The University Course Timetabling Problem (UCTP) is the problem of assigning locations (lecture halls, computer rooms) and time slots (time and date) to a set of events (lectures, labs) while satisfying a number of constraints such as avoiding double-bookings. Many variants of problem formulations exist, and most realistic variants are thought to be NP-hard. A recent trend in solving hard scheduling problems lies in the application of hybrid metaheuristics, where improvements are often found by hybridizing a population-based approach with some form of local search. In this paper, an implementation of a Genetic Algorithm (GA) that solves the UCTP is hybridized with local search in the form of Tabu Search (TS). The results show significant improvements to the performance and scalability over the non-hybridized GA. Two application strategies for the TS are investigated. The first strategy performs a switch-over from the GA to the TS, while the second interleaves the two algorithms. The effectiveness of each application strategy is seen to depend on the characteristics of the individual algorithms. / Schemaläggningsproblemet UCTP (University Course Timetabling Problem) består av problemet att tilldela platser (föreläsningssalar, laborationssalar) och tidpunkter (datum och klockslag) till en mängd tillställningar (föreläsningar, laborationer) under kravet att upprätthålla en mängd restriktioner, exempelvis att undvika dubbelbokningar. Det finns många varianter av problemformuleringen och de flesta realistiska formuleringer anses ge upphov till NP-svåra optimeringsproblem. En förhållandevis ny trend för lösningsmodeller till svåra schemaläggningsproblem ligger i tillämpningen av hybrida metaheuristiker, där förbättringar ofta ses när populationsbaserade algoritmer kombineras med någon typ av lokalsökning. I denna rapport undersöks en UCTP-lösning baserad på en Genetisk Algoritm (GA) som hybridiseratsmed en lokalsökning i form av en Tabusökning (TS). Resultaten visar på signifikanta förbättringar i prestanda och skalbarhet jämfört med den icke-hybridiserade GA:n. Två appliceringsstrategier för TS undersöks. Den första strategin utgörs av att byta algoritm från GA till TS, medan den andra utgörs av att sammanfläta de två algoritmerna. Appliceringsstrategiernas effektivitet ses bero av de individuella algoritmernas egenskaper.

Thesis (M.Com.(quantitative Management)) / Satellite Scheduling Problems (SSP) are NP-hard and constraint programming and metaheuristics solution methods yield mixed results. This study investigates a new version of the SSP, the Satellite Constellation Time-Window Optimization Problem (SCoTWOP), involving commercial satellite constellations that provide frequent earth coverage. The SCoTWOP is related to the dual of the Vehicle Routing Problem with Multiple Timewindows, suggesting binary solution vectors representing an activation of time-windows. This representation fitted well with the MatLab® Genetic Algorithm and Direct Search Toolbox subsequently used to experiment with genetic algorithms, tabu search, and simulated annealing as SCoTWOP solution methods. The genetic algorithm was most successful and in some instances activated all 250 imaging time-windows, a number that is typical for a constellation of six satellites. / Quantitative Management

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.

Thesis (M.Com.(quantitative Management)) / Satellite Scheduling Problems (SSP) are NP-hard and constraint programming and metaheuristics solution methods yield mixed results. This study investigates a new version of the SSP, the Satellite Constellation Time-Window Optimization Problem (SCoTWOP), involving commercial satellite constellations that provide frequent earth coverage. The SCoTWOP is related to the dual of the Vehicle Routing Problem with Multiple Timewindows, suggesting binary solution vectors representing an activation of time-windows. This representation fitted well with the MatLab® Genetic Algorithm and Direct Search Toolbox subsequently used to experiment with genetic algorithms, tabu search, and simulated annealing as SCoTWOP solution methods. The genetic algorithm was most successful and in some instances activated all 250 imaging time-windows, a number that is typical for a constellation of six satellites. / Quantitative Management

Les métaheuristiques sont des algorithmes génériques, souvent inspirés de la nature, conçues pour résoudre des problèmes d'optimisation complexes. Parmi les métaheuristiques les plus récentes, nous retenons celle basée sur la théorie de la biogéographie insulaire: Biogeography-based optimization (BBO).Dans cette thèse, nous considérons à la fois les problèmes d'optimisation globale à variables continues avec et sans contraintes. De nouvelles versions hybrides de BBO sont proposées comme des solutions très prometteuses pour résoudre les problèmes considérés. Les méthodes proposées visent à pallier les inconvénients de la convergence lente et du manque de diversité de l'algorithme BBO. Dans la première partie de cette thèse, nous présentons la méthode que nous avons développée, issue d'une hybridation de BBO avec l'évolution différentielle (DE) pour résoudre des problèmes d'optimisation sans contraintes. Nous montrons que les résultats de l'algorithme proposé sont plus précis, notamment pour des problèmes multimodaux, qui sont parmi les problèmes les plus difficiles pour de nombreux algorithmes d'optimisation. Pour résoudre des problèmes d'optimisation sous contraintes, nous proposons trois nouvelles variantes de BBO. Des expérimentations ont été menées pour rendre compte de l'utilité des méthodes proposées. Dans une deuxième partie, nous nous intéressons à l'étude des capacités des méthodes proposées à résoudre des problèmes d'optimisation, issus du monde réel. Nous nous proposons d'abord de résoudre le problème d'allocation optimale de puissance pour la détection décentralisée d'un signal déterministe dans un réseau de capteurs sans fil, compte tenu des fortes contraintes en ressources énergétiques et en bande passante des noeuds répartis. L'objectif est de minimiser la puissance totale allouée aux capteurs, tout en gardant la probabilité d'erreur de détection au dessous d'un seuil requis. Dans un deuxième temps, nous nous focalisons sur la segmentation d'images en niveaux de gris par seuillage multi-niveaux. Les seuils sont déterminés de manière à maximiser l'entropie floue. Ce problème d'optimisation est résolu en appliquant une variante de BBO (DBBO-Fuzzy) que nous avons développée. Nous montrons l'efficacité de la méthode proposée aux travers de résultats expérimentaux / Metaheuristics are general algorithmic frameworks, often nature-inspired, designed to solve complex optimization problems. Among representative metaheuristics, Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm. In this PhD thesis, both unconstrained and constrained global optimization problems in a continuous space are considered. New hybrid versions of BBO are proposed as promising solvers for the considered problems. The proposed methods aim to overcome the drawbacks of slow convergence and the lack of diversity of the BBO algorithm. In the first part of this thesis, we present the method we developed, based on an hybridization of BBO with the differential evolution (DE) algorithm, to solve unconstrained optimization problems. We show that the results of the proposed algorithm are more accurate, especially for multimodal problems, which are amongst the most difficult-to-handle class of problems for many optimization algorithms. To solve constrained optimization problems, we propose three new variations of BBO. Our extensive experimentations successfully demonstrate the usefulness of all these modifications proposed for the BBO algorithm. In the second part, we focus on the applications of the proposed algorithms to solve real-world optimization problems. We first address the problem of optimal power scheduling for the decentralized detection of a deterministic signal in a wireless sensor network, with power and bandwidth constrained distributed nodes. The objective is to minimize the total power spent by the whole sensor network while keeping the detection error probability below a required threshold. In a second time, image segmentation of gray-level images is performed by multilevel thresholding. The optimal thresholds for this purpose are found by maximizing the fuzzy entropy. The optimization is conducted by a newly-developed BBO variants (DBBO-Fuzzy). We show the efficiency of the proposed method through experimental results

Résumé indisponible. / A healthcare network or health system consists of all organizations, actions and people who participate to promote, restore or maintain people’s health. The health care systems in many developed countries are facing increasing costs. The major reason is the changing age distribution of the population with more elderly people in need of support. Increasing healthcare costs has created new alternatives to traditional hospitalization in which one is Home Health Care (HHC). Home health care or domiciliary care is the provision of health care and assistance to people in their own homes, according to a formal assessment of their needs. HHC has attained a specific place in healthcare network. HHC programs have now been successfully implemented in many countries. The purpose of HHC is to provide the care and support needed to assist patients to live independently in their own homes. HHC is primarily performed by means of personal visitations of healthcare workers to patients in their homes, where they provide care assistance according to patients’ needs. In this thesis we have considered different aspects of planning problems for home health care services. The efficient use of resources is necessary in continuous healthcare services. To meet the increased demand of HHC, operation research specialist can play an important role by solving the various combinatorial optimization problems arising in HHC. These problems can be tactical, strategic or operational with respect to planning horizon. Strategic problems are those which help in attaining long term goals or objectives, e.g. higher level of quality for HHC patients and efficient use of resources. These strategic objectives can be achieved through tactical i.e. medium term panning and operational planning i.e. short term planning. The main purpose of our thesis is to identify these potential optimization problems and solve them via recent metaheuristics. HHC is an alternative to traditional hospitalization and has got a significant share in the organization of healthcare in developed countries. The change in aging demographics, recent development in technology and the increase in the demand of healthcare services are major reasons for this rapid growth. Some studies show HHC as a tool to reduce costs of care, which is a major preoccupation in developed countries. Some others reveal that it leads to the improvement of patients’ satisfaction without increasing the resources. Home health care, i.e. visiting and nursing patients in their homes, is a flourishing realm in the medical industry. The number of companies has grown largely both in public and private sectors. The staffing needs for HHC companies have been expanded as well. Also they face the problem of assigning geographically dispersed patients to home healthcare workers and preparing daily schedules for these workers. The challenge of this problem is to combine aspects of vehicle routing and staff rostering. Both of them are well known NP- hard combinatorial optimization problems, it means the amount of computational time required to find solution increases exponentially with problem size. Home healthcare workers scheduling problem is difficult to solve optimally due to presence of large number of constraints. These are two types of constraints: hard constraints and soft constraints. The hard constraints are the restrictions to be fulfilled for the schedules to be applicable and soft constraints are preferences to improve the quality of these schedules. (...)

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. (...)

Les métaheuristiques sont une famille d'algorithmes stochastiques destinés à résoudre des problèmes d 'optimisation difficile . Utilisées dans de nombreux domaines, ces méthodes présentent l'avantage d'être généralement efficaces, sans pour autant que l'utilisateur ait à modifier la structure de base de l'algorithme qu'il utilise. Parmi celles-ci, l'Optimisation par Essaim Particulaire (OEP) est une nouvelle classe d'algorithmes proposée pour résoudre les problèmes à variables continues. Les algorithmes d'OEP s'inspirent du comportement social des animaux évoluant en essaim, tels que les oiseaux migrateurs ou les poissons. Les particules d'un même essaim communiquent de manière directe entre elles tout au long de la recherche pour construire une solution au problème posé, en s'appuyant sur leur expérience collective. Reconnues depuis de nombreuses années pour leur efficacité, les métaheuristiques présentent des défauts qui rebutent encore certains utilisateurs. Le réglage des paramètres des algorithmes est un de ceux-ci. Il est important, pour chaque probléme posé, de trouver le jeu de paramètres qui conduise à des performances optimales de l'algorithme. Cependant, cette tâche est fastidieuse et coûteuse en temps, surtout pour les utilisateurs novices. Pour s'affranchir de ce type de réglage, des recherches ont été menées pour proposer des algorithmes dits adaptatifs . Avec ces algorithmes, les valeurs des paramètres ne sont plus figées, mais sont modifiées, en fonction des résultats collectés durant le processus de recherche. Dans cette optique-là, Maurice Clerc a proposé TRIBES, qui est un algorithme d'OEP mono-objectif sans aucun paramètre de contrôle. Cet algorithme fonctionne comme une boite noire , pour laquelle l'utilisateur n'a qu'à définir le problème à traiter et le critàre d'arrêt de l'algorithme. Nous proposons dans cette thèse une étude comportementale de TRIBES, qui permet d'en dégager les principales qualités et les principaux défauts. Afin de corriger certains de ces défauts, deux modules ont été ajoutés à TRIBES. Une phase d'initialisation régulière est insérée, afin d'assurer, dès le départ de l'algorithme, une bonne couverture de l'espace de recherche par les particules. Une nouvelle stratégie de déplacement, basée sur une hybridation avec un algorithme à estimation de distribution, est aussi définie, afin de maintenir la diversité au sein de l'essaim, tout au long du traitement. Le besoin croissant de méthodes de résolution de problèmes multiobjectifs a conduit les concepteurs à adapter leurs méthodes pour résoudre ce type de problème. La complexité de cette opération provient du fait que les objectifs à optimiser sont souvent contradictoires. Nous avons élaboré une version multiobjectif de TRIBES, dénommée MO-TRIBES. Nos algorithmes ont été enfin appliqués à la résolution de problèmes de seuillage d'images médicales et au problème de dimensionnement de composants de circuits analogiques / Metaheuristics are a new family of stochastic algorithms which aim at solving difficult optimization problems. Used to solve various applicative problems, these methods have the advantage to be generally efficient on a large amount of problems. Among the metaheuristics, Particle Swarm Optimization (PSO) is a new class of algorithms proposed to solve continuous optimization problems. PSO algorithms are inspired from the social behavior of animals living in swarm, such as bird flocks or fish schools. The particles of the swarm use a direct way of communication in order to build a solution to the considered problem, based on their collective experience. Known for their e ciency, metaheuristics show the drawback of comprising too many parameters to be tuned. Such a drawback may rebu some users. Indeed, according to the values given to the parameters of the algorithm, its performance uctuates. So, it is important, for each problem, to nd the parameter set which gives the best performance of the algorithm. However, such a problem is complex and time consuming, especially for novice users. To avoid the user to tune the parameters, numerous researches have been done to propose adaptive algorithms. For such algorithms, the values of the parameters are changed according to the results previously found during the optimization process. TRIBES is an adaptive mono-objective parameter-free PSO algorithm, which was proposed by Maurice Clerc. TRIBES acts as a black box , for which the user has only the problem and the stopping criterion to de ne. The rst objective of this PhD is to make a global study of the behavior of TRIBES under several conditions, in order to determine the strengths and drawbacks of this adaptive algorithm. In order to improve TRIBES, two new strategies are added. First, a regular initialization process is defined in order to insure an exploration as wide as possible of the search space, since the beginning of the optimization process. A new strategy of displacement, based on an hybridation with an estimation of distribution algorithm, is also introduced to maintain the diversity in the swarm all along the process. The increasing need for multiobjective methods leads the researchers to adapt their methods to the multiobjective case. The di culty of such an operation is that, in most cases, the objectives are con icting. We designed MO-TRIBES, which is a multiobjective version of TRIBES. Finally, our algorithms are applied to thresholding segmentation of medical images and to the design of electronic components

La génération de stratégies pour les solveurs en Satisfiabilité Modulo des Théories (SMT) nécessite des outils théoriques et pratiques qui permettent aux utilisateurs d’exercer un contrôle stratégique sur les aspects heuristiques fondamentaux des solveurs de SMT, tout en garantissant leur performance. Nous nous intéressons dans cette thèse au solveur Z3 , l’un des plus efficaces lors des compétitions SMT (SMT-COMP). Dans les solveurs SMT, la définition d’une stratégie repose sur un ensemble de composants et paramètres pouvant être agencés et configurés afin de guider la recherche d’une preuve de (in)satisfiabilité d’une instance donnée. Dans cette thèse, nous abordons ce défi en définissant un cadre pour la génération autonome de stratégies pour Z3, c’est-à-dire un algorithme qui permet de construire automatiquement des stratégies sans faire appel à des connaissances d’expertes. Ce cadre général utilise une approche évolutionnaire (programmation génétique), incluant un système à base de règles. Ces règles formalisent la modification de stratégies par des principes de réécriture, les algorithmes évolutionnaires servant de moteur pour les appliquer. Cette couche intermédiaire permettra d’appliquer n’importe quel algorithme ou opérateur sans qu’il soit nécessaire de modifier sa structure, afin d’introduire de nouvelles informations sur les stratégies. Des expérimentations sont menées sur les jeux classiques de la compétition SMT-COMP. / The Strategy Challenge in Satisfiability Modulo Theories (SMT) claims to build theoretical and practical tools allowing users to exert strategic control over core heuristic aspects of high-performance SMT solvers. In this work, we focus in Z3 Theorem Prover: one of the most efficient SMT solver according to the SMT Competition, SMT-COMP. In SMT solvers, the definition of a strategy relies on a set of tools that can be scheduled and configured in order to guide the search for a (un)satisfiability proof of a given instance. In this thesis, we address the Strategy Challenge in SMT defining a framework for the autonomous generation of strategies in Z3, i.e. a practical system to automatically generate SMT strategies without the use of expert knowledge. This framework is applied through an incremental evolutionary approach starting from basic algorithms to more complex genetic constructions. This framework formalise strategies modification as rewriting rules, where algorithms acts as enginess to apply them. This intermediate layer, will allow apply any algorithm or operator with no need to being structurally modified, in order to introduce new information in strategies. Validation is done through experiments on classic benchmarks of the SMT-COMP.

Les applications réelles liées aux problèmes de satisfaction partielle de contraintes (PCSP : Partial Constraints Satisfaction Problem) sont de plus en plus nombreuses, ce qui justifie l’intérêt croissant des chercheurs pour cette classe de problèmes. La résolution d’un PCSP revient à affecter des valeurs à toutes ses variables tout en maximisant (ou minimisant) une fonction objectif prédéfinie. Ces problèmes sont NP-difficiles, par conséquent il n’existe aucune approche aussi bien exacte qu’heuristique efficace sur les grandes instances. Pour résoudre efficacement les instances difficiles, une multitude de solutions sont proposées, allant de l’hybridation à l’apprentissage en passant par la décomposition. Dans notre travail, nous nous intéressons à cette dernière proposition, qui consiste à fractionner le problème PCSP en plusieurs sous-problèmes PCSP de tailles raisonnables, puis proposer des algorithmes de résolution pour les problèmes décomposés. Cette approche a pour but de bénéficier de la structure du problème afin d’accélérer sa résolution tout en garantissant des solutions optimales ou sous-optimales. Deux grand axes sont explorés : les approches basées sur la décomposition et celles guidées par la décomposition. Les approches basées sur la décomposition consistent à résoudre séparément les parties difficiles du problème décomposé, puis combiner les solutions partielles obtenues en vue d’atteindre une solution globale du problème d’origine. Les approches guidées par la décomposition consistent à développer des métaheuristiques qui tiennent compte de la structure du problème décomposé. Les algorithmes proposés sont testés et validés sur des instances réelles des problèmes PSCP, comme le problème d’affectation de fréquences et le problème de coloration de graphes / The wide range of potential applications concerned by the resolution of Partial Constraints Satisfaction Problems (PCSP) justifies the growing interest of scientists in this class of problems. Solving a PCSP means searching for values to assign to the decision variables in order to maximize (or minimize) a predefined objective function. These problems are NP-hard, so there isn’t an exact approach nor an efficient heuristic able to provide the optimal solution for large instances. In order to solve effectively the difficult instances, numerous approaches based on hybridization, learning or decomposition are proposed. In the present work, we focus on the latter proposal, which consists in splitting the PCSP into several smaller size PCSPs and we propose some methods to solve the decomposed problem. Two wide axes are explored : the resolution based on the decomposition and the one guided by decomposition. The former solves separately the difficult parts of the decomposed problem (cuts or clusters) and then combines partial solutions obtained in order to achieve a global solution for the original problem. The latter aims at benefiting from the structure of the problem to be decomposed in order to accelerate its resolution while ensuring optimal or near optimal solutions. All the proposed algorithms are tested and validated on the well-known benchmarks of PCSP problems such as Frequency Assignment Problem (FAP) and graph coloring problem