Muitas relações min-max em otimização combinatória podem ser demonstradas através de total dual integralidade de sistemas lineares. O conceito algébrico de bases de Hilbert foi originalmente introduzido com o objetivo de melhor compreender a estrutura geral dos sistemas totalmente dual integrais. Resultados apresentados posteriormente mostraram que bases de Hilbert também são relevantes para a otimização combinatória em geral e para a caracterização de certas classes de objetos discretos. Entre tais resultados, foram provadas, a partir dessas bases, versões do teorema de Carathéodory para programação inteira. Nesta dissertação, estudamos aspectos estruturais e computacionais de bases de Hilbert e relações destas com programação inteira e otimização combinatória. Em particular, consideramos versões inteiras do teorema de Carathéodory e conjecturas relacionadas. / There are several min-max relations in combinatorial optimization that can be proved through total dual integrality of linear systems. The algebraic concept of Hilbert basis was originally introduced with the objective of better understanding the general structure of totally dual integral systems. Some results that were proved later have shown that Hilbert basis are also relevant to combinatorial optimization in a general manner and to characterize certain classes of discrete objects. Among such results, there are versions of Carathéodory\'s theorem for integer programming that were proved through those basis. In this dissertation, we study structural and computational aspects of Hilbert basis and their relations to integer programming and combinatorial optimization. In particular, we consider integer versions of Carathéodory\'s theorem and related conjectures.

In ant societies, and, more in general, in insect societies, the activities of the individuals, as well as of the society as a whole, are not regulated by any explicit form of centralized control. On the other hand, adaptive and robust behaviors transcending the behavioral repertoire of the single individual can be easily observed at society level. These complex global behaviors are the result of self-organizing dynamics driven by local interactions and communications among a number of relatively simple individuals.<p><p>The simultaneous presence of these and other fascinating and unique characteristics have made ant societies an attractive and inspiring model for building new algorithms and new multi-agent systems. In the last decade, ant societies have been taken as a reference for an ever growing body of scientific work, mostly in the fields of robotics, operations research, and telecommunications.<p><p>Among the different works inspired by ant colonies, the Ant Colony Optimization metaheuristic (ACO) is probably the most successful and popular one. The ACO metaheuristic is a multi-agent framework for combinatorial optimization whose main components are: a set of ant-like agents, the use of memory and of stochastic decisions, and strategies of collective and distributed learning.<p><p>It finds its roots in the experimental observation of a specific foraging behavior of some ant colonies that, under appropriate conditions, are able to select the shortest path among few possible paths connecting their nest to a food site. The pheromone, a volatile chemical substance laid on the ground by the ants while walking and affecting in turn their moving decisions according to its local intensity, is the mediator of this behavior.<p><p>All the elements playing an essential role in the ant colony foraging behavior were understood, thoroughly reverse-engineered and put to work to solve problems of combinatorial optimization by Marco Dorigo and his co-workers at the beginning of the 1990's.<p><p>From that moment on it has been a flourishing of new combinatorial optimization algorithms designed after the first algorithms of Dorigo's et al. and of related scientific events.<p><p>In 1999 the ACO metaheuristic was defined by Dorigo, Di Caro and Gambardella with the purpose of providing a common framework for describing and analyzing all these algorithms inspired by the same ant colony behavior and by the same common process of reverse-engineering of this behavior. Therefore, the ACO metaheuristic was defined a posteriori, as the result of a synthesis effort effectuated on the study of the characteristics of all these ant-inspired algorithms and on the abstraction of their common traits.<p><p>The ACO's synthesis was also motivated by the usually good performance shown by the algorithms (e.g. for several important combinatorial problems like the quadratic assignment, vehicle routing and job shop scheduling, ACO implementations have outperformed state-of-the-art algorithms).<p><p>The definition and study of the ACO metaheuristic is one of the two fundamental goals of the thesis. The other one, strictly related to this former one, consists in the design, implementation, and testing of ACO instances for problems of adaptive routing in telecommunication networks.<p><p>This thesis is an in-depth journey through the ACO metaheuristic, during which we have (re)defined ACO and tried to get a clear understanding of its potentialities, limits, and relationships with other frameworks and with its biological background. The thesis takes into account all the developments that have followed the original 1999's definition, and provides a formal and comprehensive systematization of the subject, as well as an up-to-date and quite comprehensive review of current applications. We have also identified in dynamic problems in telecommunication networks the most appropriate domain of application for the ACO ideas. According to this understanding, in the most applicative part of the thesis we have focused on problems of adaptive routing in networks and we have developed and tested four new algorithms.<p><p>Adopting an original point of view with respect to the way ACO was firstly defined (but maintaining full conceptual and terminological consistency), ACO is here defined and mainly discussed in the terms of sequential decision processes and Monte Carlo sampling and learning.<p><p>More precisely, ACO is characterized as a policy search strategy aimed at learning the distributed parameters (called pheromone variables in accordance with the biological metaphor) of the stochastic decision policy which is used by so-called ant agents to generate solutions. Each ant represents in practice an independent sequential decision process aimed at constructing a possibly feasible solution for the optimization problem at hand by using only information local to the decision step.<p>Ants are repeatedly and concurrently generated in order to sample the solution set according to the current policy. The outcomes of the generated solutions are used to partially evaluate the current policy, spot the most promising search areas, and update the policy parameters in order to possibly focus the search in those promising areas while keeping a satisfactory level of overall exploration.<p><p>This way of looking at ACO has facilitated to disclose the strict relationships between ACO and other well-known frameworks, like dynamic programming, Markov and non-Markov decision processes, and reinforcement learning. In turn, this has favored reasoning on the general properties of ACO in terms of amount of complete state information which is used by the ACO's ants to take optimized decisions and to encode in pheromone variables memory of both the decisions that belonged to the sampled solutions and their quality.<p><p>The ACO's biological context of inspiration is fully acknowledged in the thesis. We report with extensive discussions on the shortest path behaviors of ant colonies and on the identification and analysis of the few nonlinear dynamics that are at the very core of self-organized behaviors in both the ants and other societal organizations. We discuss these dynamics in the general framework of stigmergic modeling, based on asynchronous environment-mediated communication protocols, and (pheromone) variables priming coordinated responses of a number of ``cheap' and concurrent agents.<p><p>The second half of the thesis is devoted to the study of the application of ACO to problems of online routing in telecommunication networks. This class of problems has been identified in the thesis as the most appropriate for the application of the multi-agent, distributed, and adaptive nature of the ACO architecture.<p><p>Four novel ACO algorithms for problems of adaptive routing in telecommunication networks are throughly described. The four algorithms cover a wide spectrum of possible types of network: two of them deliver best-effort traffic in wired IP networks, one is intended for quality-of-service (QoS) traffic in ATM networks, and the fourth is for best-effort traffic in mobile ad hoc networks.<p><p>The two algorithms for wired IP networks have been extensively tested by simulation studies and compared to state-of-the-art algorithms for a wide set of reference scenarios. The algorithm for mobile ad hoc networks is still under development, but quite extensive results and comparisons with a popular state-of-the-art algorithm are reported. No results are reported for the algorithm for QoS, which has not been fully tested. The observed experimental performance is excellent, especially for the case of wired IP networks: our algorithms always perform comparably or much better than the state-of-the-art competitors.<p><p>In the thesis we try to understand the rationale behind the brilliant performance obtained and the good level of popularity reached by our algorithms. More in general, we discuss the reasons of the general efficacy of the ACO approach for network routing problems compared to the characteristics of more classical approaches. Moving further, we also informally define Ant Colony Routing (ACR), a multi-agent framework explicitly integrating learning components into the ACO's design in order to define a general and in a sense futuristic architecture for autonomic network control.<p><p>Most of the material of the thesis comes from a re-elaboration of material co-authored and published in a number of books, journal papers, conference proceedings, and technical reports. The detailed list of references is provided in the Introduction.<p><p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

In ant societies, and, more in general, in insect societies, the activities of the individuals, as well as of the society as a whole, are not regulated by any explicit form of centralized control. On the other hand, adaptive and robust behaviors transcending the behavioral repertoire of the single individual can be easily observed at society level. These complex global behaviors are the result of self-organizing dynamics driven by local interactions and communications among a number of relatively simple individuals. The simultaneous presence of these and other fascinating and unique characteristics have made ant societies an attractive and inspiring model for building new algorithms and new multi-agent systems. In the last decade, ant societies have been taken as a reference for an ever growing body of scientific work, mostly in the fields of robotics, operations research, and telecommunications. Among the different works inspired by ant colonies, the Ant Colony Optimization metaheuristic (ACO) is probably the most successful and popular one. The ACO metaheuristic is a multi-agent framework for combinatorial optimization whose main components are: a set of ant-like agents, the use of memory and of stochastic decisions, and strategies of collective and distributed learning. It finds its roots in the experimental observation of a specific foraging behavior of some ant colonies that, under appropriate conditions, are able to select the shortest path among few possible paths connecting their nest to a food site. The pheromone, a volatile chemical substance laid on the ground by the ants while walking and affecting in turn their moving decisions according to its local intensity, is the mediator of this behavior. All the elements playing an essential role in the ant colony foraging behavior were understood, thoroughly reverse-engineered and put to work to solve problems of combinatorial optimization by Marco Dorigo and his co-workers at the beginning of the 1990's. From that moment on it has been a flourishing of new combinatorial optimization algorithms designed after the first algorithms of Dorigo's et al., and of related scientific events. In 1999 the ACO metaheuristic was defined by Dorigo, Di Caro and Gambardella with the purpose of providing a common framework for describing and analyzing all these algorithms inspired by the same ant colony behavior and by the same common process of reverse-engineering of this behavior. Therefore, the ACO metaheuristic was defined a posteriori, as the result of a synthesis effort effectuated on the study of the characteristics of all these ant-inspired algorithms and on the abstraction of their common traits. The ACO's synthesis was also motivated by the usually good performance shown by the algorithms (e.g., for several important combinatorial problems like the quadratic assignment, vehicle routing and job shop scheduling, ACO implementations have outperformed state-of-the-art algorithms). The definition and study of the ACO metaheuristic is one of the two fundamental goals of the thesis. The other one, strictly related to this former one, consists in the design, implementation, and testing of ACO instances for problems of adaptive routing in telecommunication networks. This thesis is an in-depth journey through the ACO metaheuristic, during which we have (re)defined ACO and tried to get a clear understanding of its potentialities, limits, and relationships with other frameworks and with its biological background. The thesis takes into account all the developments that have followed the original 1999's definition, and provides a formal and comprehensive systematization of the subject, as well as an up-to-date and quite comprehensive review of current applications. We have also identified in dynamic problems in telecommunication networks the most appropriate domain of application for the ACO ideas. According to this understanding, in the most applicative part of the thesis we have focused on problems of adaptive routing in networks and we have developed and tested four new algorithms. Adopting an original point of view with respect to the way ACO was firstly defined (but maintaining full conceptual and terminological consistency), ACO is here defined and mainly discussed in the terms of sequential decision processes and Monte Carlo sampling and learning. More precisely, ACO is characterized as a policy search strategy aimed at learning the distributed parameters (called pheromone variables in accordance with the biological metaphor) of the stochastic decision policy which is used by so-called ant agents to generate solutions. Each ant represents in practice an independent sequential decision process aimed at constructing a possibly feasible solution for the optimization problem at hand by using only information local to the decision step. Ants are repeatedly and concurrently generated in order to sample the solution set according to the current policy. The outcomes of the generated solutions are used to partially evaluate the current policy, spot the most promising search areas, and update the policy parameters in order to possibly focus the search in those promising areas while keeping a satisfactory level of overall exploration. This way of looking at ACO has facilitated to disclose the strict relationships between ACO and other well-known frameworks, like dynamic programming, Markov and non-Markov decision processes, and reinforcement learning. In turn, this has favored reasoning on the general properties of ACO in terms of amount of complete state information which is used by the ACO's ants to take optimized decisions and to encode in pheromone variables memory of both the decisions that belonged to the sampled solutions and their quality. The ACO's biological context of inspiration is fully acknowledged in the thesis. We report with extensive discussions on the shortest path behaviors of ant colonies and on the identification and analysis of the few nonlinear dynamics that are at the very core of self-organized behaviors in both the ants and other societal organizations. We discuss these dynamics in the general framework of stigmergic modeling, based on asynchronous environment-mediated communication protocols, and (pheromone) variables priming coordinated responses of a number of ``cheap' and concurrent agents. The second half of the thesis is devoted to the study of the application of ACO to problems of online routing in telecommunication networks. This class of problems has been identified in the thesis as the most appropriate for the application of the multi-agent, distributed, and adaptive nature of the ACO architecture. Four novel ACO algorithms for problems of adaptive routing in telecommunication networks are throughly described. The four algorithms cover a wide spectrum of possible types of network: two of them deliver best-effort traffic in wired IP networks, one is intended for quality-of-service (QoS) traffic in ATM networks, and the fourth is for best-effort traffic in mobile ad hoc networks. The two algorithms for wired IP networks have been extensively tested by simulation studies and compared to state-of-the-art algorithms for a wide set of reference scenarios. The algorithm for mobile ad hoc networks is still under development, but quite extensive results and comparisons with a popular state-of-the-art algorithm are reported. No results are reported for the algorithm for QoS, which has not been fully tested. The observed experimental performance is excellent, especially for the case of wired IP networks: our algorithms always perform comparably or much better than the state-of-the-art competitors. In the thesis we try to understand the rationale behind the brilliant performance obtained and the good level of popularity reached by our algorithms. More in general, we discuss the reasons of the general efficacy of the ACO approach for network routing problems compared to the characteristics of more classical approaches. Moving further, we also informally define Ant Colony Routing (ACR), a multi-agent framework explicitly integrating learning components into the ACO's design in order to define a general and in a sense futuristic architecture for autonomic network control. Most of the material of the thesis comes from a re-elaboration of material co-authored and published in a number of books, journal papers, conference proceedings, and technical reports. The detailed list of references is provided in the Introduction.

Le problème de tarification qui nous intéresse ici consiste à maximiser le revenu généré par les usagers d'un réseau de transport. Pour se rendre à leurs destinations, les usagers font un choix de route et utilisent des arcs sur lesquels nous imposons des tarifs. Chaque route est caractérisée (aux yeux de l'usager) par sa "désutilité", une mesure de longueur généralisée tenant compte à la fois des tarifs et des autres coûts associés à son utilisation. Ce problème a surtout été abordé sous une modélisation déterministe de la demande selon laquelle seules des routes de désutilité minimale se voient attribuer une mesure positive de flot. Le modèle déterministe se prête bien à une résolution globale, mais pèche par manque de réalisme. Nous considérons ici une extension probabiliste de ce modèle, selon laquelle les usagers d'un réseau sont alloués aux routes d'après un modèle de choix discret logit. Bien que le problème de tarification qui en résulte est non linéaire et non convexe, il conserve néanmoins une forte composante combinatoire que nous exploitons à des fins algorithmiques. Notre contribution se répartit en trois articles. Dans le premier, nous abordons le problème d'un point de vue théorique pour le cas avec une paire origine-destination. Nous développons une analyse de premier ordre qui exploite les propriétés analytiques de l'affectation logit et démontrons la validité de règles de simplification de la topologie du réseau qui permettent de réduire la dimension du problème sans en modifier la solution. Nous établissons ensuite l'unimodalité du problème pour une vaste gamme de topologies et nous généralisons certains de nos résultats au problème de la tarification d'une ligne de produits. Dans le deuxième article, nous abordons le problème d'un point de vue numérique pour le cas avec plusieurs paires origine-destination. Nous développons des algorithmes qui exploitent l'information locale et la parenté des formulations probabilistes et déterministes. Un des résultats de notre analyse est l'obtention de bornes sur l'erreur commise par les modèles combinatoires dans l'approximation du revenu logit. Nos essais numériques montrent qu'une approximation combinatoire rudimentaire permet souvent d'identifier des solutions quasi-optimales. Dans le troisième article, nous considérons l'extension du problème à une demande hétérogène. L'affectation de la demande y est donnée par un modèle de choix discret logit mixte où la sensibilité au prix d'un usager est aléatoire. Sous cette modélisation, l'expression du revenu n'est pas analytique et ne peut être évaluée de façon exacte. Cependant, nous démontrons que l'utilisation d'approximations non linéaires et combinatoires permet d'identifier des solutions quasi-optimales. Finalement, nous en profitons pour illustrer la richesse du modèle, par le biais d'une interprétation économique, et examinons plus particulièrement la contribution au revenu des différents groupes d'usagers. / The network pricing problem consists in finding tolls to set on a subset of a network's arcs, so to maximize a revenue expression. A fixed demand of commuters, going from their origins to their destinations, is assumed. Each commuter chooses a path of minimal "disutility", a measure of discomfort associated with the use of a path and which takes into account fixed costs and tolls. A deterministic modelling of commuter behaviour is mostly found in the literature, according to which positive flow is only assigned to \og shortest\fg\: paths. Even though the determinist pricing model is amenable to global optimization by the use of enumeration techniques, it has often been criticized for its lack of realism. In this thesis, we consider a probabilistic extension of this model involving a logit dicrete choice model. This more realistic model is non-linear and non-concave, but still possesses strong combinatorial features. Our analysis spans three separate articles. In the first we tackle the problem from a theoretical perspective for the case of a single origin-destination pair and develop a first order analysis that exploits the logit assignment analytical properties. We show the validity of simplification rules to the network topology which yield a reduction in the problem dimensionality. This enables us to establish the problem's unimodality for a wide class of topologies. We also establish a parallel with the product-line pricing problem, for which we generalize some of our results. In our second article, we address the problem from a numerical point of view for the case where multiple origin-destination pairs are present. We work out algorithms that exploit both local information and the pricing problem specific combinatorial features. We provide theoretical results which put in perspective the deterministic and probabilistic models, as well as numerical evidence according to which a very simple combinatorial approximation can lead to the best solutions. Also, our experiments clearly indicate that under any reasonable setting, the logit pricing problem is much smoother, and admits less optima then its deterministic counterpart. The third article is concerned with an extension to an heterogeneous demand resulting from a mixed-logit discrete choice model. Commuter price sensitivity is assumed random and the corresponding revenue expression admits no closed form expression. We devise nonlinear and combinatorial approximation schemes for its evaluation and optimization, which allow us to obtain quasi-optimal solutions. Numerical experiments here indicate that the most realistic model yields the best solution, independently of how well the model can actually be solved. We finally illustrate how the output of the model can be used for economic purposes by evaluating the contributions to the revenue of various commuter groups.

Afin d'enrichir les données de corpus bilingues parallèles, il peut être judicieux de travailler avec des corpus dits comparables. En effet dans ce type de corpus, même si les documents dans la langue cible ne sont pas l'exacte traduction de ceux dans la langue source, on peut y retrouver des mots ou des phrases en relation de traduction. L'encyclopédie libre Wikipédia constitue un corpus comparable multilingue de plusieurs millions de documents. Notre travail consiste à trouver une méthode générale et endogène permettant d'extraire un maximum de phrases parallèles. Nous travaillons avec le couple de langues français-anglais mais notre méthode, qui n'utilise aucune ressource bilingue extérieure, peut s'appliquer à tout autre couple de langues. Elle se décompose en deux étapes. La première consiste à détecter les paires d’articles qui ont le plus de chance de contenir des traductions. Nous utilisons pour cela un réseau de neurones entraîné sur un petit ensemble de données constitué d'articles alignés au niveau des phrases. La deuxième étape effectue la sélection des paires de phrases grâce à un autre réseau de neurones dont les sorties sont alors réinterprétées par un algorithme d'optimisation combinatoire et une heuristique d'extension. L'ajout des quelques 560~000 paires de phrases extraites de Wikipédia au corpus d'entraînement d'un système de traduction automatique statistique de référence permet d'améliorer la qualité des traductions produites. Nous mettons les données alignées et le corpus extrait à la disposition de la communauté scientifique. / Working with comparable corpora can be useful to enhance bilingual parallel corpora. In fact, in such corpora, even if the documents in the target language are not the exact translation of those in the source language, one can still find translated words or sentences. The free encyclopedia Wikipedia is a multilingual comparable corpus of several millions of documents. Our task is to find a general endogenous method for extracting a maximum of parallel sentences from this source. We are working with the English-French language pair but our method -- which uses no external bilingual resources -- can be applied to any other language pair. It can best be described in two steps. The first one consists of detecting article pairs that are most likely to contain translations. This is achieved through a neural network trained on a small data set composed of sentence aligned articles. The second step is to perform the selection of sentence pairs through another neural network whose outputs are then re-interpreted by a combinatorial optimization algorithm and an extension heuristic. The addition of the 560~000 pairs of sentences extracted from Wikipedia to the training set of a baseline statistical machine translation system improves the quality of the resulting translations. We make both the aligned data and the extracted corpus available to the scientific community.

Thèse réalisée en cotutelle entre l'Université de Montréal et l'Université de Technologie de Troyes / Le problème de tournées de véhicules (VRP) implique de planifier les itinéraires d'une flotte de véhicules afin de desservir un ensemble de clients à moindre coût. Ce problème d'optimisation combinatoire NP-difficile apparait dans de nombreux domaines d'application, notamment en logistique, télécommunications, robotique ou gestion de crise dans des contextes militaires et humanitaires. Ces applications amènent différents contraintes, objectifs et décisions supplémentaires ; des "attributs" qui viennent compléter les formulations classiques du problème. Les nombreux VRP Multi-Attributs (MAVRP) qui s'ensuivent sont le support d'une littérature considérable, mais qui manque de méthodes généralistes capables de traiter efficacement un éventail significatif de variantes. Par ailleurs, la résolution de problèmes "riches", combinant de nombreux attributs, pose d'importantes difficultés méthodologiques. Cette thèse contribue à relever ces défis par le biais d'analyses structurelles des problèmes, de développements de stratégies métaheuristiques, et de méthodes unifiées. Nous présentons tout d'abord une étude transversale des concepts à succès de 64 méta-heuristiques pour 15 MAVRP afin d'en cerner les "stratégies gagnantes". Puis, nous analysons les problèmes et algorithmes d'ajustement d'horaires en présence d'une séquence de tâches fixée, appelés problèmes de "timing". Ces méthodes, développées indépendamment dans différents domaines de recherche liés au transport, ordonnancement, allocation de ressource et même régression isotonique, sont unifiés dans une revue multidisciplinaire. Un algorithme génétique hybride efficace est ensuite proposé, combinant l'exploration large des méthodes évolutionnaires, les capacités d'amélioration agressive des métaheuristiques à voisinage, et une évaluation bi-critère des solutions considérant coût et contribution à la diversité de la population. Les meilleures solutions connues de la littérature sont retrouvées ou améliorées pour le VRP classique ainsi que des variantes avec multiples dépôts et périodes. La méthode est étendue aux VRP avec contraintes de fenêtres de temps, durée de route, et horaires de conducteurs. Ces applications mettent en jeu de nouvelles méthodes d'évaluation efficaces de contraintes temporelles relaxées, des phases de décomposition, et des recherches arborescentes pour l'insertion des pauses des conducteurs. Un algorithme de gestion implicite du placement des dépôts au cours de recherches locales, par programmation dynamique, est aussi proposé. Des études expérimentales approfondies démontrent la contribution notable des nouvelles stratégies au sein de plusieurs cadres méta-heuristiques. Afin de traiter la variété des attributs, un cadre de résolution heuristique modulaire est présenté ainsi qu'un algorithme génétique hybride unifié (UHGS). Les attributs sont gérés par des composants élémentaires adaptatifs. Des expérimentations sur 26 variantes du VRP et 39 groupes d'instances démontrent la performance remarquable de UHGS qui, avec une unique implémentation et paramétrage, égalise ou surpasse les nombreux algorithmes dédiés, issus de plus de 180 articles, révélant ainsi que la généralité ne s'obtient pas forcément aux dépends de l'efficacité pour cette classe de problèmes. Enfin, pour traiter les problèmes riches, UHGS est étendu au sein d'un cadre de résolution parallèle coopératif à base de décomposition, d'intégration de solutions partielles, et de recherche guidée. L'ensemble de ces travaux permet de jeter un nouveau regard sur les MAVRP et les problèmes de timing, leur résolution par des méthodes méta-heuristiques, ainsi que les méthodes généralistes pour l'optimisation combinatoire. / The Vehicle Routing Problem (VRP) involves designing least cost delivery routes to service a geographically-dispersed set of customers while taking into account vehicle-capacity constraints. This NP-hard combinatorial optimization problem is linked with multiple applications in logistics, telecommunications, robotics, crisis management in military and humanitarian frameworks, among others. Practical routing applications are usually quite distinct from the academic cases, encompassing additional sets of specific constraints, objectives and decisions which breed further new problem variants. The resulting "Multi-Attribute" Vehicle Routing Problems (MAVRP) are the support of a vast literature which, however, lacks unified methods capable of addressing multiple MAVRP. In addition, some "rich" VRPs, i.e. those that involve several attributes, may be difficult to address because of the wide array of combined and possibly antagonistic decisions they require. This thesis contributes to address these challenges by means of problem structure analysis, new metaheuristics and unified method developments. The "winning strategies" of 64 state-of-the-art algorithms for 15 different MAVRP are scrutinized in a unifying review. Another analysis is targeted on "timing" problems and algorithms for adjusting the execution dates of a given sequence of tasks. Such methods, independently studied in different research domains related to routing, scheduling, resource allocation, and even isotonic regression are here surveyed in a multidisciplinary review. A Hybrid Genetic Search with Advanced Diversity Control (HGSADC) is then introduced, which combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and a bi-criteria evaluation of solutions based on cost and diversity measures. Results of remarkable quality are achieved on classic benchmark instances of the capacitated VRP, the multi-depot VRP, and the periodic VRP. Further extensions of the method to VRP variants with constraints on time windows, limited route duration, and truck drivers' statutory pauses are also proposed. New route and neighborhood evaluation procedures are introduced to manage penalized infeasible solutions w.r.t. to time-window and duration constraints. Tree-search procedures are used for drivers' rest scheduling, as well as advanced search limitation strategies, memories and decomposition phases. A dynamic programming-based neighborhood search is introduced to optimally select the depot, vehicle type, and first customer visited in the route during local searches. The notable contribution of these new methodological elements is assessed within two different metaheuristic frameworks. To further advance general-purpose MAVRP methods, we introduce a new component-based heuristic resolution framework and a Unified Hybrid Genetic Search (UHGS), which relies on modular self-adaptive components for addressing problem specifics. Computational experiments demonstrate the groundbreaking performance of UHGS. With a single implementation, unique parameter setting and termination criterion, this algorithm matches or outperforms all current problem-tailored methods from more than 180 articles, on 26 vehicle routing variants and 39 benchmark sets. To address rich problems, UHGS was included in a new parallel cooperative solution framework called "Integrative Cooperative Search (ICS)", based on problem decompositions, partial solutions integration, and global search guidance. This compendium of results provides a novel view on a wide range of MAVRP and timing problems, on efficient heuristic searches, and on general-purpose solution methods for combinatorial optimization problems.

La distance de Kendall-τ compte le nombre de paires en désaccord entre deux permuta- tions. La distance d’une permutation à un ensemble est simplement la somme des dis- tances entre cette permutation et les permutations de l’ensemble. À partir d’un ensemble donné de permutations, notre but est de trouver la permutation, appelée médiane, qui minimise cette distance à l’ensemble. Le problème de la médiane de permutations sous la distance de Kendall-τ, trouve son application en bio-informatique, en science politique, en télécommunication et en optimisation. Ce problème d’apparence simple est prouvé difficile à résoudre. Dans ce mémoire, nous présentons plusieurs approches pour résoudre le problème, pour trouver une bonne solution approximative, pour le séparer en classes caractéristiques, pour mieux com- prendre sa compléxité, pour réduire l’espace de recheche et pour accélérer les calculs. Nous présentons aussi, vers la fin du mémoire, une généralisation de ce problème et nous l’étudions avec ces mêmes approches. La majorité du travail de ce mémoire se situe dans les trois articles qui le composent et est complémenté par deux chapitres servant à les lier. / The Kendall-τ distance counts the number of pairwise disagreements between two permutations. The distance between a permutation and a set is simply the sum of the distances between the considered permutation and the permutations of the set. Given a set of permutations, we want to find the permutation, called median, that minimise that distance to the set. The problem of finding a median of permutations under the Kendall-τ distance, finds applications in bioinformatics, political science, telecommunications and optimization. This simple appearing problem is proven difficult to solve. In this master thesis, we present a few approaches to solve the problem, to find a good approximate solution, to separate it into caracteristic classes, to deepen our understanding of its complexity, to reduce the search space and to accelerate calculations. We also present, at the end of this thesis, a generalization of this problem and we study it with the same approaches. The majority of the work in this thesis is located in the three papers which compose it and is complemented by two chapters, that bound them all together.

Dans cette thèse, nous étudions la complexité algorithmique de problèmes d'optimisation impliquant un processus de diffusion dans un graphe. Plus précisément, nous nous intéressons tout d'abord au problème de sélection d'un ensemble cible. Ce problème consiste à trouver le plus petit ensemble de sommets d'un graphe à “activer” au départ tel que tous les autres sommets soient activés après un nombre fini d'étapes de propagation. Si nous modifions ce processus en permettant de “protéger” un sommet à chaque étape, nous obtenons le problème du pompier dont le but est de minimiser le nombre total de sommets activés en protégeant certains sommets. Dans ce travail, nous introduisons et étudions une version généralisée de ce problème dans laquelle plus d'un sommet peut être protégé à chaque étape. Nous proposons plusieurs résultats de complexité pour ces problèmes à la fois du point de vue de l'approximation mais également de la complexité paramétrée selon des paramètres standards ainsi que des paramètres liés à la structure du graphe. / In this thesis, we investigate the computational complexity of optimization problems involving a “diffusion process” in a graph. More specifically, we are first interested to the target set selection problem. This problem consists of finding the smallest set of initially “activated” vertices of a graph such that all the other vertices become activated after a finite number of propagation steps. If we modify this process by allowing the possibility of ``protecting'' a vertex at each step, we end up with the firefighter problem that asks for minimizing the total number of activated vertices by protecting some particular vertices. In fact, we introduce and study a generalized version of this problem where more than one vertex can be protected at each step. We propose several complexity results for these problems from an approximation point of view and a parameterized complexity perspective according to standard parameterizations as well as parameters related to the graph structure.

Résumé indisponible. / In this thesis we have concerned ourselves with university timetabling problems both course timetabling and examination timetabling problems. Most of the timetabling problems are computationally NP-complete problems, which means that the amount of computation required to find solutions increases exponentially with problem size. These are idiosyncratic nature problems, for example different universities have their own set of constraints, their own definition of good timetable, feasible timetable and their own choice about the use of constraint type (as a soft or hard constraint). Unfortunately, it is often the case that a problem solving approach which is successfully applied for one specific problem may not become suitable for others. This is a motivation, we propose a generalized problem which covers many constraints used in different universities or never used in literature. Many university timetabling problems are sub problems of this generalized problem. Our proposed algorithms can solve these sub problems easily, moreover constraints can be used according to the desire of user easily because these constraints can be used as reference to penalty attached with them as well. It means that give more penalty value to hard constraints than soft constraint. Thus more penalty value constraints are dealt as a hard constraint by algorithm. Our algorithms can also solve a problem in two phases with little modification, where in first phase hard constraints are solved. In this work we have preferred and used two phase technique to solve timetabling problems because by using this approach algorithms have broader search space in first phase to satisfy hard constraints while not considering soft constraints at all. Two types of algorithms are used in literature to solve university timetabling problem, exact algorithms and approximation algorithms. Exact algorithms are able to find optimal solution, however in university timetabling problems exact algorithms constitute brute-force style procedures. And because these problems have the exponential growth rates of the search spaces, thus these kinds of algorithms can be applied for small size problems. On the other side, approximation algorithms may construct optimal solution or not but they can produce good practically useable solutions. Thus due to these factors we have proposed approximation algorithms to solve university timetabling problem. We have proposed metaheuristic based techniques to solve timetabling problem, thus we have mostly discussed metaheuristic based algorithms such as evolutionary algorithms, simulated annealing, tabu search, ant colony optimization and honey bee algorithms. These algorithms have been used to solve many other combinatorial optimization problems other than timetabling problem by modifying a general purpose algorithmic framework. We also have presented a bibliography of linear integer programming techniques used to solve timetabling problem because we have formulated linear integer programming formulations for our course and examination timetabling problems. We have proposed two stage algorithms where hard constraints are satisfied in first phase and soft constraints in second phase. The main purpose to use this two stage technique is that in first phase hard constraints satisfaction can use more relax search space because in first phase it does not consider soft constraints. In second phase it tries to satisfy soft constraints when maintaining hard constraints satisfaction which are already done in first phase. (...)

Sejam GI = (VI ,AI) e GM = (VM,AM) dois grafos simples. Um mapeamento de GI para GM é um conjunto de associações, tal que cada vértice de VI está associado a um vértice de VM, e cada aresta de AI está associada a um par de vértices de VM. A cada possível associação é atribuído um custo. O problema de correspondência inexata entre grafos (PCIG) consiste em encontrar um mapeamento de GI para GM, tal que a soma dos custos de suas associações seja mínima. Nesta dissertação, resumimos os resultados encontrados na literatura sobre o PCIG e algumas de suas variações. Os resultados que incluímos aqui tratam sobre a questão de como formular o PCIG e algumas de suas variações, através de programação linear inteira. Provamos alguns resultados de complexidade computacional que relacionam variações do PCIG a problemas clássicos, como isomorfismo e partição de grafos. Fornecemos uma formulação através de programação linear inteira para o PCCA (uma variante do PCIG com conexidade e cobertura de arestas). Mostramos que o PCCA é NP-difícil quando os grafos de entrada são completos ou árvores (chamamos o segundo caso de PCCA para árvores). Apresentamos uma formulação linear inteira e um algoritmo - que é polinomial se o grau máximo dos vértices de VM for limitado por uma constante - para o PCCA para árvores. Mostramos um caso especia em que o PCCA para árvores pode ser resolvido em tempo polinomial. Por último, exibimos alguns resultados experimentais, inclusive com instâncias reais de uma aplicação do problema. / Let GI = (VI ,AI) and GM = (VM,AM) be two simple graphs. A mapping from GI to GM is an association set, such that each vertex in VI is associated to a vertex in VM, and each edge in AI is associated to a pair of vertices of VM. A cost is defined to each possible association. The inexact graph correspondence problem (IGCP) consists in finding a mapping from GI to GM, such that the sum of its associations costs is minimized. In this dissertation, we summarize the results found in the literature about the IGCP and some variations. The results included here address the question of how to formulate the IGCP and some variations, using integer linear programming. We prove some computational complexity results which relate IGCP variations with classical problems, like graph isomorphism and partitioning. We give an integer linear programming formulation to the ICEC (IGCP with connectivity and edges cover). We show that the ICEC is NP-hard when the input graphs are complete or trees (we call the second case ICEC for trees). We introduce an integer linear formulation and an algorithm - which has polynomial running time if the vertices of VM have maximum degree bounded by a constant - to the ICEC for trees. We show a especial case in which the ICEC for trees can be solved in polynomial time. Finally, we present some experimental results, also with instances of a real application of the problem.