactive data structures, safety conditions, and nogoods which are saved during the search process. In this paper, we show that the drawback of both EPDB and PDB is the exhaustive verification of orders, saved in safety conditions and nogoods, between variables. This verification affects remarkably search time, especially since orders are often indirectly deduced. Therefore, we propose a new approach for dynamically changing environments, the Lazy Repairing Backtracking (LRB), which is a fast version of EPDB insofar as it deduces orders directly through the used ordering heuristic. We evaluate LRB on various kinds of problems, and compare it, on the one hand, with EPDB to show its effectiveness compared to this approach, and, on the other hand, with MAC-2001 in order to conclude, from what perturbation rate resolving a DCSP with an efficient approach can be more advantageous than repair

A constraint-based framework for configuration

The research presented here aims at providing a comprehensive framework for solving configuration problems, based on the Constraint Satisfaction paradigm. This thesis is addressing the two main issues raised by a configuration task: modeling the problem and solving it efficiently. Our approach subsumes previous approaches, incorporating both Simplification and further extension, offering increased representational power and efficiency. Modeling. We advance the idea of local, context independent models for the types of objects in the application domain, and show how the model of an artifact can be built as a composition of local models of the constituent parts. Our modeling technique integrates two mechanisms for dealing with complexity, namely composition and abstraction. Using concepts such as locality, aggregation and inheritance, it offers support and guidance as to the appropriate content and organization of the domain knowledge, thus making knowledge specification and representation less error prone, and knowledge maintenance much easier. There are two specific aspects which make modeling configuration problems challenging: the complexity and heterogeneity of relations that must be expressed, manipulated and maintained, and the dynamic nature of the configuration process. We address these issues by introducing Composite Constraint Satisfaction Problems, a new, nonstandard class of problems which extends the classic Constraint Satisfaction paradigm. Efficiency. For the purpose of the work presented here, we are only interested in providing a guaranteed optimal solution to a configuration problem. To achieve this goal, our research focused on two complementary directions. The first one led to a powerful search algorithm called Maintaining Arc Consistency Extended (MACE). By maintaining arc consistency and taking advantage of the problem structure, MACE turned out to be one of the best general purpose CSP search algorithms to date. The second research direction aimed at reducing the search effort involved in proving the optimality of the proposed solution by making use of information which is specific to individual configuration problems. By adding redundant specialized constraints, the algorithm improves dramatically the lower bound computation. Using abstraction through focusing only on relevant features allows the algorithm to take advantage of context-dependent interchangeability between component instances and discard equivalent solutions, involving the same cost as solutions that have already been explored