# Contributions à la résolution générique des problèmes de satisfaction de contraintes

Abstract : We proposed several practical techniques aimed at solving the NP-complete Constraint Satisfaction Problem. We distinguish between two main approaches: search and inference.
We have contributed to the improvement of inference techniques by evolving the central Arc Consistency (AC) property. We contributed to the optimization of the best AC algorithms by exploiting properties of the underlying computer architecture. Modern computers are able to treat 32 or 64 bits in a single elementary operation. As boolean operations are at the heart of AC algorithms, we can exploit the full power of CPU and establish AC up to 64 times faster as before.
We also studied the behaviour of AC on the bounds of the discrete domains. By limiting the inference effort to the bounds of the domain, we obtain a property, called 2B Consistency, that is less powerful than AC, but that can be enforced much faster. Such bound consistencies'' had been previously developped to handle variable domains defined on the real numbers. I have studied the properties of 2B consistency when applied on discrete variable domains. For many practical applications such as scheduling, the tradeoff of filtering power versus speed is pertinent.
It also has permitted to develop additional inference methods stronger than 2B, still focused on the bounds of the domains, that proved to be an excellent alternative to AC on many industrial problems.
My final contibution involves Path Consistency (PC), which is an inference property which is stronger than AC but which takes much more time to enforce it. I studied an interesting alternative to PC: Dual Consistency (DC). This new property leads us to design new algorithms that can establish Path Consistency very efficiently. Path Consistency is also quite space consuming, and requires a lot of memory to be established. A relaxation of PC, Conservative PC, has been developped which avoids this drawback. The same relaxation can be applied to Dual Consistency. I proved that Conservative DC is stronger than Conservative PC, although Conservative DC algorithms are much faster that Conservative PC ones.
Besides, we have tried to improve the classic systematic MAC search algorithm (which uses Arc Consistency as underlying inference property), first by equipping it with Value Ordering Heuristics. We studied how the well known Jeroslow-Wang heuristic from the SAT problem, would behave when applied to the translation of a CSP problem in SAT. Finally, we studied a hybridization between a local search algorithm based on constraint weighting and MGAC, by exploiting the learning abilities of both algorithms.
A new API for the Java language, namely CSP4J, able to solve a CSP as part of any Java application, has been developed as a transversal project and is quickly acquiring maturity. This API is a black box'': as less parameters and expertise are required from a user point of view, which is a crucial component for the wide use of a solver as a component of an industrial project. A solver based on CSP4J took part in International Solver Competitions with promising results.
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https://tel.archives-ouvertes.fr/tel-00262080
Contributor : Julien Vion <>
Submitted on : Monday, March 10, 2008 - 5:17:24 PM
Last modification on : Monday, October 19, 2020 - 11:01:44 AM
Long-term archiving on: : Friday, September 28, 2012 - 11:00:15 AM

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• HAL Id : tel-00262080, version 1

### Citation

Julien Vion. Contributions à la résolution générique des problèmes de satisfaction de contraintes. Autre [cs.OH]. Université d'Artois, 2007. Français. ⟨tel-00262080⟩

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