Maher Helaoui | University of Tunis El Manar (original) (raw)

Papers by Maher Helaoui

Several combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSP... more Several combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSPs) where constraints are defined through the use of valuation functions to reflect degrees of coherence. The goal is to find an assignment of values to variables with an overall finite and optimal valuation. Despite the NP-hardness of this task, tractable versions can be obtained by forcing the allowable valuation functions to have specific features. This is the case, for instance, of VCSPs with binary and submodular valuation functions . In this paper, we are concerned with a problem generalizing submodular binary VCSP, which we will call permuted submodular binary VCSP. The latter problem is obtained by independently applying permutations on the domains of submodular binary VCSP. We show that VCSP instances built from permuted submodular binary functions satisfying an extra condition can be identified in O(n 2 d 4 ) steps and solved, by means of the algorithm used for submodular binary VCSPs [2], in O(n 3 d 3 ) steps, where n is the number of variables and d is the size of the largest domain.

Valued Constraint Satisfaction Problems (VCSPs) can model many com-binatorial problems. VCSPs tha... more Valued Constraint Satisfaction Problems (VCSPs) can model many com-binatorial problems. VCSPs that involve submodular valuation functions only is a particular class of VCSPs that have the advantage of being tractable. In this pa-per, we propose a problem decomposition strategy for binary VCSPs which con-sists in decomposing the problem to be solved into a set of submodular, and then tractable, subproblems. The decomposition strategy combines two problem solving techniques, namely domain partitioning and value permutation.

Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, 2017

Proceedings of the 10th International Conference on Operations Research and Enterprise Systems, 2021

To better model several artificial intelligence and combinatorial problems, classical Constraint ... more To better model several artificial intelligence and combinatorial problems, classical Constraint Satisfaction Problems (CSP) have been extended by considering soft constraints in addition to crisp ones. This gave rise to a Valued Constraint Satisfaction Problems (VCSP). Several real-world artificial intelligence and combinatorial problems require more than one single objective function. In order to present a more appropriate formulation for these real-world problems, a generalization of the VCSP framework called Multi-Objective Valued Constraint Satisfaction Problems (MOVCSP) has been proposed. This paper addresses combinatorial optimization problems that can be expressed as MOVCSP. Despite the NP-hardness of general MOVCSP, we can present tractable versions by forcing the allowable valuation functions to have specific mathematical properties. This is the case for MOVCSP whose dual is a binary MOVCSP with crisp binary valuation functions only and with a weak form of Neighbourhood Substitutable Valuation Functions called Directional Substitutable Valuation Functions.

Proceedings of the 11th International Conference on Agents and Artificial Intelligence, 2019

A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize... more A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize a wide range of applications related to Combinatorial Optimization and Artificial Intelligence. Most researchers have focused on the development of algorithms for solving mono-objective problems. However, many real-world satisfaction/optimization problems involve multiple objectives that should be considered separately and satisfied/optimized simultaneously. Solving a Multi-Objective Optimization Problem (MOP) consists of finding the set of all non-dominated solutions, known as the Pareto Front. In this paper, we introduce multi-objective valued constraint satisfaction problem (MO-VCSP), that is a VCSP involving multiple objectives, and we extend soft local arc consistency methods, which are widely used in solving Mono-Objective VCSP, in order to deal with the multi-objective case. Also, we present multi-objective enforcing algorithms of such soft local arc consistencies taking into account the Pareto principle. The new Pareto-based soft arc consistency (P-SAC) algorithms compute a Lower Bound Set of the efficient frontier. As a consequence, P-SAC can be integrated into a Multi-Objective Branch and Bound (MO-BnB) algorithm in order to ensure its pruning efficiency.

Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, 2017

The shortest path problem is one of the classic problems in graph theory. The problem is to provi... more The shortest path problem is one of the classic problems in graph theory. The problem is to provide a solution algorithm returning the optimum route, taking into account a valuation function, between two nodes of a graph G. It is known that the classic shortest path solution is proved if the set of valuation is R or a subset of R and the combining operator is the classic sum (+). However, many combinatorial problems can be solved by using shortest path solution but use a set of valuation not a subset of R and/or a combining operator not equal to the classic sum (+). For this reason, relations between particular valuation structure as the semiring and diod structures with graphs and their combinatorial properties have been presented. On the other hand, if the set of valuation is R or a subset of R and the combining operator is the classic sum (+), a longest path between two given nodes s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. In this paper, in order to give a general model that can be used for any valuation structure we propose to model both the valuations of a graph G and the combining operator by a valuation structure S. We discuss the equivalence between longest path and shortest path problem given a valuation structure S. And we present a generalization of the shortest path algorithms according to the properties of the graph G and the valuation structure S. As many combinatorial problems can be solved by using shortest path solution but use a set of valuation 306 Helaoui M. Extended Shortest Path Problem-Generalized Dijkstra-Moore and Bellman-Ford Algorithms.

Annals of Mathematics and Artificial Intelligence, 2013

ABSTRACT This paper addresses combinatorial problems that can be expressed as Valued Constraint S... more ABSTRACT This paper addresses combinatorial problems that can be expressed as Valued Constraint Satisfaction Problems (VCSPs). In the VCSP framework, the constraints are defined by valuation functions to reflect several constraint violation levels. Despite the NP-hardness of VCSPs, tractable versions can be obtained by forcing the allowable valuation functions to have specific mathematical properties. This is the case of VCSPs with submodular valuation functions only. In this paper, we propose a problem decomposition scheme for binary VCSPs that takes advantage of modular valuation functions even when the studied problem is not limited to these functions. Modular functions are less frequent than submodular ones but, in compensation, they are easier to process. The proposed scheme works within a backtrack-based search and consists in decomposing the original problem into a set of modular, and then tractable, subproblems. Our decomposition scheme is distinguished by the possibility of instantiating variables by assigning to them subsets of values instead of single values.

International Journal on Artificial Intelligence Tools, 2013

Many combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSPs).... more Many combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSPs). In this framework, the constraints are defined by means of valuation functions to reflect several degrees of coherence. Despite the NP-hardness of the VCSP, tractable versions can be obtained by forcing the allowable valuation functions to have specific features. This is the case for submodular VCSPs, i.e. VCSPs that involve submodular valuation functions only. In this paper, we propose a problem decomposition scheme for binary VCSPs that takes advantage of submodular functions even when the studied problem is not submodular. The proposed scheme consists in decomposing the problem to be solved into a set of submodular, then tractable, subproblems. The decomposition scheme combines two techniques that where already used in the framework of constraint-based reasoning, but in separate manner. These techniques are domain partitioning and value permutation.

Proceedings of the 11th International Conference on Agents and Artificial Intelligence, Oct 14, 2019

La notion de substituabilite directionnelle est uneforme faible de la substituabilite de voisin... more La notion de substituabilite directionnelle est uneforme faible de la substituabilite de voisinage [6] quia ete proposee dans [17] pour ameliorer la resolutionde problemes de satisfaction de contraintes (CSP)binaires. On part du fait que me^me si deux valeurs nesont pas voisinage substituables, elles peuvent l'e^tre sion restreint le voisinage en se referant a un ordre surles variables. La substituabilitedirectionnelle permet dedecomposer les domaines de valeurs des variables ende sous-ensembles de valeurs qui peuvente^tre essayeessimultanement lors de la resolution du probleme par unalgorithme du type\ Backtracking ".Dans le present article, nous proposons deux extensionsau travail presentedans [17] :{ Tout d'abord, nous generalisons davantage la no-tion de substituabilite directionnelle en conside-rant, comme reference, une orientation du graphed'inconsistance au lieu d'un ordre sur les variables.{ Ensuite, nous introduisons des condi...

La \emph{Logique Mathématique} est une branche puissante et fondamentale de l'\emph{Informati... more La \emph{Logique Mathématique} est une branche puissante et fondamentale de l'\emph{Informatique Théorique}. Elle se divise en plusieurs \emph{sous-domaines}. Chaque sous-domaine est une théorie qui présente une modélisation mathématique profitant des nouveautés Informatique.\\ Nous présentons dans ce travail: - la notion de déduction, le calcul propositionnel et de prédicats. - les opérations des ensembles et une bijection qui, pour chaque élément des formalismes logiques vus précédemment, présente une image dans les opérations des ensembles.

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-485-5, pages 218-225. , 2021

In Proceedings of the 11th International Conference on Agents and Artificial Intelligence (ICAART 2019) - Volume 2, pages 294-305, 2019

A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize... more A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize a wide range of applications related to Combinatorial Optimization and Artificial Intelligence. Most researchers have focused on the development of algorithms for solving mono-objective problems. However, many real-world satisfaction/optimization problems involve multiple objectives that should be considered separately and satisfied/optimized simultaneously. Solving a Multi-Objective Optimization Problem (MOP) consists of finding the set of all non-dominated solutions, known as the Pareto Front.
In this paper, we introduce multi-objective valued constraint satisfaction problem (MO-VCSP), that is a VCSP involving multiple objectives, and we extend soft local arc consistency methods, which are widely used in solving Mono-Objective VCSP, in order to deal with the multi-objective case. Also, we present multi-objective enforcing algorithms of such soft local arc consistencies taking into account the Pareto principle. The new Pareto-based soft arc consistency (P-SAC) algorithms compute a Lower Bound Set of the efficient frontier. As a consequence, P-SAC can be integrated into a Multi-Objective Branch and Bound (MO-BnB) algorithm in order to ensure its pruning efficiency.

Several combinatorial problems can be formulated as valued constraint satisfaction problems (VCSP... more Several combinatorial problems can be formulated as valued constraint satisfaction problems (VCSP) where constraints are defined through the use of valuation functions to reflect degrees of coherence. The goal is to find an assignment of values to variables with an overall optimal valuation, a computationally fastidious task especially for large problems. This article presents a domain decomposition method for solving binary VCSPs based on the class of modular functions. The decomposition pro-cess yields subproblems whose valuation functions are exclusively mod-ular. For such VCSPs, we propose a O(ed 2) identification algorithm and a O(ed) solution algorithm.

The shortest path problem is one of the classic problems in graph theory. The problem is to provi... more The shortest path problem is one of the classic problems in graph theory. The problem is to provide a solution algorithm returning the optimum route, taking into account a valuation function, between two nodes of a graph G. It is known that the classic shortest path solution is proved if the set of valuation is IR or a subset of IR and the combining operator is the classic sum (+). However, many combinatorial problems can be solved by using shortest path solution but use a set of valuation not a subset of IR and/or a combining operator not equal to the classic sum (+). For this reason, relations between particular valuation structure as the semiring and diod structures with graphs and their combinatorial properties have been presented. On the other hand, if the set of valuation is IR or a subset of IR and the combining operator is the classic sum (+), a longest path between two given nodes s and t in a weighted graph G is the same thing as a shortest path in a graph -G derived from G by changing every weight to its negation. In this paper, in order to give a general model that can be used for any valuation structure we propose to model both the valuations of a graph G and the combining operator by a valuation structure S. We discuss the equivalence between longest path and shortest path problem given a valuation structure S. And we present a generalization of the shortest path algorithms according to the properties of the graph G and the valuation structure S.

La \emph{\textbf{Logique Mathématique}}, la \emph{\textbf{Théorie des Graphes}} et la \emph{\text... more La \emph{\textbf{Logique Mathématique}}, la \emph{\textbf{Théorie des Graphes}} et la \emph{\textbf{Théorie des Langages}} sont trois branches puissantes et fondamentales de l'\emph{Informatique Théorique}.\\ \begin{itemize} \item \textbf{La première: la \emph{Logique Mathématique}} se divise en plusieurs \emph{sous-domaines}. Chaque sous-domaine est une théorie qui présente une modélisation mathématique profitant des nouveautés Informatique.\\ Depuis sa naissance à la fin du XIXeˋmeXIX^{ème}XIXeˋme siècle, la logique mathématique n'a pas cessé de résoudre la crise des fondements provoquée par la complexification des mathématiques et l'apparition des paradoxes.\\ Elle nous offre une \emph{modélisation} et une \emph{formalisation mathématiques} puissantes et riches profitant des \emph{systèmes logiques}.\\ \item \textbf{La seconde: la \emph{Théorie des Graphes}} propose des solutions algorithmiques pour résoudre des problèmes dans tous les domaines liés à: \begin{itemize} \item la no...

International Journal on Artificial Intelligence Tools, 2013

ABSTRACT Many combinatorial problems can be formulated as Valued Constraint Satisfaction Problems... more ABSTRACT Many combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSPs). In this framework, the constraints are defined by means of valuation functions to reflect several degrees of coherence. Despite the NP-hardness of the VCSP, tractable versions can be obtained by forcing the allowable valuation functions to have specific features. This is the case for submodular VCSPs, i.e. VCSPs that involve submodular valuation functions only. In this paper, we propose a problem decomposition scheme for binary VCSPs that takes advantage of submodular functions even when the studied problem is not submodular. The proposed scheme consists in decomposing the problem to be solved into a set of submodular, then tractable, subproblems. The decomposition scheme combines two techniques that where already used in the framework of constraint-based reasoning, but in separate manner. These techniques are domain partitioning and value permutation.

Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, 2017

Proceedings of the 10th International Conference on Operations Research and Enterprise Systems, 2021

Proceedings of the 11th International Conference on Agents and Artificial Intelligence, 2019

Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, 2017

Annals of Mathematics and Artificial Intelligence, 2013

International Journal on Artificial Intelligence Tools, 2013

Proceedings of the 11th International Conference on Agents and Artificial Intelligence, Oct 14, 2019

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-485-5, pages 218-225. , 2021

In Proceedings of the 11th International Conference on Agents and Artificial Intelligence (ICAART 2019) - Volume 2, pages 294-305, 2019

A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize... more A valued constraint satisfaction problem (VCSP) is a soft constraint framework that can formalize a wide range of applications related to Combinatorial Optimization and Artificial Intelligence. Most researchers have focused on the development of algorithms for solving mono-objective problems. However, many real-world satisfaction/optimization problems involve multiple objectives that should be considered separately and satisfied/optimized simultaneously. Solving a Multi-Objective Optimization Problem (MOP) consists of finding the set of all non-dominated solutions, known as the Pareto Front.
In this paper, we introduce multi-objective valued constraint satisfaction problem (MO-VCSP), that is a VCSP involving multiple objectives, and we extend soft local arc consistency methods, which are widely used in solving Mono-Objective VCSP, in order to deal with the multi-objective case. Also, we present multi-objective enforcing algorithms of such soft local arc consistencies taking into account the Pareto principle. The new Pareto-based soft arc consistency (P-SAC) algorithms compute a Lower Bound Set of the efficient frontier. As a consequence, P-SAC can be integrated into a Multi-Objective Branch and Bound (MO-BnB) algorithm in order to ensure its pruning efficiency.

The shortest path problem is one of the classic problems in graph theory. The problem is to provi... more The shortest path problem is one of the classic problems in graph theory. The problem is to provide a solution algorithm returning the optimum route, taking into account a valuation function, between two nodes of a graph G. It is known that the classic shortest path solution is proved if the set of valuation is IR or a subset of IR and the combining operator is the classic sum (+). However, many combinatorial problems can be solved by using shortest path solution but use a set of valuation not a subset of IR and/or a combining operator not equal to the classic sum (+). For this reason, relations between particular valuation structure as the semiring and diod structures with graphs and their combinatorial properties have been presented. On the other hand, if the set of valuation is IR or a subset of IR and the combining operator is the classic sum (+), a longest path between two given nodes s and t in a weighted graph G is the same thing as a shortest path in a graph -G derived from G by changing every weight to its negation. In this paper, in order to give a general model that can be used for any valuation structure we propose to model both the valuations of a graph G and the combining operator by a valuation structure S. We discuss the equivalence between longest path and shortest path problem given a valuation structure S. And we present a generalization of the shortest path algorithms according to the properties of the graph G and the valuation structure S.

International Journal on Artificial Intelligence Tools, 2013

L’Homme a utilisé l’algorithmique depuis l’époque des Babyloniens et l’écriture cunéiforme sur le... more L’Homme a utilisé l’algorithmique depuis l’époque des Babyloniens et l’écriture cunéiforme sur les pierres. Avec le français Blaise Pascal en 1642, il a commencé à inventer des machines pour exécuter les algorithmes. Alain Turing en 1937 a présenté une machine
virtuelle intitulée la machine de Turing qui a servi pour la conception d’une architecture de base pour les ordinateurs. La machine RAM a été utilisée par la suite comme modèle de base pour la conception des architectures des ordinateurs. L’évolution technologique lors de la construction des ordinateurs a permis la construction des ordinateurs avec un processeur multi-cœurs ou même des ordinateurs multi-processeurs.
Cet ouvrage cherche à étudier la notion de parallélisme dans la modélisation des architectures des ordinateurs multi-cœurs ou multi-processeurs. Quel est le modèle de l’architecture multi-processeurs ou multi-cœurs optimale ?
En effet, l’objectif de ce document est de fournir au lecteur les outils pour
{ Comprendre l’architecture des machines parallèles ;
{ L’inviter et l’encourager à modéliser une nouvelle architecture pour les machines parallèles ou à faire évoluer une architecture existante ;
{ Etre capable à programmer de manière optimale sur les machines parallèles.
Ainsi, le premier Chapitre sera dédié à introduire la notion de parallélisme et calcul de haute performance afin de familiariser le lecteur aux notions de parallélisme et de le sensibiliser à l’utilité de comprendre les architectures parallèles existantes et de l’inviter à les optimiser et les mieux utiliser en adoptant une programmation adaptée au parallèlisme.
Dans un deuxième Chapitre, nous allons étudier les architectures des machines parallèles.
Le lecteur est invité à une réflexion sur les axes de modéliser de nouvelles architectures plus optimales. Dans le troisième Chapitre, afin de pouvoir exploiter l’évolution technologique des machines parallèles, et de la possibilité de communiquer, par internet, un nombre très grand d’ordinateurs et de téléphones pour résoudre le même problème P, le lecteur sera invité à programmer de manière optimale sur les machines parallèles disponibles.

Le rôle d'un développeur SL diffère selon son degrés d'expertise. Un développeur expert, connu, s... more Le rôle d'un développeur SL diffère selon son degrés d'expertise. Un développeur expert, connu, son rôle sera principalement de répondre aux exigences clients : besoins fonctionnels et techniques. Cette opération passera souvent par déduction de ces exigences suite un ensemble de réunion avec les acteurs ``utilisateurs" de la solution SL à produire.

Le rôle d'un développeur SL débutant, comme votre cas, en absence de portefeuille clients, est encore plus difficile qu'un développeur SL confirmé. Vous êtes invités à développer des solutions SL distinguées, capables à attirer un portefeuille clients. Pour ce faire, vous êtes sensés vous distinguer à travers des solutions innovantes et originales. Vous êtes invités à identifier un problème mathcalP\mathcal{P}mathcalP pour un, éventuel, portefeuille clients mathcalC\mathcal{C}mathcalC et produire une solution SL mathcalA\mathcal{A}mathcalA à partir d'un ensemble de données récolté mathcalS\mathcal{S}mathcalS.

Les prérequis d'un développeur SL (débutant) est simplement la volonté de réussir et un peu d'imagination. Comme vous êtes tous intelligents, capables à faire des raisonnements logiques (comme tous les Humains :-) ) et vous êtes entrain de suivre une excellente formation dans le cadre de votre licence système informatique et logiciels (nous allons faire appel à tous ce que vous avez et vous allez apprendre :-) ).

Comme vous êtes des développeurs débutants, afin de vous distinguer et pour pouvoir présenter des solutions innovantes et originales, et comme vous avez tous les prérequis nécessaires, il est fortement recommandé de contribuer sous forme d'idée originale lors de la présentation d'une solution SL.

Dans la suite de ce Cours et afin de créer une solution SL efficace, à mes connaissances, il n'existe pas de solution unique parfaite. Heureusement, car sinon, il est possible de la programmer et dans ce cas le métier développeur SL disparaîtra :-). Tout de même, nous allons présenter une approche de développement de SL, exploitant tous vos prérequis, basée sur la définition de génie logiciel.