21 research outputs found
Une heuristique basée sur l'historique des conflits pour les problèmes de satisfaction de contraintes
National audienceL’heuristique de choix de variables est une brique importante pour les algorithmes de résolution du problème de satisfaction de contraintes (CSP). Elle a une influence souvent considérable sur l’efficacité de la recherche et permet, d’une certaine manière, d’exploiter la structure des instances. Dans cet article, nous proposons l’heuristique CHS (pour Conflict-History Search) qui est une heuristique dynamique et adaptative pour la résolution d’instances CSP. Elle repose sur les échecs rencontrés durant la recherche et considère leur temporalité tout au long de la résolution. Une technique d’apprentissage par renforcement est exploitée pour estimer l’évolution de la difficulté des contraintes durant la recherche. Les expérimentations réalisées sur des instances au format XCSP3 permettent de montrer que l’intégration de CHS au sein d’un solveur basé sur l’algorithme MAC s’avère pertinente, conduisant notamment à des résultats meilleurs que ceux obtenusavec des heuristiques de l’état de l’art comme dom/wdeg et ABS
Conflict History Based Branching Heuristic for CSP Solving
International audienceAn important feature in designing algorithms to solve Constraint Satisfaction Problems (CSP) is the definition of a branching heuristic to explore efficiently the search space and exploit the problem structure. We propose Conflict-History Search (CHS), a new dynamic and adaptive branching heuristic for CSP solving. It is based on the search history by considering the temporality of search failures. To achieve that, we use the exponential recency weighted average to estimate the evolution of the hardness of constraints throughout the search. The experimental evaluation on XCSP3 instances shows that integrating CHS to solvers based on MAC obtains competitive results and can improve those obtained through other heuristics of the state of the art
Conflict History based Search for Constraint Satisfaction Problem
International audienc
A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples
We enumerate all circulant good matrices with odd orders divisible by 3 up to
order 70. As a consequence of this we find a previously overlooked set of good
matrices of order 27 and a new set of good matrices of order 57. We also find
that circulant good matrices do not exist in the orders 51, 63, and 69, thereby
finding three new counterexamples to the conjecture that such matrices exist in
all odd orders. Additionally, we prove a new relationship between the entries
of good matrices and exploit this relationship in our enumeration algorithm.
Our method applies the SAT+CAS paradigm of combining computer algebra
functionality with modern SAT solvers to efficiently search large spaces which
are specified by both algebraic and logical constraints
An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem
Although Path-Relinking is an effective local search method for many
combinatorial optimization problems, its application is not straightforward in
solving the MAX-SAT, an optimization variant of the satisfiability problem
(SAT) that has many real-world applications and has gained more and more
attention in academy and industry. Indeed, it was not used in any recent
competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a
new local search algorithm called IPBMR for the MAX-SAT, that remedies the
drawbacks of the Path-Relinking method by using a careful combination of three
components: a new strategy named Path-Breaking to avoid unpromising regions of
the search space when generating trajectories between two elite solutions; a
weak and a strong mutation strategies, together with restarts, to diversify the
search; and stochastic path generating steps to avoid premature local optimum
solutions. We then present experimental results to show that IPBMR outperforms
two of the best state-of-the-art MAX-SAT solvers, and an empirical
investigation to identify and explain the effect of the three components in
IPBMR
A SAT-based Resolution of Lam's Problem
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved
Lam's problem from projective geometry\unicode{x2014}the long-standing
problem of determining if a projective plane of order ten exists. Both the
original search and an independent verification in 2011 discovered no such
projective plane. However, these searches were each performed using highly
specialized custom-written code and did not produce nonexistence certificates.
In this paper, we resolve Lam's problem by translating the problem into Boolean
logic and use satisfiability (SAT) solvers to produce nonexistence certificates
that can be verified by a third party. Our work uncovered consistency issues in
both previous searches\unicode{x2014}highlighting the difficulty of relying
on special-purpose search code for nonexistence results.Comment: To appear at the Thirty-Fifth AAAI Conference on Artificial
Intelligenc
Exponential Recency Weighted Average Branching Heuristic for SAT Solvers
Modern conflict-driven clause-learning SAT solvers routinely solve large real-world instances with millions of clauses and variables in them. Their success crucially depends on effective branching heuristics. In this paper, we propose a new branching heuristic inspired by the exponential recency weighted average algorithm used to solve the bandit problem. The branching heuristic, we call CHB, learns online which variables to branch on by leveraging the feedback received from conflict analysis. We evaluated CHB on 1200 instances from the SAT Competition 2013 and 2014 instances, and showed that CHB solves significantly more instances than VSIDS, currently the most effective branching heuristic in widespread use. More precisely, we implemented CHB as part of the MiniSat and Glucose solvers, and performed an apple-to-apple comparison with their VSIDS-based variants. CHB-based MiniSat (resp. CHB-based Glucose) solved approximately 16.1% (resp. 5.6%) more instances than their VSIDS-based variants. Additionally, CHB-based solvers are much more efficient at constructing first preimage attacks on step-reduced SHA-1 and MD5 cryptographic hash functions, than their VSIDS-based counterparts. To the best of our knowledge, CHB is the first branching heuristic to solve significantly more instances than VSIDS on a large, diverse benchmark of real-world instances