A geração de quadros de horários escolares é um problema clássico de otimização que tem sido largamente estudado devido a sua importâncias prática e teórica. O problema consiste em alocar um conjunto de aulas entre professor-turma em períodos de tempo pré-determinados, satisfazendo diferentes tipos de requisitos. Devido a natureza combinatória do problema, a resolução de instâncias médias e grandes torna-se uma tarefa desafiadora. Quando recursos são escassos, mesmo uma solução factível pode ser difícil de ser encontrada. Várias técnicas tem sido propostas na literatura científica para resolver o problema de geração de quadros de horários escolares, no entanto, métodos robustos ainda não existem. Visto que o uso de métodos exatos, como por exemplo, técnicas de programação matemática, não podem ser utilizados na prática, para resolver instâncias grandes da realidade, meta-heurísticas e meta-heurísticas híbridas são usadas com frequência como abordagens de resolução. Nesta pequisa, são desenvolvidas técnicas que combinam programação matemática e heurísticas, denominadas mateheurísticas, para resolver de maneira eficiente e robusta algumas variações de problemas de geração de quadros de horários escolares. Embora neste trabalho sejam abordados problemas encontrados no contexto de instituições brasileiras, os métodos propostos também podem ser aplicados em problemas similares oriundo de outros países. / The school timetabling is a classic optimization problem that has been extensively studied due to its practical and theoretical importance. It consists in scheduling a set of class-teacher meetings in a prefixed period of time, satisfying requirements of different types. Given the combinatorial nature of this problem, solving medium and large instances of timetabling to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Several techniques have been developed in the scientific literature to tackle the high school timetabling problem, however, robust solvers do not exist yet. Since the use of exact methods, such as mathematical programming techniques, is considered impracticable to solve large real world instances, metaheuristics and hybrid metaheuristics are the most used solution approaches. In this research we develop techniques that combine mathematical programming and heuristics, so-called matheuristics, to solve efficiently and in a robust way some variants of the high school timetabling problem. Although we pay special attention to problems arising in Brazilian institutions, the proposed methods can also be applied to problems from different countries.

This doctoral thesis investigates the application of simulation-based optimization (SBO) as an alternative to conventional optimization techniques when the inherent uncertainty and complex features of real manufacturing systems need to be considered. Inspired by a real-world production planning setting, we provide a general formulation of the situation as an extended knapsack problem. We proceed by proposing a solution approach based on single and multi-objective SBO models, which use simulation to capture the uncertainty and complexity of the manufacturing system and employ meta-heuristic optimizers to search for near-optimal solutions. Moreover, we consider the design of matheuristic approaches that combine the advantages of population-based meta-heuristics with mathematical programming techniques. More specifically, we consider the integration of mathematical programming techniques during the initialization stage of the single and multi-objective approaches as well as during the actual search process. Using data collected from a manufacturing company, we provide evidence for the advantages of our approaches over conventional methods (integer linear programming and chance-constrained programming) and highlight the synergies resulting from the combination of simulation, meta-heuristics and mathematical programming methods. In the context of the same real-world problem, we also analyse different single and multi-objective SBO models for robust optimization. We demonstrate that the choice of robustness measure and the sample size used during fitness evaluation are crucial considerations in designing an effective multi-objective model.

[pt] Esta tese faz um estudo do problema do Conjunto Dominante, um problema NP-difícil de grande relevância em aplicações relacionadas ao projeto de rede sem fio, mineração de dados, teoria de códigos, dentre outras. O conjunto dominante mínimo em um grafo é um conjunto mínimo de vértices de modo que cada vértice do grafo pertence a este conjunto ou é adjacente a um vértice que pertence a ele. Três variantes do problema foram estudadas; primeiro, uma variante na qual considera pesos nos vértices, buscando um conjunto dominante com menor peso total; segundo, uma variante onde o subgrafo induzido pelo conjunto dominante está conectado; e, finalmente, a variante que engloba essas duas características. Para resolver esses três problemas, propõe-se um algoritmo híbrido baseado na meta-heurística busca tabu com componentes adicionais de programação matemática, resultando em um método por vezes chamado de mateurística, (matheuristic, em inglês). Diversas técnicas adicionais e vizinhanças largas foram propostas afim de alcançar regiões promissoras no espaço de busca. Análises experimentais demonstram a contribuição individual de todos esses componentes. Finalmente, o algoritmo é testado no problema do código de cobertura mínima, que pode ser visto como um caso especial do problema do conjunto dominante. Os códigos são estudados na métrica Hamming e na métrica Rosenbloom-Tsfasman. Neste último, diversos códigos menores foram encontrados. / [en] This thesis addresses the Dominating Set Problem, an NP- hard problem with great relevance in applications related to wireless network design, data mining, coding theory, among others. The minimum dominating set in a graph is a minimal set of vertices so that each vertex of the graph belongs to it or is adjacent to a vertex of this set. We study three variants of the problem: first, in the presence of weights on vertices, searching for a dominating set with smallest total weight; second, a variant where the subgraph induced by the dominating set needs to be connected, and,finally, the variant that encompasses these two characteristics. To solve these three problems, we propose a hybrid algorithm based on tabu search with additional mathematical-programming components, leading to a method sometimes called matheuristic. Several additional techniques and large neighborhoods are also employed to reach promising regions in the search space. Our experimental analyses show the good contribution of all these individual components. Finally, the algorithm is tested on the covering code problem, which can be viewed as a special case of the minimum dominating set problem. The codes are studied for the Hamming metric and the Rosenbloom-Tsfasman metric. For this last case, several shorter codes were found.

Dans le secteur électrique et chez EDF, l'optimisation mathématique est utilisée pour modéliser et résoudre des problèmes de gestion de la production d'électricité.Citons quelques applications : la modélisation des problèmes d'équilibre des marchés, la gestion des risques d'épuisement des barrages, la programmation des arrêts de tranches nucléaires.Plus particulièrement l'hydroélectricté est une énergie renouvelable, peu chère, flexible mais limitée.Exploiter l'hydraulique constitue donc un enjeu important.Nous nous intéressons à des problèmes d'optimisation de Programmation Non Linéaire en Nombres Entiers (PNLNE) dont les variables de décision sont continues ou discrètes et dont les fonctions exprimant l'objectif et les contraintes sont linéaires ou non.Les non-linéarités et la combinatoire induite par les variables entières rendent les PNLNE difficiles à résoudre.En effet les méthodes existantes n'arrivent pas toujours à résoudre les grands PNLNE à l'optimalité avec des temps de calcul limités.En amont des performances de résolution, la faisabilité est une question préliminaire à aborder puisqu'il faut s'assurer que les PNLNE à résoudre admettent des solutions.Lorsqu'il y a des infaisabilités dans des modèles complexes, il est très utile mais très difficile de les analyser.Par ailleurs la résolution de PNLNE est plus difficile si l'on requiert une certification de la précision exacte des résultats.En effet les méthodes résolutions sont en général mises en oeuvre en arithmétique flottante, ce qui peut donner lieu à une précision approchée.Nous abordons deux problèmes d'optimisation liés à la planification de la production hydraulique, Hydro Unit-Commitment (HUC) en Anglais.Etant données des ressources d'eau finies dans les barrages l'objet du HUC est de prescrire des programmes de production les plus rentables qui soient compatibles avec les spécifications techniques des usines hydrauliques.Le volume, le débit et la puissance sont représentés par des variables continues tandis que l'activation des turbines est communément formulée avec des variables binaires.Les non-linéarités proviennent en général des fonctions qui expriment la puissance générée en fonction du volume et du débit.Nous distinguons deux problèmes : un PLNE avec des caractéristiques linéaires et discrètes et un PNL avec des caractéristiques non linéaires et continues.Dans le 2ème chapitre, nous traitons de la faisabilité d'un HUC réel en PLNE.Comparé à un HUC standard le modèle inclut deux spécifications supplémentaires : des points de fonctionnements discrets sur la courbe puissance-débit ainsi que des niveaux cibles pour le volume des réservoirs.Les complications liées aux données réelles et au calcul numérique, associées aux spécifications du modèle rendent notre problème difficile à résoudre et souvent infaisable.Nous procédons par étape pour identifier et traiter les sources d'infaisabilité, à savoir les erreurs numériques et les infaisabilités de modélisation, pour rendre le problème faisable.Des résultats numériques étayent l'efficacité de notre méthode sur un ensemble de test de 66 instances réelles qui contient de nombreuses infaisabilités.Le 3ème chapitre porte sur l'adaptation de l'algorithme Multiplicative Weights Update (MWU) à la PNLNE.Cette adaptation est fondée sur une reformulation paramétrée spécifique dénommée pointwise.Nous définissons des propriétés souhaitables pour obtenir de bonnes reformulations pointwise et nous fournissons des règles pour adapter l'algorithme étape par étape.Nous démontrons que notre matheuristique du MWU conserve une garantie d'approximation relative contrairement à la plupart des heuristiques.Le MWU est comparée à la méthode Multi-Start pour résoudre un HUC en PNL et les résultats numériques penchent en faveur du MWU. / In the electricity industry, and more specifically at the French utility company EDF, mathematical optimization is used to model and solve problems related to electricity production management.To name a few applications: planning for capacity investments, managing depletion risks of hydro-reservoirs, scheduling outages and refueling for nuclear plants.More specifically, hydroelectricity is a renewable, cheap, flexible but limited source of energy.Harnessing hydroelectricity is thus critical for electricity production management.We are interested in Mixed-Integer Non-Linear Programming (MINLP) optimization problems.They are optimization problems whose decision variables can be continuous or discrete and the functions to express the objective and constraints can be linear or non-linear.The non-linearities and the combinatorial aspect induced by the integer variables make these problems particularly difficult to solve.Indeed existing methods cannot always solve large MINLP problems to the optimum within limited computational timeframes.Prior to solution performance, feasibility is preliminary challenge to tackle since we want to ensure the MINLP problems to solve admit feasible solutions.When infeasibilities occur in complex models, it is useful but not trivial to analyze their causes.Also, certifying the exactness of the results compounds the difficulty of solving MINLP problems as solution methods are generally implemented in floating-point arithmetic, which may lead to approximate precision.In this thesis, we work on two optimization problems - a Mixed-Integer Linear Program (MILP) and a Non-Linear Program (NLP) - related to Short-Term Hydropower production Scheduling (STHS).Given finite resources of water in reservoirs, the purpose of STHS is to prescribe production schedules with largest payoffs that are compatible with technical specifications of the hydroelectric plants.While water volumes, water flows, and electric powers can be represented with continuous variables, commitment statuses of turbine units usually have to be formulated with binary variables.Non-linearities commonly originate from the Input/Output functions that model generated power according to water volume and water flow.We decide to focus on two distinguished problems: a MILP with linear discrete features and a NLP with non-linear continuous features.In the second chapter, we deal with feasibility issues of a real-world MILP STHS.Compared with a standard STHS problem, the model features two additional specifications:discrete operational points of the power-flow curve and mid-horizon and final strict targets for reservoir levels.Issues affecting real-world data and numerical computing, together with specific model features, make our problem harder to solve and often infeasible.Given real-world instances, we reformulate the model to make the problem feasible.We follow a step-by-step approach to exhibit and cope with one source of infeasility at a time, namely numerical errors and model infeasibilities.Computational results show the effectiveness of the approach on an original test set of 66 real-world instances that demonstrated a high occurrence of infeasibilities.The third chapter is about the transposition of the Multiplicative Weights Update algorithm to the (nonconvex) nonlinear and mixed integer nonlinear programming setting, based on a particular parametrized reformulation of the problem - denoted pointwise.We define desirable properties for deriving pointwise reformulation and provide generic guidelines to transpose the algorithm step-by-step.Unlike most metaheuristics, we show that our MWU metaheuristic still retains a relative approximation guarantee in the NLP and MINLP settings.We benchmark it computationally to solve a hard NLP STHS.We find it compares favorably to the well-known Multi-Start method, which, on the other hand, offers no approximation guarantee.

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Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-05-22T20:04:01Z No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-31T13:43:27Z (GMT) No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-31T13:43:34Z (GMT) No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Made available in DSpace on 2017-05-31T13:52:08Z (GMT). No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) Previous issue date: 2017-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Vehicle routing problems occur in many practical situations where the distribution of goods and / or services to different demand points is necessary. In this context, this research aims to study a ship routing and scheduling problem that arises at the collection and delivery operations of different types of crude oil from offshore platforms to coastal terminals. In the paradigm adopted for the representation of the problem, the transportation is largely the result of the need to maintain inventories at each supply point (platforms) between minimum and maximum levels, considering production rates on these operating points and the demand attendance of each product in the coastal terminals. The routing and scheduling of the fleet aims to achieve minimum variable cost solutions, and considers various operational constraints, such as the maximum cargo volume transported on each ship, the ships mooring in the operational points ports, the simultaneous unloading of the ships in terminals with more than one berth, among many others. In this research, Inventory Constrained Routing Problem (ICRP) models in the maritime context have been modified and extended for appropriately representating and solving real problems based on data collected in a case study performed on a Brazilian oil company, involving relatively short distances and time horizons. Small sized instances are solved by a mathematical programming software. Given the difficulties of solving larger examples, this study proposes a multistart heuristic method that includes a metaheuristic GRASP and improvement procedures, and also a rolling horizon heuristic. Both methods provide feasible good quality solutions in reasonable computing times. In order to improve the quality of the solutions found by these constructive methods, it is also discussed a procedure that combines the mathematical programming software and local search heuristic methods (matheuristic). The results show the potential of the proposed models and solution methods to tackle the problem and produce competitive solutions. / Problemas de roteirização de veículos ocorrem em diversas situações práticas onde se faz necessária a distribuição de bens e/ou serviços a pontos dispersos de demanda. Nesse contexto, a presente pesquisa visa o estudo de um problema de roteirização e programação de navios presente em operações de coleta e entrega de diferentes tipos de óleo cru de diversas plataformas offshore para vários terminais costeiros. No paradigma adotado para representação do problema, o transporte dos produtos é em grande parte o resultado da necessidade de manutenção dos estoques em cada ponto de suprimento (plataformas) entre níveis mínimos e máximos, considerando-se as taxas de produção nesses pontos operacionais, assim como o atendimento da demanda de cada produto nos terminais costeiros para abastecer as refinarias. A roteirização e programação da frota visa a obtenção de soluções de mínimo custo variável e considera várias restrições operacionais, tais como o volume máximo de carga transportada em cada navio, a viabilidade de atracação de navios em portos dos pontos operacionais, os descarregamentos simultâneos de navios em terminais com mais de um berço, dentre várias outras. Nesse sentido, modelos de otimização da literatura de roteirização veículos com restrições de estoque (Inventory Constrained Routing Problem – ICRP) no contexto marítimo foram modificados e estendidos para representação do problema e resolução de exemplares de uma situação real, definidos a partir de dados coletados em um estudo de caso realizado em uma empresa petrolífera nacional, envolvendo distâncias relativamente curtas e com horizontes de planejamento de curto prazo (poucas semanas). Exemplares de pequeno porte são resolvidos por meio da utilização de um software de programação matemática. Dada a dificuldade de resolução dos exemplos de maior porte, é proposto um método heurístico de múltiplos reinícios composto por uma metaheurística GRASP e procedimentos de melhoria, além de uma heurística de horizonte rolante, que proporcionaram a obtenção de soluções factíveis de boa qualidade em tempos computacionais aceitáveis. Com intuito de melhorar a qualidade das soluções encontradas pelos métodos construtivos, é também discutido um procedimento que combina o software de programação matemática e métodos heurísticos com busca local (mateheurística). Os resultados mostram o potencial dos modelos e métodos de solução aqui desenvolvidos e propostos para abordar o problema e produzir soluções competitivas em relação às soluções da empresa.