L’optimisation de la planification de la maintenance des équipements de production d’électricité est une question importante pour éviter des temps d’arrêt inutiles et des coûts opérationnels excessifs. Dans cette thèse, nous présentons une classification multidimensionnelle des études de Recherche Opérationnelle portant sur ce sujet. Le secteur des énergies renouvelables étant en pleine expansion, nous présentons et discutons ensuite d’un problème de maintenance de parcs éoliens terrestres. Le problème est traité sur un horizon à court terme et l’objectif est de construire un planning de maintenance qui maximise le revenu lié à production d’électricité des éoliennes tout en prenant en compte des prévisions de vent et en gérant l’affectation de techniciens. Nous présentons plusieurs modélisations du problème basées sur la programmation linéaire. Nous décrivons aussi une recherche à grands voisinages basée sur la programmation par contraintes.Cette méthode heuristique donne des résultats probants.Nous résolvons ensuite le problème avec une approche exacte basée sur une décomposition du problème. Dans cette méthode, nous construisons successivement des plannings de maintenance optimisés et rejetons, à l’aide de coupes spécifiques, ceux pour lesquels la disponibilité des techniciens est insuffisante. Les résultats suggèrent que cette méthode est la mieux adaptée pour ce problème. Enfin, pour prendre en compte l’incertitude inhérente à la prévision de vitesses de vent, nous proposons une approche robuste dans laquelle nous prenons des décisions garantissant la réalisabilité du planning de maintenance et le meilleur revenu pour les pires scénarios de vent. / Efficiently scheduling maintenance operations of generating units is key to prevent unnecessary downtime and excessive operational costs. In this work, we first present a multidimensional classification of the body of work dealing with the optimization of the maintenance scheduling in the operations research literature. Motivated by the recent emergence of the renewable energy sector as an Environmental priority to produce low-carbon power electricity, we introduce and discuss a challenging Maintenance scheduling problem rising in the onshore wind industry. Addressing the problem on a short-term horizon, the objective is to find a maintenance plan that maximizes the revenue generated by the electricity production of the turbines while taking into account wind predictions, multiple task execution modes, and technician-to-task assignment constraints. We start by presenting several integer linear Programming formulations of the problem. We then describe a constraint programming-based large neighborhood search which proves to be an efficient heuristic solution method. We then design an exact branch-and-check approach based on a decomposition of the problem. In this method, we successively build maintenance plans while discarding – using problem-specific cuts – those that cannot be performed by the technicians. The results suggest that this method is the best suited to the problem. To tackle the Inherent uncertainty on the wind speed, we also propose a robust approach in which we aim to take risk-averse decisions regarding the revenue associated with the maintenance plan and its feasibility.

Currently a growing number of users depend on the Edge Cloud Computing Paradigm in a Metro Optical Network (MON). This has led to increased competition among the Cloud Service Providers (CPs) to supply incentives for the user through guaranteed Quality of Service (QoS). If the CP fails to guarantee the QoS for the accepted request, then the user will move to another CP. Making an informed decision dynamically in such a sensitive situation demands that the CP knows the user's application requirements. The Software Defined Networking (SDN) paradigm enabled the CP to achieve such desired requirement. Therefore, a framework called Virtual Network Embedding on SDN-based Metro Optical Network (VNE-MON) is proposed in this Thesis. The use of SDN paradigm in the framework guarantees profit to the CP as well as QoS to the user.\par The design concept of the SDN control plane, raises concerns regarding its scalability, reliability and performance compared to a traditionally distributed network. To justify concerns regarding the SDN, the performance of VNE-MON and its possible dependancy on the controller location is investigated. Several strategies are proposed and formulated using Integer Linear Programming to determine the controller location in a MON. Performance results from the assessment of the VNE-MON illustrates that it is more stable compare to GMPLS-based network. It is evident that the controller location's attributes have a significant effect on the efficacy of the accepted VN request.

Neste trabalho, estudamos o problema a recoloração convexa de grafos, denotado por RC. Dizemos que uma coloração dos vértices de um grafo G é convexa se, para cada cor tribuída d, os vértices de G com a cor d induzem um subgrafo conexo. No problema RC, é dado um grafo G e uma coloração de seus vértices, e o objetivo é recolorir o menor número possível de vértices de G tal que a coloração resultante seja convexa. A motivação para o estudo deste problema surgiu em contexto de árvores filogenéticas. Sabe-se que este problema é NP-difícil mesmo quando G é um caminho. Mostramos que o problema RC parametrizado pelo número de mudanças de cor é W[2]-difícil mesmo se a coloração inicial usa apenas duas cores. Além disso, provamos alguns resultados sobre a inaproximabilidade deste problema. Apresentamos uma formulação inteira para a versão com pesos do problema RC em grafos arbitrários, e então a especializamos para o caso de árvores. Estudamos a estrutura facial do politopo definido como a envoltória convexa dos pontos inteiros que satisfazem as restrições da formulação proposta, apresentamos várias classes de desigualdades que definem facetas e descrevemos os correspondentes algoritmos de separação. Implementamos um algoritmo branch-and-cut para o problema RC em árvores e mostramos os resultados computacionais obtidos com uma grande quantidade de instâncias que representam árvores filogenéticas reais. Os experimentos mostram que essa abordagem pode ser usada para resolver instâncias da ordem de 1500 vértices em 40 minutos, um desempenho muito superior ao alcançado por outros algoritmos propostos na literatura. / In this work we study the convex recoloring problem of graphs, denoted by CR. We say that a vertex coloring of a graph G is convex if, for each assigned color d, the vertices of G with color d induce a connected subgraph. In the CR problem, given a graph G and a coloring of its vertices, we want to find a recoloring that is convex and minimizes the number of recolored vertices. The motivation for investigating this problem has its roots in the study of phylogenetic trees. It is known that this problem is NP-hard even when G is a path. We show that the problem CR parameterized by the number of color changes is W[2]-hard even if the initial coloring uses only two colors. Moreover, we prove some inapproximation results for this problem. We also show an integer programming formulation for the weighted version of this problem on arbitrary graphs, and then specialize it for trees. We study the facial structure of the polytope defined as the convex hull of the integer points satisfying the restrictions of the proposed ILP formulation, present several classes of facet-defining inequalities and the corresponding separation algorithms. We also present a branch-and-cut algorithm that we have implemented for the special case of trees, and show the computational results obtained with a large number of instances. We considered instances which are real phylogenetic trees. The experiments show that this approach can be used to solve instances up to 1500 vertices in 40 minutes, comparing favorably to other approaches that have been proposed in the literature.

This diploma thesis deals with optimization models with design of a new waste management infrastructure in the Czech Republic, such that combustible waste, which is not utilized by the material recovering, can be used by energy recovering. This task is handled by optimization models, including trac and mixing problems. First of all, the concepts of graph theory and optimization are presented in this paper. Subsequently, some of the GAMS functions are discussed, and later the VBA programming language used to handle the larger data quickly is presented. In the main part, three gradually expanding models are developed. At the end the data from the waste management information system are implemented into them.

La 1ere partie de ce travail traite l'optimisation des tournées sous forme d'un problème d'optimisation nommé Le problème de Voyageur de Commerce. Dans cette partie nous nous intéressons à faire une riche présentation du problème de Voyageur de Commerce, ses variantes, puis nous proposons une stratégie de génération de contrainte pour la résolution du TSP. Ensuite on traite sa version stochastique : le problème de Voyageur de commerce Probabiliste. Nous proposons une formulation mathématique du PTSP et nous présentons des résultats numériques obtenus par résolution exacte pour une série d'instances de petite taille. Dans la seconde partie, nous proposons une méthode d'approximation générale permettant d'approcher différents type de données, d'abord nous traitons l'approximation d'un signal de vent (cas simple, ID), ensuite l'approximation d'un champ de vecteurs avec prise en compte de la topographie qui constitue la principale contribution de cette partie. / The first part of this work deals with route optimization in the form of an optimization problem named The Traveler's Business Problem. In this part we are interested to make a rich presentation of the problem of Traveler Commerce, its variants, then we propose a strategy of constraint generation for the resolution of the TSP. Then we treat its stochastic version : the probabilistic business traveler problem. We propose a mathematical formulation of the PTSP and we present numerical results obtained by exact resolution for a series of small instances. In the second part, we propose a method of general approximation to approximate different type of data, first we treat the approximation of a wind signal (simple case, 1D), then the approximation of a vector field taking into account the topography which is the main contribution of this part.

Orientador: Fábio Bertequini Leão / Resumo: Este trabalho apresenta modelos de programação não linear e linear inteira binária como novos métodos para resolver o problema de diagnóstico de faltas em sistemas de transmissão de energia elétrica. Os modelos de otimização são desenvolvidos com base no conjunto de coberturas mínimas e possui como restrições as equações que descrevem a lógica e a filosofia de proteção empregadas por empresas de energia elétrica. As equações de restrições modelam a associação dos alarmes dos relés de proteção informados pelo sistema de supervisão e aquisição de dados (SCADA) com os estados esperados das funções dos relés de proteção. Os modelos de programação matemática realizam o diagnóstico de falta em uma única etapa, identificando a seção em falta através da análise dos estados dos disjuntores e das funções de proteção associadas a cada equipamento do sistema elétrico. O modelo proposto é um problema muito complexo de programação não linear inteira binária, portanto é reformulado como outro problema, em que algumas expressões são linearizadas, o que resulta em um modelo matemático de programação linear inteiro binário. A solução ótima obtida pelo modelo proposto é encontrada utilizando solvers comerciais de programação matemática. Os resultados obtidos mostram eficiência e robustez do modelo matemático. Na literatura, o problema de diagnóstico de falta é resolvido principalmente por técnicas heurísticas, portanto, o método proposto é inovador. / Doutor

Dans un graphe non orienté, le Problème de Coloration de Graphe (PCG) consiste à assigner à chaque sommet du graphe une couleur de telle sorte qu'aucune paire de sommets adjacents n'aient la même couleur et le nombre total de couleurs est minimisé. DSATUR est un algorithme exact efficace pour résoudre le PCG. Un de ses défauts est qu'une borne inférieure est calculée une seule fois au noeud racine de l'algorithme de branchement, et n'est jamais mise à jour. Notre nouvelle version de DSATUR surpasse l'état de l'art pour un ensemble d'instances aléatoires à haute densité, augmentant significativement la taille des instances résolues. Nous étudions trois formulations PLNE pour le Problème de la Somme Chromatique Minimale (PSCM). Chaque couleur est représentée par un entier naturel. Le PSCM cherche à minimiser la somme des cardinalités des sous-ensembles des sommets recevant la même couleur, pondérés par l'entier correspondant à la couleur, de telle sorte que toute paire de sommets adjacents reçoive des couleurs différentes. Nous nous concentrons sur l'étude d'une formulation étendue et proposons un algorithme de Branch-and-Price. / Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph such that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR is an effective exact algorithm for the VCP. We introduce new lower bounding techniques enabling the computing of a lower bound at each node of the branching scheme. Our new DSATUR outperforms the state of the art for random VCP instances with high density, significantly increasing the size of solvable instances. Similar results can be achieved for a subset of high density DIMACS instances. We study three ILP formulations for the Minimum Sum Coloring Problem (MSCP). The problem is an extension of the classical Vertex Coloring Problem in which each color is represented by a positive natural number. The MSCP asks to minimize the sum of the cardinality of subsets of vertices receiving the same color, weighted by the index of the color, while ensuring that vertices linked by an edge receive different colors. We focus on studying an extended formulation and devise a complete Branch-and-Price algorithm.

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The development of sustainable business models is a challenging task since various factors might influence the results of an assessment. Given the complexity at the municipal level, system interdependencies between different alternatives need to be considered. One possibility to support decision makers is to apply energy system optimization models. Existing optimization models, however, ignore the roles different actors play and the resulting impact they have. To address this research issue, this thesis presents an integrated techno-economic optimization framework called IRPopt (Integrated Resource Planning and Optimization). A proven graph-based energy system approach allows the accurate modeling of deployment systems by considering different energy carriers and technical processes. In addition, a graph-based commercial association approach enables the integration of actor-oriented coordination. This is achieved by the explicit modeling of market actors on one layer and technology processes on another layer as well as resource flow interrelations and commercial agreements mechanism among and between the different layers. Using the optimization framework, various optimization problems are solvable on the basis of a generic objective function. For demonstration purposes, this thesis assesses the business models demand response and community storage. The applied examples demonstrate the modeling capabilities of the developed optimization framework. Further, the dispatch results show the usefulness of the described optimization approach.

In this thesis we address the problem of integrated software pipelining for clustered VLIW architectures. The phases that are integrated and solved as one combined problem are: cluster assignment, instruction selection, scheduling, register allocation and spilling. As a first step we describe two methods for integrated code generation of basic blocks. The first method is optimal and based on integer linear programming. The second method is a heuristic based on genetic algorithms. We then extend the integer linear programming model to modulo scheduling. To the best of our knowledge this is the first time anybody has optimally solved the modulo scheduling problem for clustered architectures with instruction selection and cluster assignment integrated. We also show that optimal spilling is closely related to optimal register allocation when the register files are clustered. In fact, optimal spilling is as simple as adding an additional virtual register file representing the memory and have transfer instructions to and from this register file corresponding to stores and loads. Our algorithm for modulo scheduling iteratively considers schedules with increasing number of schedule slots. A problem with such an iterative method is that if the initiation interval is not equal to the lower bound there is no way to determine whether the found solution is optimal or not. We have proven that for a class of architectures that we call transfer free, we can set an upper bound on the schedule length. I.e., we can prove when a found modulo schedule with initiation interval larger than the lower bound is optimal. Experiments have been conducted to show the usefulness and limitations of our optimal methods. For the basic block case we compare the optimal method to the heuristic based on genetic algorithms. This work has been supported by The Swedish national graduate school in computer science (CUGS) and Vetenskapsrådet (VR).