168 research outputs found
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
Quantum-accelerated constraint programming
Constraint programming (CP) is a paradigm used to model and solve constraint
satisfaction and combinatorial optimization problems. In CP, problems are
modeled with constraints that describe acceptable solutions and solved with
backtracking tree search augmented with logical inference. In this paper, we
show how quantum algorithms can accelerate CP, at both the levels of inference
and search. Leveraging existing quantum algorithms, we introduce a
quantum-accelerated filtering algorithm for the global
constraint and discuss its applicability to a broader family of global
constraints with similar structure. We propose frameworks for the integration
of quantum filtering algorithms within both classical and quantum backtracking
search schemes, including a novel hybrid classical-quantum backtracking search
method. This work suggests that CP is a promising candidate application for
early fault-tolerant quantum computers and beyond.Comment: published in Quantu
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
Global Constraint Catalog, 2nd Edition (revision a)
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
Global Constraint Catalog, 2nd Edition
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
Conjunctions of Among Constraints
Many existing global constraints can be encoded as a conjunction of among
constraints. An among constraint holds if the number of the variables in its
scope whose value belongs to a prespecified set, which we call its range, is
within some given bounds. It is known that domain filtering algorithms can
benefit from reasoning about the interaction of among constraints so that
values can be filtered out taking into consideration several among constraints
simultaneously. The present pa- per embarks into a systematic investigation on
the circumstances under which it is possible to obtain efficient and complete
domain filtering algorithms for conjunctions of among constraints. We start by
observing that restrictions on both the scope and the range of the among
constraints are necessary to obtain meaningful results. Then, we derive a
domain flow-based filtering algorithm and present several applications. In
particular, it is shown that the algorithm unifies and generalizes several
previous existing results.Comment: 15 pages plus appendi
Exploiting Global Constraints for Search and Propagation
Résumé
Cette thèse se concentre sur la Programmation par contraintes (PPC), qui est un
paradigme émergent pour résoudre des problèmes complexes d’optimisation combinatoire.
Les principales contributions tournent autour du filtrage des contraintes et de la recherche;
les deux sont des composantes cl´e dans la résolution de problèmes complexes à travers la PPC. D’un côté, le filtrage des contraintes permet de réduire la taille de l’espace de recherche,
d’autre part, la recherche définit la manière dont cet espace sera exploré. Les progrès sur ces
sujets sont essentiels pour élargir l’applicabilité de CP à des problèmes réels.
En ce qui concerne le filtrage des contraintes, les contributions sont les suivantes:
premièrement, on propose une amélioration sur un algorithme existant de la version relaxée
d’une contrainte commune qui apparaît souvent dans les problèmes d’affectation (soft gcc).
L’algorithme proposé améliore en termes de complexité soit pour la cohérence, soit pour le
filtrage et en termes de facilité d’implémentation. Deuxièmement, on introduit une nouvelle
contrainte (soit dure soit relaxée) et les algorithmes de filtrage pour une sous-structure
récurrente qui se produit dans les problèmes d’affectation des ressources hétérogènes
(hierarchical gcc). Nous montrons des résultats encourageants par rapport à une
d´écomposition équivalente basée sur gcc.
En ce qui concerne la recherche, nous présentons tout d’abord les algorithmes pour
compter le nombre de solutions pour deux importantes familles de contraintes: les contraintes
sur les occurrences, par exemple, alldifferent, symmetric alldifferent et gcc,
et les contraintes de séquence admissible, telles que regular. Ces algorithmes sont à la base
d’une nouvelle famille d’heuristiques de recherche, centrées sur les contraintes et basées sur
le d´énombrement. Ces heuristiques extraient des informations sur le nombre de solutions
des contraintes, pour guider la recherche vers des parties de l’espace de recherche qui contiennent
probablement un grand nombre de solutions. Les résultats expérimentaux sur huit
différents problèmes montrent une performance impressionnante par rapport à l’état de l’art
des heuristiques génériques.
Enfin, nous expérimentons une forme forte, déjà connue, de filtrage qui est guidée par
la recherche (quick shaving). Cette technique donne des résultats soit encourageants soit
mauvais lorsqu’elle est appliquée aveuglément à tous les problèmes. Nous avons introduit
un estimateur simple mais très efficace pour activer ou désactiver dynamiquement le quick
shaving; de tests expérimentaux ont montré des résultats très prometteurs.----------Abstract
This thesis focuses on Constraint Programming (CP), that is an emergent paradigm to
solve complex combinatorial optimization problems. The main contributions revolve around
constraint filtering and search that are two main components of CP. On one side, constraint
filtering allows to reduce the size of the search space, on the other, search defines how this
space will be explored. Advances on these topics are crucial to broaden the applicability of
CP to real-life problems.
For what concerns constraint filtering, the contribution is twofold: we firstly propose an
improvement on an existing algorithm of the relaxed version of a constraint that frequently
appears in assignment problems (soft gcc). The algorithm proposed outperforms the previously
known in terms of time-complexity both for the consistency check and for the filtering
and in term of ease of implementiation. Secondly, we introduce a new constraint (both hard
and soft version) and associated filtering algorithms for a recurrent sub-structure that occurs
in assignment problems with heterogeneous resources (hierarchical gcc). We show
promising results when compared to an equivalent decomposition based on gcc.
For what concerns search, we introduce algorithms to count the number of solutions for
two important families of constraints: occurrence counting constraints, such as alldifferent,
symmetric alldifferent and gcc, and sequencing constraints, such as regular. These algorithms
are the building blocks of a new family of search heuristics, called constraint-centered
counting-based heuristics. They extract information about the number of solutions the individual
constraints admit, to guide search towards parts of the search space that are likely to
contain a high number of solutions. Experimental results on eight different problems show
an impressive performance compared to other generic state-of-the-art heuristics.
Finally, we experiment on an already known strong form of constraint filtering that is
heuristically guided by the search (quick shaving). This technique gives mixed results when
applied blindly to any problem. We introduced a simple yet very effective estimator to
dynamically disable quick shaving and showed experimentally very promising results
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