Maher Helaoui

University of Tunis El Manar, Institut supérieur de l'informatique, Faculty Member

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Maher Helaoui is Doctor of Computer Science. He is currently an assistant professor at the Higher Institute of Computer Science, Ariana, Tunisia. He is a researcher in Artificial Intelligence and combinatorial optimization since 2005.Books:-Maher Helaoui. Informatique Théorique: Cours et Exercices Corrigés. Editions universitaires européennes (2016).Journals:-Maher Helaoui and Wady Naanaa. Modularity-based Decomposing for Valued CSP. Annals of Mathematics and Artificial Intelligence (AMAI) 67 (2): 165-187 (2013).-Maher Helaoui, Wady Naanaa and Bechir Ayeb. Submodularity-based Decomposing for Valued CSP. International Journal on Artificial Intelligence Tools (IJAIT) 22 (2) (2013).Proceedings:-Maher Helaoui. Extended Shortest Path Problem: Generalized Dijkstra-Moore and Bellman-Ford Algorithms. The Sixth "International Conference on Operations Research and Enterprise Systems" (ICORES 2017). -Maher Helaoui and Wady Naanaa. A submodular-based decomposition strategy for valued CSPs. The Sixth "Starting Artificial Intelligence Research" Symposium (STAIRS 2012), 149-161, Montpellier, France. -Maher Helaoui and Wady Naanaa. Domain permutation reduction for valued CSPs, 11th Workshop on Preferences and Soft Constraints, (Co-located with CP 2011),76-90, SofT'11.
Address: Tunisia

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Papers by Maher Helaoui

Domain permutation reduction for Valued CSPs

by Wady Naanaa and 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.

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A submodular-based decomposition strategy for valued CSPs

by Wady Naanaa and Maher Helaoui

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.

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Extended Shortest Path Problem

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

Cours : Méthodes et outils pour le raisonnement

Cours Complexité Algorithmique

Soft Directional Substitutable based Decompositions for MOVCSP

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.

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Pareto-based Soft Arc Consistency for Multi-objective Valued CSPs

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.

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Extended Shortest Path Problem - Generalized Dijkstra-Moore and Bellman-Ford Algorithms

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.

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Modularity-based decompositions for valued CSP

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.

Submodularity-Based Decomposing for Valued CSP

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.

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Pareto-based Soft Arc Consistency for Multi-objective Valued CSPs

by Limeme Ben Ali and Maher Helaoui

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

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Cours Compilation

Algorithme de d ecomposition de domaine pour la satisfaction et l'optimisation de contraintes

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...

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Support de cours Logique Mathématique

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.

Soft Directional Substitutable based Decompositions for MOVCSP

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

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Pareto-based Soft Arc Consistency for Multi-Objective Valued CSPs

by Limeme Ben Ali and Maher Helaoui

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.

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A decomposition method for valued CSPs

by Wady Naanaa and 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 (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.

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Extended Shortest Path Problem - Generalized Dijkstra-Moore and Bellman-Ford Algorithms

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.

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Informatique Théorique: cours et exercices corrigés

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 $XIX^{ème}$ 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...

Submodularity-Based Decomposing for Valued CSP

by Wady Naanaa and Maher Helaoui

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.

Maher Helaoui

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