Les réseaux de chauffage urbain (DHN) sont un moyen efficace de fournir de l'énergie thermique aux consommateurs. L'état actuel de la technique montre que les DHN évoluent vers des réseaux thermiques intelligents dans des systèmes énergétiques intégrés alors que leur conception est basée sur les principes de durabilité. Sur cette base, cette thèse couvre deux domaines de recherche principaux : Fonctionnement et conception des systèmes de chauffage urbain. Dans la partie A de cette thèse, des méthodes avancées pour le fonctionnement de la DHN sont développées à l'aide d'analyses exergétiques et thermoéconomiques. Cela inclut la formulation de bilans de coûts exergétiques pour les modèles de réseau basés sur des graphiques. La partie intrinsèque est le déploiement d'une matrice algébrique, qui détermine les coûts exergétiques pour la modélisation dynamique du système. Une étude de cas d'un réseau réel prouve que la méthodologie proposée offre de nouvelles perspectives sur l'allocation individuelle des coûts, ce qui aide à évaluer la faisabilité de l'intégration par des tiers et l'intégration des sources d'énergie distribuées. Dans la partie B de cette thèse, un nouvel indicateur appelé «load deviation index (LDI)» est proposé pour lier les mesures de la demande (DSM) à la conception durable des systèmes DHN. Pour cela, un cadre de conception axé sur les affaires est proposé, qui prend en compte les influences critiques dans le DHN tout en évitant un trop grand détail. Le comportement du DSM est analysé du point de vue du système et son impact sur la conception du DHN est étudié dans deux études de cas. Alors que l'un se concentre sur les benchmarks pour différentes options de conception en utilisant une métrique de durabilité multicritères, un autre donne des indications détaillées sur l'utilité du cadre proposé pour la conception en évaluant l'impact de DSM sur les améliorations de conception possibles. / District heating networks (DHN) arean efficient way of providing thermal energy to consumers. Current state of the art shows that DHNs are developing towards smart thermal networks in integrated energy systems while their design is based upon the principles of sustainability. Based on that, this thesis covers two main research areas: Operation and design of district heating systems. In part A of this thesis, advanced methods for DHN operation are developed with the help of exergetic and thermoeconomic analysis. This includes the formulation of exergetic cost balances for graph-based network models. Intrinsic part is the deployment of an algebraic matrix, which determines the exergetic costs for dynamic system modeling. A case study of areal-existing network provides evidence that the proposed methodology offers new insights into individual allocation of costs which helps to assess the feasibility of third-party integration and the integration of distributed energy sources. In part B of this thesis, a new indicator called “load deviation index (LDI)” is proposed to link demand side measures (DSM) with the sustainable design of DHN systems. For that, abusiness-focused design frameworks proposed which takes the critical influences of DHN into account while avoiding a too high detail. DSM behavior is analyzed from a system perspective and its impact on DHN design is studied in two case studies. While one focuses on benchmarks for different design options using a multi-criteria sustainability metric, another gives detailed insights into the usefulness of the proposed framework for design purposes through assessing the impact of DSM on possible design improvements using a multi-objective optimization approach.

Cette thèse s’intéresse à trouver des solutions informatiques à certains problèmes de l’optimisation combinatoire, à savoir les problèmes de tournées de véhicules. Elle aborde les problèmes de Transport A la Demande (TAD). L’objectif principal visé dans cette thèse fait appel à certaines approches exactes et certaines approches méta-heuristiques pour résoudre des problèmes d’optimisation multi-objective de Transport A la Demande avec plusieurs véhicules. En effet, nos principaux objectifs de recherche consistent à : -I) Résoudre un problème multi-objectif de Transport A La Demande multi-véhicules basé sur la qualité de service ; - II) Résoudre un autre problème de Transport A la Demande multi-objectifs multi-véhicules. Ce problème traite un cas spécifique et qui consiste à l’application de ce problème aux domaines de l’Hospitalisation A Domicile (HAD). Nous avons appliqué des algorithmes exacts de "Branch and Bound" et des méthodes méta-heuristiques telles que l’algorithme évolutionnaire "Algorithme Génétique" et l’algorithme de "Colonie de Fourmis" pour apporter des solutions efficaces à ces différents problèmes. Un ensemble de résultats numériques est présenté pour chacune de ces méthodes pour montrer leurs capacités de produire des solutions de haute qualité en temps de calcul raisonnables. / This thesis focuses on finding computer science solutions for some combinatorial optimization problems, namely Vehicle Routing Problems (VRP). The thesis addresses the Dial A Ride Problems (DARP). Its main objective is to use some exact and meta-heuristics approaches to solve multi-objective optimization of Dial A Ride Problem with multi-vehicles. Hence, our main research aims are : - I)Solve a multi-objective Dial A Ride Problem with multi-vehicles based on quality of service, this problem treats a general case ; - II) Solve another multi-objective Dial A Ride Problem with multi-vehicles, this problem deals with a specific case which is an application of the Dial A Ride Problem in Home Health Care (HHC). We have also applied exact algorithms "Branch and Bound" and meta-heuristic algorithms such as evolutionary algorithms "Genetic Algorithm" and "Ant Colony" algorithm to provide effective solutions to these different problems. A set of numerical results are presented for each of these methods. Our results show that they produce high quality solutions in a reasonable execution time for all the treated problems.

Encontrar a configuração de mínimas perdas ôhmicas ou que forneça um adequado plano de restabelecimento aptos a ocorrência de faltas permanentes são problemas de natureza combinatorial, com múltiplos objetivos e restrições, que envolvem funções cujas características, em geral, dificultam o uso de técnicas de programação matemática. Algoritmos Evolutivos têm apresentado resultados animadores para esses problemas, especialmente quando aplicados em sistemas de distribuição de grande porte. Neste trabalho são propostas duas novas metodologias, baseadas em Algoritmos Evolutivos Multi-Objetivo, para reconfiguração de redes em sistemas de distribuição, que podem ser aplicadas para o tratamento dos problemas de redução de perdas ôhmicas e restabelecimento de energia em sistemas de grande porte (com milhares de barras, linhas e chaves). Para o desenvolvimento dessas metodologias, foi utilizado uma estrutura de dados para manipular grafos produzindo exclusivamente configurações radiais e conexas, chamada Representação Nó-profundidade. As metodologias propostas foram testadas para diversos sistemas, dentre os quais destaca-se um com 30:880 barras, tendo sido satisfatórios os resultados obtidos. Para o problema de restabelecimento de energia foram testados falta única e múltiplas faltas. / Find the distribution system configuration of minimum power losses or that provides an adequate service restoration plan is a combinatorial, multi-objective and multi constraint problems, which involves functions whose characteristics, in general, difficult the use of mathematical programming techniques. Evolutionary Algorithms have shown relevant results for these problems, especially for Large-Scale Distribution Systems. This work proposes two methodologies for network reconfiguration based on Multi-Objective Evolutionary Algorithms, which can be applied to treat the problems of power loss reduction and service restoration in large scale distribution systems (with thousands of buses, lines and switches). In order to develop these methodolgies, it was used a data structure to manipulate graphs producing exclusively radial and connected connections, called Node Depth Encoding. The proposed methodologies were successfully tested in several distribution systems, among them one with 30,880 buses. The problem of service restoration is analyzed considering cases of single and multiple faults.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-08-29T15:51:26Z No. of bitstreams: 2 Dissertação_pós_defesa.pdf: 13484145 bytes, checksum: d45c9d8ffd66532d7cea17f178e2fe9c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-08-29T15:51:26Z (GMT). No. of bitstreams: 2 Dissertação_pós_defesa.pdf: 13484145 bytes, checksum: d45c9d8ffd66532d7cea17f178e2fe9c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This study aimed to develop and calibrate a distributed hydrological model used for a one-dimensional drainage of a peri-urban catchment using the optimization multi-objective method Non -dominated Sorting Genetic Algorithm (NSGA - II) for model calibration. Computational algorithms developed in MATLAB environment were adopted to make this study possible. This model allows a precipitation event to set the surface runoff hydrograph at any position of the watershed (planes or channels) regarding infiltration effect and soil physical characteristics. Objective functions were defined and used simultaneously to calibrate the model. From sensitivity analysis performed, it was found that the model is more affected by the parameters related to permeable areas. The model fit was very good, illustrating the applicability of multi-objective calibration in exploring ideal area and to obtain ideal solutions. Validation proved the efficiency of the model used for other different rainfall events in Samambaia stream basin, generating outputs with good accuracy and optimal theoretical value results for Nash & Sutcliffe coefficients of efficiency near the area region. / O presente trabalho propôs desenvolver e calibrar um modelo hidrológico distribuído unidimensional aplicado a drenagem de uma bacia hidrográfica peri-urbana utilizando o método de otimização multi-objetivo Non-dominated Sorting Genetic Algorithm (NSGA-II) para a calibração do modelo. Para tornar possível a realização deste trabalho foram adotadas rotinas computacionais desenvolvidas em ambiente MATLAB. O modelo desenvolvido permite, para um evento de precipitação, determinar o hidrograma de escoamento superficial em qualquer posição da bacia hidrográfica (planos ou canais) considerando o efeito da infiltração e das características físicas do solo. Foram definidas funções objetivo e aplicadas simultaneamente na calibração do modelo. Da análise de sensibilidade realizada, verificou-se que o modelo é mais impactado pelos parâmetros relativos às áreas permeáveis. O ajuste do modelo foi muito bom, ilustrando a aplicabilidade da calibração multi-objetivo em explorar a região ideal e obter soluções ideais. A validação comprovou a eficiência do modelo, aplicada a outros eventos chuvosos diferentes ocorridos na bacia do córrego Samamabaia, gerando saídas com acurácia satisfatória e resultados para os coeficientes de eficiência Nash & Sutcliffe próximos à região do valor ótimo teórico.

As distribuidoras de energia elétrica anualmente elaboram o Plano de Investimentos, que se constitui parte extremamente relevante do Plano de Negócios da Companhia, composto pelos investimentos a serem feitos nos próximos anos. Em função da conjuntura do sistema e dos estudos de planejamento, há sempre diversas propostas de investimento a serem cotejadas e, para selecionar os projetos a serem desenvolvidos, é necessária uma meticulosa análise econômica e financeira. Nesse tipo de análise, torna-se crucial ponderar as exigências do Órgão Regulador para o reconhecimento tarifário de um investimento, bem como as incertezas quanto à evolução da conjuntura sistêmica, aplicando técnicas da Engenharia Econômica para avaliar o retorno sobre o capital investido. A diferença principal deste trabalho, em relação à análise convencional de viabilidade de Projetos de Distribuição, decorre do fato de que se desenvolveu uma metodologia para avaliação de viabilidade e comparação entre si de alternativas de planos de expansão, ao invés da análise individualizada de projetos tradicional. Nesse contexto, a melhor decisão de investimento fica condicionada por variáveis exógenas ao tradicional processo de planejamento em si e, para viabilizar a inclusão das principais variáveis de comportamento aleatório, optou-se pela utilização de metodologia baseada em Opções Reais, que é uma técnica utilizada no mercado financeiro. Para melhor incorporar todas as nuances que condicionam o desempenho econômico-financeiro das alternativas em cotejo e aprimorar o processo de tomada de decisão, utiliza-se, também, técnicas de análise multi-objetivo para imputar os benefícios sociais na avaliação final, feita na etapa de tomada de decisão. / The electrical distribution companies annually prepare their Investment Plan, which is an important part of the company Business Plan, presenting the investments to be made for the coming years. There are several investment proposals, and to select the projects to be invested is necessary a precise economic and financial analysis considering the requirements of the tariff regulator for the recognition of an investment. The project feasibility analysis should to apply techniques of Economic Engineering to assess the rate of return of the invested capital. The main feature of this work, when compared to the feasibility conventional analysis of Distribution Projects, is that a new methodology was developed for feasibility assessment and comparison between alternative expansion plans, featuring important component of the investments contemplated in a Investment Plan. In this context, the best investment decisions is conditioned by additional variables besides that of the traditional planning process itself. In order to make an easier inclusion of the main variables presenting random behavior, it was used a methodology based on \"Real Options\", which is a technique used in the financial market. To better incorporate all the nuances that affect the financial performance of the alternatives under comparison, as well as to improve the decision making process, multi-objective analytical techniques was also used, aiming at to allocate welfare benefits in the decision-making final evaluation.

Desenvolver um sistema de distribuição de energia confiável é certamente um desafio inerente aos profissionais do setor elétrico. Porém, os sistemas estão sujeitos a falhas e, sendo assim, o rápido restabelecimento traz a satisfação do cliente e reduz as compensações pagas pelas concessionárias de energia. Neste contexto a presente dissertação visa avaliar a metodologia para restabelecimento de energia denominada AEMT-H que se baseia em algoritmos evolutivos multi-objetivo se na estrutura de dados chamada Representação Nó- Profundidade (RNP). Esta avaliação ocorrerá através da aplicação do AEMT-H para obtenção de planos de restabelecimento de energia após a ocorrência de faltas simples no sistema COPEL da cidade de Londrina. Os resultados gerados serão avaliados estatisticamente e ainda subjetivamente pelos profissionais do COD da concessionária. Os algoritmos evolutivos têm apresentado resultados animadores para os problemas de restabelecimento de energia. Em especial, os resultados obtidos, quando da representação computacional de sistemas de distribuição de grande porte (com milhares de barras e chaves) através da RNP, possuem como característica o tempo de resposta da ordem de segundos, instigando a evolução das pesquisas para utilização desta metodologia inclusive em aplicativos de tempo real. O sistema de Londrina possui 30.156 barras, 2.660 chaves \"NF\", 250 chaves \"NA\" e atende um universo de mais de 231.000 consumidores ligados diretamente ao sistema de 13,8 kV ou, após os transformadores de distribuição, nas tensões de 220V e 127V. Neste sistema estão presentes 6 subestações 138 kV/13,8 kV e 64 circuitos alimentadores, totalizando uma capacidade de transformação de energia de 541,7 MVA. / The development of a reliable distribution system is certainly a challenge to electrical industry professionals. However, these systems are subject to failures and thus the fast restoration brings customer satisfaction and reduces the compensation paid by the electricity utilities. In this context, this dissertation aims to evaluate the methodology for service restoration called \"AEMT-H\", which is based on multi-objective evolutionary algorithms and in the data structure called Node Depth Encoding (NDE). This evaluation will occur by applying the \"AEMT-H\" to obtain service restoration plans considering the occurrence of simple faults in the COPEL system of the city of Londrina. The obtained results will bee valuated statistically and subjectively by professionals of the Distribution Operation Center. It is important to highlight that Evolutionary algorithms have shown promising results to treat the service restoration problem in distribution systems. In particular, the results obtained when using NDE tocomputationally represent the electrical topology of large distribution systems (with thousand of buses and switchers) are very interesting in terms of time processing (in the order of seconds). The system of Londrina has 30,156 buses, 2,660 switchers normally closed, 250 switchers normally opened and supplies a universe of more than 231,000 consumers connected directly to the system with voltage of 13.8 kV or, after distribution transformers, with voltages of 220V and 127V. This system contains 6 substations 138 kV/13,8 kV and 64 feeders, and a installed power of 541.7 MVA.

Le covoiturage se présente comme une solution de transport alternative qui vient soigner l’image environnementale, économique et sociétale de la voiture personnelle. Le problème du covoiturage dynamique consiste à élaborer en temps réel des tournées de véhicules optimisés, afin de répondre au mieux aux demandes instantanées de transport.C’est dans ce cadre que s’inscrivent nos travaux où l’optimisation et le temps réel sont les maître-mots. Étant donné la complexité exponentielle du problème, nous optons pour des méthodes approximatives pour le résoudre. Nous présentons notre première contribution en proposant une métaheuristique basée sur la recherche tabou. L'algorithme utilise un système de mémoire explicite et plusieurs stratégies de recherches développées pour éviter le piégeage par des optimums locaux. Ensuite, nous introduisons notre deuxième contribution qui se présente sous la forme d’une approche évolutionnaire supportée par un codage dynamique et basée sur des opérateurs génétiques contrôlés. La complexité exponentielle du problème nous amène à dévoiler notre troisième méthodologie, en proposant une approche évolutionnaire originale dans laquelle les chromosomes sont définis comme des agents autonomes et intelligents. Grâce à un protocole de négociation puissant, les Agents Chromosomes gèrent les opérateurs génétiques et orientent la recherche afin de trouver des solutions optimales dans un temps de calcul réduit. Dans la perspective d’une meilleure combinaison entre le covoiturage et les autres modes de transport, nous concevons un système baptisé DyCOS, intégrant nos approches et applications dédiées à la résolution du problème du covoiturage dynamique. / Carpooling is presented as an alternative transport solution that comes treat environmental image, economic and societal personal car. The dynamic carpooling problem is to develop real-time optimized touring vehicles to better respond to the instantaneous transport demands.Our work belongs within this context, where optimization and real time are the key words. Given the exponential complexity of the dynamic ridematching problem, we opt for the approximate methods to solve it. We present our first contribution by proposing a metaheuristic based on the multi-criteria tabu search. The proposed algorithm employs an explicit memory system and several searching strategies developed to avoid the entrapment by local solutions. Afterward, we introduce our second contribution which is in the form of an evolutionary approach supported by a dynamic coding and based on controlled genetic operators. However, the exponential complexity of the problem leads us to consider that a simple metaheuristics is not sufficient to solve effectively the problem of dynamic ridematching. It is with this in mind that we are unveiling our third solving methodology by developing an original evolutionary approach in which chromosomes are defined as autonomous and intelligent agents. Thanks to an accurate protocol negotiation, the Chromosomes Agents can control the genetic operators and guide search for finding optimal solutions within a reasonable period of time. With the prospect of a better combination between carpooling and other modes of transport, we design a system called DyCOS, integrating our approaches and applications dedicated to solving the problem of dynamic ridesharing.

RESUMO Simulações de aeroacústica computacional demandam uma quantidade considerável de tempo, o que torna complicada a realização de estudos paramétricos. O presente trabalho propõe uma metodologia viável para otimização aeroacústica. Através da análise numérica utilizando dinâmica dos fluidos computacional, foi estudada a aplicação de uma placa separadora desacoplada como método de controle passivo da esteira turbulenta de um cilindro e avaliou-se a irradiação de ruído causado pela interação do escoamento com ambos os corpos, empregando ferramentas de aeroacústica computacional baseadas no método de Ffowcs-Williams e Hawkings. Algumas abordagens distintas de metodologias de otimização de projeto foram aplicadas neste problema, com o objetivo de chegar a uma configuração otimizada que permita a redução do nível sonoro ao longe. Assim, utilizando uma ferramenta de otimização multidisciplinar, pode-se avaliar a capacidade de modelos heurísticos e a grande vantagem do emprego de algoritmos baseados em método de superfície de resposta quando aplicados em um problema não linear, pois requerem a avaliação de um menor número de alternativas para se obter um ponto ótimo. Além disso, foi possível identificar e agrupar os resultados em 5 clusters baseados em seus parâmetros geométricos, nível de pressão sonora global e o valor quadrático médio do coeficiente de arrasto, confirmando a eficiência da aplicação de placas separadoras longas desacopladas posicionadas próximas ao cilindro na estabilização da esteira turbulenta, enquanto que o posicionamento de placas acima de um espaçamento crítico aumentou o nível de pressão acústica irradiado devido à formação de vórtices no espaço entre o cilindro e a placa separadora. / Computational aeroacoustics simulations require a considerable amount of time, which makes the comparison of a large number of different geometric designs a difficult task. The goal of the present study is to provide a suitable methodology for aeroacustic optimization. By means of numerical analyses using computational fluid dynamics tools, the application of a detached splitter plate as a passive control method for the turbulent wake of a circular cylinder was investigated. The irradiation of noise caused by the interaction between the flow and both bodies was evaluated using computational aeroacoustics tools based on the Ffowcs-Williams and Hawkings method. Various design optimization methodologies were applied to this flow in order to achieve a possible optimal configuration, i.e., one which is capable of reducing the far field noise level without increasing the aerodynamic forces. Using a multidisciplinary optimization tool, it was possible to evaluate the behavior of heuristic optimization algorithms and the major advantage of algorithms based on response surface methods when applied to a nonlinear aeroacoustics problem, since they require a smaller number of calculated designs to reach the optimal configuration. In addition, it was possible to identify and group the outcomes into 5 clusters based on their geometric parameters, overall sound pressure level and drag coefficient, confirming the efficiency of the application of long detached splitter plates placed next to the cylinder in stabilizing the turbulent wake, whereas the positioning of splitter plates at a distance larger than a critical gap increased the overall sound pressure level radiated due to the formation of vortices in the gap.

Encontrar a configuração de mínimas perdas ôhmicas ou que forneça um adequado plano de restabelecimento aptos a ocorrência de faltas permanentes são problemas de natureza combinatorial, com múltiplos objetivos e restrições, que envolvem funções cujas características, em geral, dificultam o uso de técnicas de programação matemática. Algoritmos Evolutivos têm apresentado resultados animadores para esses problemas, especialmente quando aplicados em sistemas de distribuição de grande porte. Neste trabalho são propostas duas novas metodologias, baseadas em Algoritmos Evolutivos Multi-Objetivo, para reconfiguração de redes em sistemas de distribuição, que podem ser aplicadas para o tratamento dos problemas de redução de perdas ôhmicas e restabelecimento de energia em sistemas de grande porte (com milhares de barras, linhas e chaves). Para o desenvolvimento dessas metodologias, foi utilizado uma estrutura de dados para manipular grafos produzindo exclusivamente configurações radiais e conexas, chamada Representação Nó-profundidade. As metodologias propostas foram testadas para diversos sistemas, dentre os quais destaca-se um com 30:880 barras, tendo sido satisfatórios os resultados obtidos. Para o problema de restabelecimento de energia foram testados falta única e múltiplas faltas. / Find the distribution system configuration of minimum power losses or that provides an adequate service restoration plan is a combinatorial, multi-objective and multi constraint problems, which involves functions whose characteristics, in general, difficult the use of mathematical programming techniques. Evolutionary Algorithms have shown relevant results for these problems, especially for Large-Scale Distribution Systems. This work proposes two methodologies for network reconfiguration based on Multi-Objective Evolutionary Algorithms, which can be applied to treat the problems of power loss reduction and service restoration in large scale distribution systems (with thousands of buses, lines and switches). In order to develop these methodolgies, it was used a data structure to manipulate graphs producing exclusively radial and connected connections, called Node Depth Encoding. The proposed methodologies were successfully tested in several distribution systems, among them one with 30,880 buses. The problem of service restoration is analyzed considering cases of single and multiple faults.

The objective of this thesis is to model and solve the problem of placing thermal imaging camera for monitoring piles of combustible bio-fuels. The cameras, of different models, can be mounted at discrete heights on poles at fixed positions and at discrete angles, and one seeks camera model and mounting combinations that monitor as much of the piles as possible to as low cost as possible. Since monitoring all piles may not be possible or desired, due to budget or customer constrains, the solution to the problem is a set of compromises between coverage and cost. We denote such a set of compromises a frontier. In the first part of the thesis a way of modelling the problem is presented. The model uses a discrete formulation where the area to monitor is partitioned into a grid of cells. Further, a pool of candidate camera placements is formed, containing all combinations of camera models and mounting positions. For each camera in this pool, all cells monitored are deduced using ray-casting. Finally, an optimization model is formulated, based on the pool of candidate cameras and their monitoring of the grid. The optimization model has the two objectives of minimizing the cost while maximizing the number of covered cells. In the second part, a number of heuristic optimization algorithms to solve the problem is presented: Greedy Search, Random Greedy Search, Fear Search, Unique Search, Meta-RaPS and Weighted Linear Neighbourhood Search. The performance of these heuristics is evaluated on a couple of test cases from existing real world depots and a few artificial test instances. Evaluation is made by comparing the solution frontiers using various result metrics and graphs. Whenever practically possible, frontiers containing all optimal cost and coverage combinations are calculated using a state-of-the-art solver. Our findings indicate that for the artificial test instances, the state-of-the-art solver is unmatched in solution quality and uses similar execution time as the heuristics. Among the heuristics, Fear Search and Greedy Search were the strongest performing. For the smaller real world instances, the state-of-the-art solver was still unmatched in terms of solution quality, but generating the frontiers in this way was fairly time consuming. By generating the frontiers using Greedy Search or Random Greedy Search we obtained solutions of similar quality as the state-of-the-art solver up to 70-80% coverage using one hundredth and one tenth of the time, respectively. For the larger real world problem instances, generating the frontier using the state-of-the-art solver was extremely time consuming and thus sometimes impracticable. Hence the use of heuristics is often necessary. As for the smaller instances, Greedy Search and Random Greedy Search generated the frontiers with the best quality. Often even better full coverage solutions could be found by the more time consuming Fear Search or Unique Search. / Syftet med detta examensarbete är att modellera och lösa kameraplaceringsproblemet då IR-kameror ska användas för brandövervakning av fastbränslehögar. Problemet består i att givet ett antal kamera modeller och monteringsstolpar bestämma de kombinationer av placeringar och modeller sådana att övervakningen av högarna är maximal, för alla möjliga kostnadsnivåer. I den första delen av examensarbetet presenteras en modell för detta kameraplaceringsproblem. Modellen använder sig av en diskret formulering, där området om ska övervaras är representerad av ett rutnät. De möjliga kameravalen beskrivas med en diskret mängd av möjliga kameraplaceringar. För att utröna vilka celler inom rutnätet som en kameraplacering övervakar används metoden ray-casting. Utifrån mängden av möjliga kameraplaceringar kan en optimeringsmodell med två målfunktioner formuleras. Målet i den första målfunktionen är att minimera kostnaden för övervakningen och i den andra att maximera storleken på det övervakade området. Utgående från denna modell presenteras därefter ett antal algoritmer för att lösa modellen. Dessa är: Greedy Search, Random Greedy Search, Fear Search, Unique Search, Meta-RaPS och Weighted Linear Neighbourhood Search. Algoritmerna utvärderas på två konstgjorda testproblem och ett antal problem från verkliga fastbränslelager. Utvärderingen baseras på lösningsfronter (grafer över de icke-dominerade lösningarna med de bästa kombinationerna av kostnad och täckning) samt ett antal resultatmått som tid, lägsta kostnad för lösning med full täckning, etc... Vid utvärderingen av resultaten framkom att för de konstgjorda testinstanserna presterade ingen av heuristikerna jämförbart med en standardlösare, varken i termer av kvalitén på lösningarna eller med hänsyn tagen till tidsåtgången. De heuristiker som presterade bäst på dessa problem var framförallt Fear Search och Greedy Search. Även på de mindre probleminstanserna från existerande fastbränslelager hittade standardlösaren optimala lösningsfronter och en lösning med full täckning, men tidsåtgången var här flera gånger större jämfört med vissa av heuristikerna. På en hundra- respektive en tiondel av tiden kan Greedy Search eller Random Greedy Search heuristikerna finna en lösningsfront som är jämförbar med standardlösare, upp till 70-80% täckning. För de största probleminstanserna är tidsåtgången vid användning av standardlösare så pass stor att det i många fall är praktiskt svårt att lösa problemen, både för att generera fronten och att hitta en lösning med full täckning. I dessa fall är heuristiker oftast de enda möjliga alternativen. Vi fann att Greedy Search och Random Greedy Search var de heuristiker som, liksom för de mindre probleminstanserna, genererade de bästa lösningsfronterna. Ofta kunde dock en bättre lösning för full täckning hittas med hjälp av Fear Search eller Unique Search.