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GMMEDA : A demonstration of probabilistic modeling in continuous metaheuristic optimization using mixture modelsNaveen Kumar Unknown Date (has links)
Optimization problems are common throughout science, engineering and commerce. The desire to continually improve solutions and resolve larger, complex problems has given prominence to this field of research for several decades and has led to the development of a range of optimization algorithms for different class of problems. The Estimation of Distribution Algorithms (EDAs) are a relatively recent class of metaheuristic optimization algorithms based on using probabilistic modeling techniques to control the search process. Within the general EDA framework, a number of different probabilistic models have been previously proposed for both discrete and continuous optimization problems. This thesis focuses on GMMEDAs; continuous EDAs based on the Gaussian Mixture Models (GMM) with parameter estimation performed using the Expectation Maximization (EM) algorithm. To date, this type of model has only received limited attention in the literature. There are few previous experimental studies of the algorithms. Furthermore, a number of implementation details of Continuous Iterated Density Estimation Algorithm based on Gaussian Mixture Model have not been previously documented. This thesis intends to provide a clear description of the GMMEDAs, discuss the implementation decisions and details and provides experimental study to evaluate the performance of the algorithms. The effectiveness of the GMMEDAs with varying model complexity (structure of covariance matrices and number of components) was tested against five benchmark functions (Sphere, Rastrigin, Griewank, Ackley and Rosenbrock) with varying dimensionality (2−, 10− and 30−D). The effect of the selection pressure parameters is also studied in this experiment. The results of the 2D experiments show that a variant of the GMMEDA with moderate complexity (Diagonal GMMEDA) was able to optimize both unimodal and multimodal functions. Further, experimental analysis of the 10 and 30D functions optimized results indicates that the simpler variant of the GMMEDA (Spherical GMMEDA) was most effective of all three variants of the algorithm. However, a greater consistency in the results of these functions is achieved when the most complex variant of the algorithm (Full GMMEDA) is used. The comparison of the results for four artificial test functions - Sphere, Griewank, Ackley and Rosenbrock - showed that the GMMEDA variants optimized most of complex functions better than existing continuous EDAs. This was achieved because of the ability of the GMM components to model the functions effectively. The analysis of the results evaluated by variants of the GMMEDA showed that number of the components and the selection pressure does affect the optimum value of artificial test function. The convergence of the GMMEDA variants to the respective functions best local optimum has been caused more by the complexity in the GMM components. The complexity of GMMEDA because of the number of components increases as the complexity owing to the structure of the covariance matrices increase. However, while finding optimum value of complex functions the increased complexity in GMMEDA due to complex covariance structure overrides the complexity due to increase in number of components. Additionally, the affect on the convergence due to the number of components decreases for most functions when the selection pressure increased. These affects have been noticed in the results in the form of stability of the results related to the functions. Other factors that affect the convergence of the model to the local optima are the initialization of the GMM parameters, the number of the EM components, and the reset condition. The initialization of the GMM components, though not visible graphically in the 10D optimization has shown: for different initialization of the GMM parameters in 2D, the optimum value of the functions is affected. The initialization of the population in the Evolutionary Algorithms has shown to affect the convergence of the algorithm to the functions global optimum. The observation of similar affects due to initialization of GMM parameters on the optimization of the 2D functions indicates that the convergence of the GMM in the 10D could be affected, which in turn, could affect the optimum value of respective functions. The estimated values related to the covariance and mean over the EM iteration in the 2D indicated that some functions needed a greater number of EM iterations while finding their optimum value. This indicates that lesser number of EM iterations could affect the fitting of the components to the selected population in the 10D and the fitting can affect the effective modeling of functions with varying complexity. Finally, the reset condition has shown as resetting the covariance and the best fitness value of individual in each generation in 2D. This condition is certain to affect the convergence of the GMMEDA variants to the respective functions best local optimum. The rate at which the reset condition was invoked could certainly have caused the GMM components covariance values to reset to their initials values and thus the model fitting the percentage of the selected population could have been affected. Considering all the affects caused by the different factors, the results indicates that a smaller number of the components and percentage of the selected population with a simpler S-GMMEDA modeled most functions with a varying complexity.
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A model-driven design-space exploration tool for the HIPAO 2 methodology / Ferramenta de exploração de espaço de projeto baseada em modelos para a metodologia HIPAO2Lerm, Rafael Andréas Raffi January 2015 (has links)
Hoje em dia, desenvolvedores de sistemas embarcados enfrentam uma crescente complexidade de projeto, tanto nas aplicações quanto nas plataformas usadas para executá-las. O uso de plataformas complexas faz com que os engenheiros precisem fazer escolhas não-triviais, e muitas vezes contra-intuitivas durante a fase de projeto. Para permitir que os projetistas gerenciem esta complexidade, o uso de metodologias baseadas em modelos tem atraído atenção, e dentro deste contexto, a metodologia HIPAO2 está sendo desenvolvida dentro da UFRGS. Dentre os problemas que os engenheiros precisam enfrentar, o mapeamento entre tarefas e processadores em sistemas multiprocessados heterogêneos é um problema NP-completo, onde o espaço de projeto rapidamente se torna grande demais para que seja explorado satisfatoriamente de maneira manual. Este trabalho detalha a extensão das ferramentas que suportam a metodologia HIPAO2, de maneira a incluir facilidades de Exploração de Espaço de Projeto semi-automática para a solução deste problema. A ferramenta proposta faz uso de um algoritmo genético multiobjetivo para evidenciar tradeoffs existentes no projeto, e algoritmos de análise de aplicações modeladas como synchronous dataflow para avaliar possíveis mapeamentos sem um custo computacional proibitivo. / Designers of today’s embedded systems are faced with increasing complexity both in the applications being developed and the platforms they run on. The use of complex platforms means that the engineers need to make non-trivial and many times non-intuitive decisions during the design phase. To help developers work with this complexity, model-driven techniques are gaining attention, and in this context, the HIPAO2 model-driven engineering methodology is being developed at UFRGS. Among the problems that designers must solve, the task-to-processor mapping in heterogeneous multiprocessor systems is an NP-complete problem and the design space will quickly become too large to be explored adequately by humans. This work details the extension of the tools that support HIPAO2 to include semiautomatic Design-Space Exploration capabilities for the mapping problem. The proposed tool includes the use of a multiobjective genetic algorithm to make tradeoffs explicit to the designers; it also uses synchronous dataflow analysis algorithms to evaluate potential alternatives with a reasonable computational cost.
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Towards Fault Reactiveness in Wireless Sensor Networks with Mobile Carrier RobotsFalcon Martinez, Rafael Jesus 04 April 2012 (has links)
Wireless sensor networks (WSN) increasingly permeate modern societies nowadays. But in spite of their plethora of successful applications, WSN are often unable to surmount many operational challenges that unexpectedly arise during their lifetime. Fortunately, robotic agents can now assist a WSN in various ways. This thesis illustrates how mobile robots which are able to carry a limited number of sensors can help the network react to sensor faults, either during or after its deployment in the monitoring region.
Two scenarios are envisioned. In the first one, carrier robots surround a point of interest
with multiple sensor layers (focused coverage formation). We put forward the first known algorithm
of its kind in literature. It is energy-efficient, fault-reactive and aware of the bounded
robot cargo capacity. The second one is that of replacing damaged sensing units with spare,
functional ones (coverage repair), which gives rise to the formulation of two novel combinatorial
optimization problems. Three nature-inspired metaheuristic approaches that run at a centralized location are proposed. They are able to find good-quality solutions in a short time. Two frameworks for the identification of the damaged nodes are considered. The first one leans upon diagnosable systems, i.e. existing distributed detection models in which individual units perform tests upon each other. Two swarm intelligence algorithms are designed to quickly and reliably spot faulty sensors in this context. The second one is an evolving risk management framework for WSNs that is entirely formulated in this thesis.
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Towards Fault Reactiveness in Wireless Sensor Networks with Mobile Carrier RobotsFalcon Martinez, Rafael Jesus 04 April 2012 (has links)
Wireless sensor networks (WSN) increasingly permeate modern societies nowadays. But in spite of their plethora of successful applications, WSN are often unable to surmount many operational challenges that unexpectedly arise during their lifetime. Fortunately, robotic agents can now assist a WSN in various ways. This thesis illustrates how mobile robots which are able to carry a limited number of sensors can help the network react to sensor faults, either during or after its deployment in the monitoring region.
Two scenarios are envisioned. In the first one, carrier robots surround a point of interest
with multiple sensor layers (focused coverage formation). We put forward the first known algorithm
of its kind in literature. It is energy-efficient, fault-reactive and aware of the bounded
robot cargo capacity. The second one is that of replacing damaged sensing units with spare,
functional ones (coverage repair), which gives rise to the formulation of two novel combinatorial
optimization problems. Three nature-inspired metaheuristic approaches that run at a centralized location are proposed. They are able to find good-quality solutions in a short time. Two frameworks for the identification of the damaged nodes are considered. The first one leans upon diagnosable systems, i.e. existing distributed detection models in which individual units perform tests upon each other. Two swarm intelligence algorithms are designed to quickly and reliably spot faulty sensors in this context. The second one is an evolving risk management framework for WSNs that is entirely formulated in this thesis.
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Towards Fault Reactiveness in Wireless Sensor Networks with Mobile Carrier RobotsFalcon Martinez, Rafael Jesus 04 April 2012 (has links)
Wireless sensor networks (WSN) increasingly permeate modern societies nowadays. But in spite of their plethora of successful applications, WSN are often unable to surmount many operational challenges that unexpectedly arise during their lifetime. Fortunately, robotic agents can now assist a WSN in various ways. This thesis illustrates how mobile robots which are able to carry a limited number of sensors can help the network react to sensor faults, either during or after its deployment in the monitoring region.
Two scenarios are envisioned. In the first one, carrier robots surround a point of interest
with multiple sensor layers (focused coverage formation). We put forward the first known algorithm
of its kind in literature. It is energy-efficient, fault-reactive and aware of the bounded
robot cargo capacity. The second one is that of replacing damaged sensing units with spare,
functional ones (coverage repair), which gives rise to the formulation of two novel combinatorial
optimization problems. Three nature-inspired metaheuristic approaches that run at a centralized location are proposed. They are able to find good-quality solutions in a short time. Two frameworks for the identification of the damaged nodes are considered. The first one leans upon diagnosable systems, i.e. existing distributed detection models in which individual units perform tests upon each other. Two swarm intelligence algorithms are designed to quickly and reliably spot faulty sensors in this context. The second one is an evolving risk management framework for WSNs that is entirely formulated in this thesis.
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A model-driven design-space exploration tool for the HIPAO 2 methodology / Ferramenta de exploração de espaço de projeto baseada em modelos para a metodologia HIPAO2Lerm, Rafael Andréas Raffi January 2015 (has links)
Hoje em dia, desenvolvedores de sistemas embarcados enfrentam uma crescente complexidade de projeto, tanto nas aplicações quanto nas plataformas usadas para executá-las. O uso de plataformas complexas faz com que os engenheiros precisem fazer escolhas não-triviais, e muitas vezes contra-intuitivas durante a fase de projeto. Para permitir que os projetistas gerenciem esta complexidade, o uso de metodologias baseadas em modelos tem atraído atenção, e dentro deste contexto, a metodologia HIPAO2 está sendo desenvolvida dentro da UFRGS. Dentre os problemas que os engenheiros precisam enfrentar, o mapeamento entre tarefas e processadores em sistemas multiprocessados heterogêneos é um problema NP-completo, onde o espaço de projeto rapidamente se torna grande demais para que seja explorado satisfatoriamente de maneira manual. Este trabalho detalha a extensão das ferramentas que suportam a metodologia HIPAO2, de maneira a incluir facilidades de Exploração de Espaço de Projeto semi-automática para a solução deste problema. A ferramenta proposta faz uso de um algoritmo genético multiobjetivo para evidenciar tradeoffs existentes no projeto, e algoritmos de análise de aplicações modeladas como synchronous dataflow para avaliar possíveis mapeamentos sem um custo computacional proibitivo. / Designers of today’s embedded systems are faced with increasing complexity both in the applications being developed and the platforms they run on. The use of complex platforms means that the engineers need to make non-trivial and many times non-intuitive decisions during the design phase. To help developers work with this complexity, model-driven techniques are gaining attention, and in this context, the HIPAO2 model-driven engineering methodology is being developed at UFRGS. Among the problems that designers must solve, the task-to-processor mapping in heterogeneous multiprocessor systems is an NP-complete problem and the design space will quickly become too large to be explored adequately by humans. This work details the extension of the tools that support HIPAO2 to include semiautomatic Design-Space Exploration capabilities for the mapping problem. The proposed tool includes the use of a multiobjective genetic algorithm to make tradeoffs explicit to the designers; it also uses synchronous dataflow analysis algorithms to evaluate potential alternatives with a reasonable computational cost.
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A model-driven design-space exploration tool for the HIPAO 2 methodology / Ferramenta de exploração de espaço de projeto baseada em modelos para a metodologia HIPAO2Lerm, Rafael Andréas Raffi January 2015 (has links)
Hoje em dia, desenvolvedores de sistemas embarcados enfrentam uma crescente complexidade de projeto, tanto nas aplicações quanto nas plataformas usadas para executá-las. O uso de plataformas complexas faz com que os engenheiros precisem fazer escolhas não-triviais, e muitas vezes contra-intuitivas durante a fase de projeto. Para permitir que os projetistas gerenciem esta complexidade, o uso de metodologias baseadas em modelos tem atraído atenção, e dentro deste contexto, a metodologia HIPAO2 está sendo desenvolvida dentro da UFRGS. Dentre os problemas que os engenheiros precisam enfrentar, o mapeamento entre tarefas e processadores em sistemas multiprocessados heterogêneos é um problema NP-completo, onde o espaço de projeto rapidamente se torna grande demais para que seja explorado satisfatoriamente de maneira manual. Este trabalho detalha a extensão das ferramentas que suportam a metodologia HIPAO2, de maneira a incluir facilidades de Exploração de Espaço de Projeto semi-automática para a solução deste problema. A ferramenta proposta faz uso de um algoritmo genético multiobjetivo para evidenciar tradeoffs existentes no projeto, e algoritmos de análise de aplicações modeladas como synchronous dataflow para avaliar possíveis mapeamentos sem um custo computacional proibitivo. / Designers of today’s embedded systems are faced with increasing complexity both in the applications being developed and the platforms they run on. The use of complex platforms means that the engineers need to make non-trivial and many times non-intuitive decisions during the design phase. To help developers work with this complexity, model-driven techniques are gaining attention, and in this context, the HIPAO2 model-driven engineering methodology is being developed at UFRGS. Among the problems that designers must solve, the task-to-processor mapping in heterogeneous multiprocessor systems is an NP-complete problem and the design space will quickly become too large to be explored adequately by humans. This work details the extension of the tools that support HIPAO2 to include semiautomatic Design-Space Exploration capabilities for the mapping problem. The proposed tool includes the use of a multiobjective genetic algorithm to make tradeoffs explicit to the designers; it also uses synchronous dataflow analysis algorithms to evaluate potential alternatives with a reasonable computational cost.
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Towards Fault Reactiveness in Wireless Sensor Networks with Mobile Carrier RobotsFalcon Martinez, Rafael Jesus January 2012 (has links)
Wireless sensor networks (WSN) increasingly permeate modern societies nowadays. But in spite of their plethora of successful applications, WSN are often unable to surmount many operational challenges that unexpectedly arise during their lifetime. Fortunately, robotic agents can now assist a WSN in various ways. This thesis illustrates how mobile robots which are able to carry a limited number of sensors can help the network react to sensor faults, either during or after its deployment in the monitoring region.
Two scenarios are envisioned. In the first one, carrier robots surround a point of interest
with multiple sensor layers (focused coverage formation). We put forward the first known algorithm
of its kind in literature. It is energy-efficient, fault-reactive and aware of the bounded
robot cargo capacity. The second one is that of replacing damaged sensing units with spare,
functional ones (coverage repair), which gives rise to the formulation of two novel combinatorial
optimization problems. Three nature-inspired metaheuristic approaches that run at a centralized location are proposed. They are able to find good-quality solutions in a short time. Two frameworks for the identification of the damaged nodes are considered. The first one leans upon diagnosable systems, i.e. existing distributed detection models in which individual units perform tests upon each other. Two swarm intelligence algorithms are designed to quickly and reliably spot faulty sensors in this context. The second one is an evolving risk management framework for WSNs that is entirely formulated in this thesis.
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Robust Turnaround Management: Ground Operations under UncertaintyAsadi, Ehsan 15 April 2024 (has links)
Efficient ground handling at airports greatly adds to the performance of the entire air transportation network. In this network, airports are connected via aircraft that rely on passenger and crew connections, successful local airport operations, and efficient ground handling resource management. In addition, airport stakeholders’ decision-making processes must take into account various time scales (look-ahead times), process estimates, and both limited and multiple-dependent solution spaces. Most airlines have created integrated hub and operations control centers to monitor and adapt tactical operations. Despite this, decisions in such control centers should be made quickly in case of disruption. The decisions should also include the interests of various airline departments and local stakeholders.
Taking into account the Airport Collaborative Decision Making (A-CDM) concept, the joint venture between Airports Council International Europe (ACI EUROPE) - European Organization for the Safety of Air Navigation (EUROCONTROL) - International Air Transport Association (IATA) - Civil Air Navigation Services Organization (CANSO), this study creates different tools to manage turnaround in normal and disrupted contexts, hence facilitating decision-making in an Airport Operations Control Center (AOCC) and a Hub Control Center (HCC). This research focuses on the airline role in the collaborative decision-making process.
Regarding A-CDM milestones, turnaround time estimation is computed by four modeling methodologies, namely Critical Path Method (CPM), Project Evaluation and Review Technique (PERT), Fuzzy Critical Path Method (FCPM), and Analytical Convolution in deterministic and nondeterministic domains. In addition, the study develops mathematical models to return the airline schedule to its original plan in the event of delays. Chance-constrained and Robust optimization are also created for optimal decision-making when airlines confront uncertainty during real-world operations.
The study also develops a novel Hybrid Shuffled Frog-Leaping Algorithm (SFLA)-Grasshopper Optimization Algorithm (GOA) to expedite the process of finding recovery solutions, allowing AOCC and HCC for real-time applications to send this information to the relevant departments.
In comparison to common linear solvers, the solution process is sped up by 18 percent and the quality of the solutions is enhanced by 24 percent on average. Initial results are generated in less than 2 minutes, and global optimal results are achieved in near 15 minutes allowing the system to be applied in real-time applications.:Abstract
1 Introduction
1.1 Problem Description
1.1.1 Decision Scope
1.1.2 Airport Collaborative Decision Making (A-CDM)
1.1.3 Total Airport Management
1.1.4 Ground Handlers
1.1.5 Turnaround Management
1.2 Aims and Objectives
1.3 Thesis Contribution
1.4 Structure
2 Literature Review
2.1 Turnaround
2.2 Ground Handling
2.3 Flights and Networks
2.4 Apron and Gate Assignment
2.5 Scopes Combination
2.5.1 Gate Assignment and Turnaround
2.5.2 Gate Assignment and Flights
2.5.3 Gate Assignment and Ground Handling
2.5.4 Turnaround and Flights
2.5.5 Turnaround and Ground Handling
2.5.6 Flights and Ground Handling
2.6 Turnaround Operations
2.7 Conclusion
3 Turnaround Definition
3.1 Turnaround in A-CDM System
3.2 Turnaround and Ground Handling
3.3 Turnaround Operations
3.3.1 In-Block (INB) and Acceptance (ACC)
3.3.2 Deboarding (DEB) and Boarding (BOA)
3.3.3 Fueling (FUE)
3.3.4 Catering (CAT)
3.3.5 Cleaning (CLE)
3.3.6 Unloading (UNL) and Loading (LOA)
3.3.7 Water service (WAT) and Toilette (TOI)
3.3.8 Finalization (FIN)
4 Total Turnaround Time (TTT) Calculation
4.1 Critical Path Method (CPM)
4.2 Project Evaluation and Review Technique (PERT)
4.3 Fuzzy Critical Path Method (FCPM)
4.3.1 Fuzzy Numbers and Fuzzy Sets
4.3.2 Fuzzy Membership Functions of Turnaround Tasks
4.3.3 Probability-possibility Transformation of Turnaround Tasks
4.3.4 Fuzzy Critical Path Method (FCPM) in Total Turnaround Time (TTT) Calculation
4.3.5 Discussion
4.4 Analytical Convolution
4.4.1 Convolution Method
4.4.2 Monte Carlo (MC) Simulation Evaluation
4.4.3 Application of Convolution in Turnaround Control
5 Disruption Management
5.1 Airline Disruption Management
5.1.1 Airport Operations Control Center (AOCC)
5.1.2 Delay in the Airline Networks
5.1.3 Recovery Options
5.2 Deterministic Model
5.2.1 Mathematical Model
5.2.2 Solution Approaches
5.2.3 Problem Setting
5.3 Non Deterministic Model
5.3.1 Stochastic Arrivals
5.3.2 Stochastic Duration
6 Conclusion
6.1 Discussion around Research Questions
6.1.1 Integration of All Actors
6.1.2 Turnaround Time Prediction
6.1.3 Quick and Robust Reaction
6.2 Future Research
6.2.1 Scope Development
6.2.2 Algorithm Development
6.2.3 Parameter Development
List of Acronyms
List of Figures
List of Tables
Bibliography
Acknowledgement
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Amélioration de la précision de modèles des fours radiatifs et optimisation des paramètres de chauffage par méthodes métaheuristiques : Application au procédé de thermoformage de pare-brise / Precision improvement of radiant furnaces model and heating control optimization using metaheuristic methods : Application to the thermoforming process of windshieldTajouri, Afif 13 December 2012 (has links)
La fabrication du pare-brise automobile est réalisée par un procédé de thermoformage dans un four tunnel où des feuilles de verre subissent un chauffage différentiel par rayonnement par des centaines d'éléments chauffants électriques contrôlés individuellement. Ces travaux ont pour objectif final de répondre à une problématique industrielle formulée en tant que problème d'optimisation. Elle consiste à aider le conducteur du four à retrouver la cartographie de puissance qui permet d'obtenir le champ de température nécessaire à la surface du verre afin d'aboutir à une forme souhaitée. Pour y parvenir, un modèle du four basé sur la méthode de réseau de composants est utilisé afin de simuler le cycle de chauffage. Dans un premier temps, la précision de la température calculée est améliorée par identification paramétrique en se référant à des données de mesures effectuées in situ. Une étude de sensibilité locale et globale a été réalisée au préalable. Par la suite, dans le but d'accélérer ces calculs, une méthode d'optimisation originale est proposée. Elle consiste à combiner la méthode métaheuristique du Recuit Simulé et l'Algorithme de Re-revêtement pour identifier l'émissivité multi-bande des matériaux. Après avoir effectué une validation sur un modèle simplifié 3D de four radiatif de traitement de matériaux, la méthode originale est appliquée pour le modèle du four réel. Outre l'amélioration de la précision des résultats de la simulation, la nouvelle démarche réduit considérablement le temps de calcul. Dans la deuxième partie du travail, plusieurs méthodes métaheuristiques, telles que l'Algorithme Génétique, le Recuit Simulé, la Recherche Tabou ainsi que leur hybridation sont expérimentées pour un modèle simplifié d'une enceinte radiative. Les résultats montrent que la combinaison de l'Algorithme Génétique et du Recuit Simulé a permis d'accélérer la convergence pour atteindre les champs de températures souhaités sur la surface du produit. Cette méthode est par la suite appliquée avec succès pour inverser le modèle du four afin de retrouver les paramètres de commande du four. / The manufacturing of automobile windshield is produced by a thermoforming process in a tunnel furnace where glass undergoes differential heating radiation by hundreds of electrical heating elements individually controlled. The final purpose of this work is to answer a real industrial problem, which is formulated as an optimization problem. It aims at assisting the furnace driver to find the setting that allows obtaining the required temperature distribution on the glass design in order to achieve the desired shape. Based on the method of network components, a model of the furnace is used to simulate the heating cycle. As a first step of this work, the accuracy of the temperature calculated is improved by parametric identification by referring to the data of measurements taken in situ. A local and global sensitivity analysis was performed beforehand. Thereafter, in order to accelerate these calculations, an original and optimization method is proposed. It consists in combining the Simulated Annealing metaheuristic method and the Replating Algorithm to identify multi-band emissivity. First, the original method validation is performed on a simplified 3D model of radiative enclosure, and then applied to the real furnace model. The new approach significantly reduces the computation time while improving the accuracy of the simulation results. In the second part of this work, several metaheuristic methods, such as Genetic Algorithm, Simulated Annealing, Tabu Search, and their hybridization are tested on a simplified model of a radiative enclosure. Results show that the combination of Genetic Algorithm and Simulated Annealing has accelerated the convergence to achieve the desired temperature fields on the product surface. This new method is successfully applied to the real furnace model to find the optimal control parameters.
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