Thierry Petit

• Ph.D
• Researcher at IMT Atlantique, Nantes

Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions and problem-specific desires that may only be discovered or articulated by the user after further analysis of solver output. We propose a general framewo...

Constraint Programming (CP) users need significant expertise in order to model their problems appropriately, notably to select propagators and search strategies. This puts the brakes on a broader uptake of CP. In this paper, we introduce MICE, a complete Java CP modeler that can use any Mixed Integer Linear Programming (MILP) solver as a solution t...

In biology, the construction of plasmids is a routine technique, yet under-optimal, expensive and time-consuming. In this paper, we model the Plasmid Cloning Problem (PCP) in constraint programing, in order to optimize the construction of plasmids. Our technique uses a new propagator for the AtMostNVector constraint. This constraint allows the desi...

This paper is originally motivated by an application where the objective is to generate a video summary, built using intervals extracted from a video source. In this application, the constraints used to select the relevant pieces of intervals are based on Allen’s algebra. The best state-of-the-art results are obtained with a small set of ad hoc sol...

La programmation par contraintes (PPC) a pour objet de résoudre des problèmes ayant une structure combinatoire, qui impliquent des contraintes de formes diverses. Les outils de PPC sont génériques et composables. Ils peuvent facilement être hybridés avec d’autres technologies. Depuis son apparition dans les années soixante-dix, la PPC a suscité un...

Energetic Reasoning (ER) is a powerful filtering algorithm for the Cumulative constraint. Unfortunately, ER is generally too costly to be used in practice. One reason of its bad behavior is that many intervals are considered as relevant, although most of them should be ignored. In the literature, heuristic approaches have been developed in order to...

This paper investigates cumulative scheduling in uncertain environments, using constraint programming. We present a new declarative characterization of robustness, which preserves solution quality. We highlight the significance of our framework on a crane assignment problem with business constraints.

We investigate cumulative scheduling in uncertain environments, using constraint programming. We detail in this paper the dynamic sweep filtering algorithm of the FlexC global constraint.

Scalability becomes more and more critical to decision support technologies. In order to address this issue in Constraint Programming, we introduce the family of self-decomposable constraints. These constraints can be satisfied by applying their own filtering algorithms on variable subsets only. We introduce a generic framework which dynamically de...

Energetic Reasoning (ER) is a powerful filtering algorithm for the Cumulative constraint. Unfortunately, ER is generally too costly to be used in practice. One reason of its bad behavior is that many intervals are considered as relevant by the checker of ER, although most of them should be ignored. In this paper, we provide a sharp characterization...

The FOCUS constraint expresses the notion that solutions are concentrated. In practice, this constraint suffers from the rigidity of its semantics. To tackle this issue, we propose three generalizations of the FOCUS constraint. We provide for each one a complete filtering algorithm as well as discussing decompositions.

Many Constraint Programming models use integer cost variables aggregated in an objective criterion. In this context, some constraints involving exclusively cost variables are often imposed. Such constraints are complementary to the objective function. They characterize the solutions which are acceptable in practice. This paper deals with the case w...

We propose a new definition for characterizing levels of consistency. A perspective is to provide new tools for classifying filtering algorithms, including incomplete algorithms based on the semantics of constraints.

This paper gives an O(n log n) bound-consistency filtering algorithm for the conjunction alldifferent(V0, V1,⋯, V n-1) A f(V0) ⊕ f(V1) ⊕ ··· ⊕ f(Vn-1) ≤ cst, (V0, V1,⋯, Vn-1, cst ∈ N+), where (ℕ, ⊕) is a commutative group, f is a unary function, and both ⊕; and f are monotone increasing. This complexity is equal to the complexity of the bound-consi...

This paper introduces the SEQ BIN meta-constraint with a polytime algorithm achieving general- ized arc-consistency according to some properties. SEQ BIN can be used for encoding counting con- straints such as CHANGE, SMOOTH or INCREAS- ING NVALUE. For some of these constraints and some of their variants GAC can be enforced with a time and space co...

Given a sequence of variables X = 〈x 0, x 1, …, x n − 1 〉, we consider the IncreasingSum constraint, which imposes ∀ i ∈ [0, n − 2] x i ≤ x i + 1, and \(\sum_{x_i \in X} x_i = s\). We propose an Θ(n) bound-consistency algorithm for IncreasingSum.

Many cumulative problems are such that the horizon is fixed and cannot be delayed. In this situation, it often occurs that all the activities cannot be scheduled without exceeding the capacity at some points in time. Moreover, this capacity is not necessarily always the same during the scheduling period. This article introduces a new constraint for...

This paper introduces the SEQ BIN meta-constraint with a polytime algorithm achieving generalized arc-consistency. SEQ BIN can be used for encoding counting constraints such as CHANGE, SMOOTH, or INCREASING NVALUE. For all of them the time and space complexity is linear in the sum of domain sizes, which improves or equals the best known results of...

Constraint toolkits generally propose a sum constraint where a global objective variable should be equal to a sum of local objective variables, on which bound-consistency is achieved. To solve optimization problems this propagation is poor. Therefore, ad-hoc techniques are designed for pruning the global objective variable by taking account of the...

This article deals with the resolution of over-constrained problems us- ing constraint programming, which often imposes to add to the constraint network new side constraints. These side constraints control how the ini- tial constraints of the model should be satised or violated, to obtain solutions that have a practical interest. They are specic to...

In this paper we introduce a new cardinality constraint: Ordered Distribute. Given a set of variables, this constraint limits for each value v the number of times v or any value greater than v is taken. It extends the global cardinality constraint, that constrains only the number of times a value v is taken by a set of variables and does not consid...

This paper introduces the Increasing_Nvalue constraint, which restricts the number of distinct values assigned to a sequence of variables so that each variable in the sequence is less than or equal to its successor. This constraint is a specialization of the Nvalue constraint, motivated by symmetry breaking. Propagating the Nvalue constraint is kno...

Cet article introduit la contrainte Increasing NValue, qui restreint le nombre de valeurs distinctes affectées à une séquence de variables, de sorte que chaque variable de la séquence soit inférieure ou égale à la variable la succédant immédiatement. Cette contrainte est une spécialisation de la contrainte NValue, motivée par le besoin de casser de...

This paper presents the constraint class seq bin(N;X;C;B) where N is an integer variable, X is a sequence of integer variables and C and B are two binary constraints. A constraint of the seq bin class enforces the two following conditions: (1) N is equal to the number of times that the constraint C is satised on two consecutive variables in X, and...

We study under what conditions bound consistency (BC) and arc consistency (AC), two forms of prop- agation used in constraint solvers, are equivalent to each other. We show that they prune exactly the same values when the propagated constraint is con- nected row convex / closed under median and its complement is row convex. This characterization is...

This research report presents an extension of Cumulative of Choco constraint solver, which is useful to encode over-constrained cumulative problems. This new global constraint uses sweep and task interval violation-based algorithms.

This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of const...

Non disponible

Partial constraint satisfaction [5] was widely studied in the 90's, and notably Max-CSP solving algorithms [21, 20, 1, 10]. These algo-rithms compute a lower bound of violated constraints without using prop-agation. Therefore, recent methods focus on the exploitation of propaga-tion mechanisms to improve the solving process. Soft arc-consistency al...

Dans le but d’accélérer la résolution d’un CSP, nous nous intéressons au problème consistant à modifier l’ordre sur les valeurs qui est induit par la définition de chaque domaine. Nous discutons de l’intérêt de cette technique de reformulation et définissons les problèmes pertinents. Nous montrons qu’on peut trouver un ordre rendant un réseau de co...

This article shows the advantages of a variable-based framework for solving over-constrained problems with practicability constraints. The case-study is a cumulative scheduling problem with over-loads.

So as to speed up the task of solving a CSP, we study the problem consisting of modifying the order on values which is induced by the definition of each domain. We discuss the usefulness of this reformulation technique and define the relevant problems. We show that one can find an order which makes a constraint network monotonic (if any) in polynom...

The catalogue of global constraints is reviewed, focusing on the graph-based de- scription of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area.

Finding a constraint network that will be efficiently solved by a constraint solver requires a strong ex- pertise in Constraint Programming. Hence, there is an increasing interest in automatic reformulation. This paper presents a general framework for learn- ing implied global constraints in a constraint net- work assumed to be provided by a non-ex...

This article presents a basic scheme for deriving systematically a filtering algorithm from the graph properties based representation of global constraints. This scheme is based on the bounds of the graph parameters used in the description of a global constraint. The article provides bounds for the most common used graph parameters.

This article presents a generic filtering scheme, based on th e graph de- scription of global constraints. This description is define d by a network of binary constraints and a list of elementary graph properties: each solution of the global constraint corresponds to a subgraph of the initial network, retaining only the sat- isfied binary constrain...

Cet article présente un schéma de filtrage générique, basé sur la description de contraintes globales sous la forme de propriétés de graphes. Cette description est définie par un réseau de contraintes binaires et une liste de propriétés de graphe élémentaires : chaque solution de la contrainte globale correspond à un sous-graphe du réseau initial,...

Graph-Properties Based Filtering

Cet article présente un schéma de filtrage générique, basé sur la description de contraintes globales sous la forme de propriétés de graphes. Cette description est définie par un réseau de contraintes binaires et une liste de propriétés de graphe élémentaires : chaque solution de la contrainte globale correspond à un sous-graphe du réseau initial,...

This article deals with global constraints for which the set of solu- tions can be recognized by an extended nite automaton whose size is bounded by a polynomial in n, where n is the number of variables of the corresponding global constraint. By reducing the automaton to a conjunction of signature and transition constraints we show how to systemati...

This report presents a basic scheme,for deriving systematically a ltering algorithm from the graph properties based representation of global constraints. This scheme,is based on the bounds of the graph characteristics used in the description of a global constraint. The report provides bounds,for the most common,used graph characteristics.

This paper presents a technique for learning parameterized implied constraints. They can be added to a model to improve the solving process. Exper- iments on implied Gcc constraints show the interest of our approach.

This short paper presents a basic scheme for deriving systematically a filtering algorithm from the graph properties based representation of global constraints. This scheme is based on the bounds of the graph characteristics used in the description of a global constraint. The article provides bounds for the most common used graph characteristics.

http://www710.univ-lyon1.fr/~csolnon

http://www710.univ-lyon1.fr/~csolnon

This article deals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in n, where n is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction of signature and transition constraints we show how to syst...

This paper shows that existing denitions of costs associated with soft global constraints are not sucien t to deal with all the usual global constraints. We propose more expressive denitions: rene d variable- based cost, object-based cost and graph properties based cost. For the rst two ones we provide ad-hoc algorithms to compute the cost from a c...

A Max-CSP consists of searching for a solution which minimizes the number of violated constraints. The best existing solving algorithm is PFC-MRDAC. It is based on the computation of a lower bound of the number of violations. To compute this lower bound it is required to evaluate the violations with respect to each value of each domain. Unfortunate...

A Max-CSP consists of searching for a solution which minimizes the number of violated constraints. The best existing solving algorithm is PFC-MRDAC. It is based on the computation of a lower bound of the number of violations. To compute this lower bound it is required to evaluate the violations with respect to each value of each domain. Unfortunate...

In recent years, many works have been carried out to solve over-constrained problems, and more specically the Maximal Constraint Satisfaction Problem (Max-CSP), where the goal is to minimize the number of constraint violations. Some lower bounds on this number of violations have been proposed in the literature. In this paper, we characterize the co...

In recent years, many constraint-specific filtering algorithms have been introduced. Such algorithms use the semantics of the constraint to perform filtering more eciently than a generic algorithm. The usefulness of such methods has been widely proven for solving constraint satisfaction problems. In this paper, we extend this concept to overconstra...

In recent years, many works have been carried out to solve over-constrained problems, and more speci cally the Maximal Constraint Satisfaction Problem (Max-CSP), where the goal is to minimize the number of constraint violations. Some lower bounds on this number of violations have been proposed in the literature.

In this paper we present a new framework for over constrained problems. We suggest to define an over-constrained network as a global constraint. We introduce two new lower bounds of the number of violations, without making any assumption on the arity of constraints.

Constraint programming techniques are widely used to solve real-world problems. It often happens that such problems are over-constrained and do not have any solution. In such a case, the goal is to find a good compromise. A simple theoretical framework is the Max-CSP, where the goal is to minimize the number of constraint violations. However, in re...

Encoding real-world problems often leads to dene over constrained networks, which do not have any solution that satises all the constraints. In this situation the goal is to nd the best compromise. One of the most well-known theoretical frameworks for over constrained problems is the Maximal Constraint Satisfaction Problem (Max-CSP). In a MaxCSP, t...

Ces derniËres annÈes, de nombreux algorithmes de filtrage basÈs sur la sÈmantique des contraintes ont ÈtÈ proposÈs. Leur intÈrêt s'est avÈrÈ crucial pour la rÈsolution des problËmes de satisfaction de contraintes (CSP). Dans ce papier, nous Ètendons ce concept aux problËmes sur-contraints. Nous proposons de prendre en compte la sÈmantique d'une con...

In recent years, many works have been carried out to solve over-constrained problems, and more specifically the Maximal Constraint Satisfaction Problem (Max-CSP), where the goal is to minimize the number of constraint violations. Some lower bounds on this number of violations have been proposed in the literature.In this paper, we characterize the c...

In recent years, many constraint-specific filtering algorithms have been introduced. Such algorithms use the semantics of the constraint to perform filtering more efficiently than a generic algorithm. The usefulness of such methods has been widely proven for solving constraint satisfaction problems. In this paper, we extend this concept to over-con...

Constraint programming techniques are widely used to solve real-world problems. It often happens that such problems are over-constrained and do not have any solution. In such a case, the goal is to find a good compromise. A simple theoretical framework is the Max-CSP, where the goal is to minimize the number of constraint violations. However, in re...

In this paper we present a new framework for over constrained problems. We suggest to define an over-constrained network as a global constraint. We introduce two new lower bounds of the number of violations, without making any assumption on the arity of constraints.

This report presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use dierent levels of consistency for dierent subsets of constraint...

When a problem has no solution satisfying all constraints, the issue is to provide solutions that remain acceptable in practice despite some violations of constraints. This technical report analyzes the e- ciency of using global constraints to express practicability criteria, trough a case-study of cumulative scheduling problems. When resources are...

This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use dierent levels of consistency for dierent subsets of constrain...

Global constraints involving cost variables provide an expres- sive modelling tool for optimization problems. These constraints are used to characterize solutions which have a practical interest. When costs rep- resent undesirable quantities, e.g., over-loads of resource in a scheduling cumulative problem, their values are generally totally ordered...