Dissertations / Theses on the topic 'Evolutionary Optimiser'

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1

Damp, Lloyd Hollis. "Multi-Objective and Multidisciplinary Design Optimisation of Unmanned Aerial Vehicle Systems using Hierarchical Asynchronous Parallel Multi-Objective Evolutionary Algorithms." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/1858.

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The overall objective of this research was to realise the practical application of Hierarchical Asynchronous Parallel Evolutionary Algorithms for Multi-objective and Multidisciplinary Design Optimisation (MDO) of UAV Systems using high fidelity analysis tools. The research looked at the assumed aerodynamics and structures of two production UAV wings and attempted to optimise these wings in isolation to the rest of the vehicle. The project was sponsored by the Asian Office of the Air Force Office of Scientific Research under contract number AOARD-044078. The two vehicles wings which were optimised were based upon assumptions made on the Northrop Grumman Global Hawk (GH), a High Altitude Long Endurance (HALE) vehicle, and the General Atomics Altair (Altair), Medium Altitude Long Endurance (MALE) vehicle. The optimisations for both vehicles were performed at cruise altitude with MTOW minus 5% fuel and a 2.5g load case. The GH was assumed to use NASA LRN 1015 aerofoil at the root, crank and tip locations with five spars and ten ribs. The Altair was assumed to use the NACA4415 aerofoil at all three locations with two internal spars and ten ribs. Both models used a parabolic variation of spar, rib and wing skin thickness as a function of span, and in the case of the wing skin thickness, also chord. The work was carried out by integrating the current University of Sydney designed Evolutionary Optimiser (HAPMOEA) with Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) tools. The variable values computed by HAPMOEA were subjected to structural and aerodynamic analysis. The aerodynamic analysis computed the pressure loads using a Boeing developed Morino class panel method code named PANAIR. These aerodynamic results were coupled to a FEA code, MSC.Nastran® and the strain and displacement of the wings computed. The fitness of each wing was computed from the outputs of each program. In total, 48 design variables were defined to describe both the structural and aerodynamic properties of the wings subject to several constraints. These variables allowed for the alteration of the three aerofoil sections describing the root, crank and tip sections. They also described the internal structure of the wings allowing for variable flexibility within the wing box structure. These design variables were manipulated by the optimiser such that two fitness functions were minimised. The fitness functions were the overall mass of the simulated wing box structure and the inverse of the lift to drag ratio. Furthermore, six penalty functions were added to further penalise genetically inferior wings and force the optimiser to not pass on their genetic material. The results indicate that given the initial assumptions made on all the aerodynamic and structural properties of the HALE and MALE wings, a reduction in mass and drag is possible through the use of the HAPMOEA code. The code was terminated after 300 evaluations of each hierarchical level due to plateau effects. These evolutionary optimisation results could be further refined through a gradient based optimiser if required. Even though a reduced number of evaluations were performed, weight and drag reductions of between 10 and 20 percent were easy to achieve and indicate that the wings of both vehicles can be optimised.
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2

Damp, Lloyd Hollis. "Multi-Objective and Multidisciplinary Design Optimisation of Unmanned Aerial Vehicle Systems using Hierarchical Asynchronous Parallel Multi-Objective Evolutionary Algorithms." University of Sydney, 2007. http://hdl.handle.net/2123/1858.

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Master of Engineering (Research)
The overall objective of this research was to realise the practical application of Hierarchical Asynchronous Parallel Evolutionary Algorithms for Multi-objective and Multidisciplinary Design Optimisation (MDO) of UAV Systems using high fidelity analysis tools. The research looked at the assumed aerodynamics and structures of two production UAV wings and attempted to optimise these wings in isolation to the rest of the vehicle. The project was sponsored by the Asian Office of the Air Force Office of Scientific Research under contract number AOARD-044078. The two vehicles wings which were optimised were based upon assumptions made on the Northrop Grumman Global Hawk (GH), a High Altitude Long Endurance (HALE) vehicle, and the General Atomics Altair (Altair), Medium Altitude Long Endurance (MALE) vehicle. The optimisations for both vehicles were performed at cruise altitude with MTOW minus 5% fuel and a 2.5g load case. The GH was assumed to use NASA LRN 1015 aerofoil at the root, crank and tip locations with five spars and ten ribs. The Altair was assumed to use the NACA4415 aerofoil at all three locations with two internal spars and ten ribs. Both models used a parabolic variation of spar, rib and wing skin thickness as a function of span, and in the case of the wing skin thickness, also chord. The work was carried out by integrating the current University of Sydney designed Evolutionary Optimiser (HAPMOEA) with Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) tools. The variable values computed by HAPMOEA were subjected to structural and aerodynamic analysis. The aerodynamic analysis computed the pressure loads using a Boeing developed Morino class panel method code named PANAIR. These aerodynamic results were coupled to a FEA code, MSC.Nastran® and the strain and displacement of the wings computed. The fitness of each wing was computed from the outputs of each program. In total, 48 design variables were defined to describe both the structural and aerodynamic properties of the wings subject to several constraints. These variables allowed for the alteration of the three aerofoil sections describing the root, crank and tip sections. They also described the internal structure of the wings allowing for variable flexibility within the wing box structure. These design variables were manipulated by the optimiser such that two fitness functions were minimised. The fitness functions were the overall mass of the simulated wing box structure and the inverse of the lift to drag ratio. Furthermore, six penalty functions were added to further penalise genetically inferior wings and force the optimiser to not pass on their genetic material. The results indicate that given the initial assumptions made on all the aerodynamic and structural properties of the HALE and MALE wings, a reduction in mass and drag is possible through the use of the HAPMOEA code. The code was terminated after 300 evaluations of each hierarchical level due to plateau effects. These evolutionary optimisation results could be further refined through a gradient based optimiser if required. Even though a reduced number of evaluations were performed, weight and drag reductions of between 10 and 20 percent were easy to achieve and indicate that the wings of both vehicles can be optimised.
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3

Lease, Basil Andy. "Weed/Plant Classification Using Evolutionary Optimised Ensemble Based On Local Binary Patterns." Thesis, Curtin University, 2022. http://hdl.handle.net/20.500.11937/88106.

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This thesis presents a novel pixel-level weed classification through rotation-invariant uniform local binary pattern (LBP) features for precision weed control. Based on two-level optimisation structure; First, Genetic Algorithm (GA) optimisation to select the best rotation-invariant uniform LBP configurations; Second, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in the Neural Network (NN) ensemble to select the best combinations of voting weights of the predicted outcome for each classifier. The model obtained 87.9% accuracy in CWFID public benchmark.
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4

Kaylani, Assem. "AN ADAPTIVE MULTIOBJECTIVE EVOLUTIONARY APPROACH TO OPTIMIZE ARTMAP NEURAL NETWORKS." Doctoral diss., University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2538.

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This dissertation deals with the evolutionary optimization of ART neural network architectures. ART (adaptive resonance theory) was introduced by a Grossberg in 1976. In the last 20 years (1987-2007) a number of ART neural network architectures were introduced into the literature (Fuzzy ARTMAP (1992), Gaussian ARTMAP (1996 and 1997) and Ellipsoidal ARTMAP (2001)). In this dissertation, we focus on the evolutionary optimization of ART neural network architectures with the intent of optimizing the size and the generalization performance of the ART neural network. A number of researchers have focused on the evolutionary optimization of neural networks, but no research has been performed on the evolutionary optimization of ART neural networks, prior to 2006, when Daraiseh has used evolutionary techniques for the optimization of ART structures. This dissertation extends in many ways and expands in different directions the evolution of ART architectures, such as: (a) uses a multi-objective optimization of ART structures, thus providing to the user multiple solutions (ART networks) with varying degrees of merit, instead of a single solution (b) uses GA parameters that are adaptively determined throughout the ART evolution, (c) identifies a proper size of the validation set used to calculate the fitness function needed for ART's evolution, thus speeding up the evolutionary process, (d) produces experimental results that demonstrate the evolved ART's effectiveness (good accuracy and small size) and efficiency (speed) compared with other competitive ART structures, as well as other classifiers (CART (Classification and Regression Trees) and SVM (Support Vector Machines)). The overall methodology to evolve ART using a multi-objective approach, the chromosome representation of an ART neural network, the genetic operators used in ART's evolution, and the automatic adaptation of some of the GA parameters in ART's evolution could also be applied in the evolution of other exemplar based neural network classifiers such as the probabilistic neural network and the radial basis function neural network.
Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Engineering PhD
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5

Guan, C. "Evolutionary and swarm algorithm optimized density-based clustering and classification for data analytics." Thesis, University of Liverpool, 2017. http://livrepository.liverpool.ac.uk/3021212/.

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Clustering is one of the most widely used pattern recognition technologies for data analytics. Density-based clustering is a category of clustering methods which can find arbitrary shaped clusters. A well-known density-based clustering algorithm is Density- Based Spatial Clustering of Applications with Noise (DBSCAN). DBSCAN has three drawbacks: firstly, the parameters for DBSCAN are hard to set; secondly, the number of clusters cannot be controlled by the users; and thirdly, DBSCAN cannot directly be used as a classifier. With addressing the drawbacks of DBSCAN, a novel framework, Evolutionary and Swarm Algorithm optimised Density-based Clustering and Classification (ESA-DCC), is proposed. Evolutionary and Swarm Algorithm (ESA), has been applied in various different research fields regarding optimisation problems, including data analytics. Numerous categories of ESAs have been proposed, such as, Genetic Algorithms (GAs), Particle Swarm Optimization (PSO), Differential Evaluation (DE) and Artificial Bee Colony (ABC). In this thesis, ESA is used to search the best parameters of density-based clustering and classification in the ESA-DCC framework to address the first drawback of DBSCAN. As method to offset the second drawback, four types of fitness functions are defined to enable users to set the number of clusters as input. A supervised fitness function is defined to use the ESA-DCC as a classifier to address the third drawback. Four ESA- DCC methods, GA-DCC, PSO-DCC, DE-DCC and ABC-DCC, are developed. The performance of the ESA-DCC methods is compared with K-means and DBSCAN using ten datasets. The experimental results indicate that the proposed ESA-DCC methods can find the optimised parameters in both supervised and unsupervised contexts. The proposed methods are applied in a product recommender system and image segmentation cases.
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6

White, William E. "Use of Empirically Optimized Perturbations for Separating and Characterizing Pyloric Neurons." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1368055391.

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7

Fong, Kwong Fai. "Optimized design and energy management of heating, ventilating and air conditioning systems by evolutionary algorithm." Thesis, De Montfort University, 2006. http://hdl.handle.net/2086/5216.

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8

Lakshminarayanan, Srivathsan. "Nature Inspired Grey Wolf Optimizer Algorithm for Minimizing Operating Cost in Green Smart Home." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1438102173.

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9

Ferreira, David. "Résistance au stress lors de la phase de latence en fermentation œnologique et développement de levures optimisées." Thesis, Montpellier, SupAgro, 2017. http://www.theses.fr/2017NSAM0051.

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Résumé : Saccharomyces cerevisiae, utilisée depuis des millénaires pour la fermentation du vin du fait de son endurance et de ses qualités inégalables, est de nos jours largement utilisée pour inoculer les mouts de raisin. Néanmoins, lors de l'inoculation, les souches oenologiques doivent faire face à des stress spécifiques qui peuvent compromettre le début de la fermentation. L’objectif de ce travail est d'élucider les bases métaboliques et moléculaires de la résistance multi-stress pendant la phase de latence en conditions oenologiques. Nous avons tout d'abord caractérisé un ensemble de levures oenologiques en mettant l'accent sur des facteurs de stress caractéristiques des vins rouges et des vins blancs. La température et le stress osmotique affectent fortement cette phase pour toutes les souches, alors que le SO2, les lipides et la thiamine ont un effet souche-dépendant. Ces données ont servi de base à deux approches parallèles. Une approche d'évolution expérimentale a permis, en appliquant des pressions sélectives caractéristiques de la phase de latence, de sélectionner des souches évoluées présentant une phase de latence plus courte. Plusieurs mutations de novo potentiellement impliquées dans le phénotype évolué ont été identifiées par séquençage de leur génome. En parallèle, une approche QTL combinant des croisements inter-souches, une étape de propagation industrielle et séchage des descendants, et la sélection de cellules bourgeonnantes par FACS a été développée. Ces deux stratégies ont permis d’identifier plusieurs variants alléliques impliqués dans la paroi cellulaire, le transport du glucose, le cycle cellulaire et la résistance au stress, jouant un rôle potentiellement important pendant la phase de latence. L’ensemble de ces résultats apporte de nouvelles connaissances sur la diversité et les bases génétiques de l'adaptation des levures à la phase de latence oenologique et offre un cadre d’amélioration des propriétés des souches. De plus, nous avons montré que K. marxianus a un potentiel pour des cultures mixtes et des contributions aromatiques positives en conditions oenologiques, ouvrant de nouvelles possibilités pour des études ultérieures.Titre : Résistance au stress lors de la phase de latence en fermentation oenologique et développement de levures optimiséesMots clés : Fermentation oenologique, levure, phase de latence, résistance multi-stress, QTL, évolution adaptative, K. marxianus
Abstract: Saccharomyces cerevisiae has been used for millennia to perform wine fermentation due to its endurance and unmatched qualities and is nowadays widely used as wine yeast starter. Nevertheless, at the moment of inoculation, wine yeasts must cope with specific stress factors that can compromise the fermentation start. The objective of this work was to elucidate the metabolic and molecular bases of multi-stress resistance during wine fermentation lag phase. We first characterized a set of commercialized wine yeast strains by focusing on stress factors typically found at this stage in red wines and in white wines. Temperature and osmotic stress had a drastic impact in lag phase for all strains whereas SO2, low lipids and thiamine had a more strain dependent effect. Based on these data, we developed two parallel approaches. Using an evolutionary engineering approach where selective pressures typically present in lag phase were applied, we obtained evolved strains with a shorter lag phase in winemaking conditions. Whole genome sequencing allowed to identify several de novo mutations potentially involved in the evolved phenotype. In parallel, a QTL mapping approach was conducted, combining an intercross strategy, industrial propagation and drying of the progeny populations and selection of the first budding cells by FACS. Both strategies allowed the identification of several allelic variants involved in cell wall, glucose transport, cell cycle and stress resistance, as important in lag phase phenotype. Overall, these results provide a deeper knowledge of the diversity and the genetic bases of yeast adaptation to wine fermentation lag phase and a framework for improving yeast lag phase. Additionally, we showed that K. marxianus has potential for mixed cultures and positive aromatic contributions under oenological conditions, opening new possibilities for further studies.Title: Stress resistance during the lag phase of wine fermentation and development of optimized yeastsKeywords: Wine fermentation, yeast, lag phase, multi-stress resistance, QTL, adaptive evolution, K. marxianus
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10

Cheng, Yo-Hao, and 鄭又豪. "Application of Interactive Evolutionary Algorithms to Optimize Multimedia Mobile Advertising Problems." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/64245044542540829058.

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碩士
高苑科技大學
資訊科技應用研究所
101
Mobile marketing and advertising for specific consumer groups different time periods and regions associated effective advertising, is a new type of mobile ad can be customized mobile ad is targeted customer base would like to know the correctrelevant and valuable even be allowed in advance commercial information Main object of study for the promotional message of supermarkets in Taiwan mobile applications, mobile ads which many advertising messages, promotional messages for each grade produce the maximum effect is no way of knowing whether consumers to discuss in this marketing planning. various grades of store activities to be presented in the mobile advertising, product prices and stores follow the unspoken rules.Mobile phone mobile ad promotional messages and layout for the order on the degree of importance, such as consumers are most directly feel the price, followed by the shelf life, you must meet the first two commodities message put into the forefront of the forum to help consumersFor the latest news Paper, will be an interactive genetic algorithm optimized for marketing planning.Interactive Genetic Algorithms (Interactive Genetic Algorithm IGA) is to solve the deeper problem of subjective consciousness of the future development, IGA main concept is the basis of GA, it is desirable to replace the subjective judgment of the people, GA the direction of the fitness function, which is to determine by the human individual evolution Interactive quiz by interactive algorithms and planning staff, multimedia advertising message presentation order to optimize the work will also explore multimedia advertising messages kinds of parameters marketing planning focus on the direction and the resulting optimal solution reverseobtained results can be used to automatically configure new marketing activities, the order of presentation of multimedia advertising message
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11

Lai, Kuan-Yu, and 賴貫郁. "A Multi-Objective Evolutionary Approach to Optimize Operating Room Scheduling Problems." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/79056640078768159434.

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碩士
中華大學
資訊工程學系碩士班
100
The operating room is one of the most expensive parts of hospital operating costs. The cost of operating room is closely related to the operating room scheduling operations. In this thesis, operating rooms, surgical teams and patient information are integrated and constructed into a mathematical optimization model. The objective of this model is to plan a week of operating room schedule list. Therefore, a multi-objective genetic algorithm (MOGA) is applied to automatically assign the patient and surgical team to the operating room. Our approach can optimize the four cost objective function at the same time: minimize the cost of all the surgical team and operating room, and matching the preferences of the surgical team to reduce patient waiting days. The experimental results show that the proposed approach can provide a good tool for hospital decision-makers, and indirectly improve healthcare efficiency and quality, while reducing unnecessary waste.
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12

Michener, Joshua Kieran. "Combining Rational and Evolutionary Approaches to Optimize Enzyme Activity in Saccharomyces cerevisiae." Thesis, 2012. https://thesis.library.caltech.edu/7017/5/Michener_2012_Thesis.pdf.

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Metabolic engineering has become an increasingly important tool for the production of bulk and fine chemicals. New biosynthetic pathways can be built in a tractable production host using enzymes from a wide variety of organisms. However, these enzymes did not evolve to function in their new host, and as a result their activity may be unacceptably low. Additionally, the host has not adapted to support this new pathway, and its response to any new stresses imposed by the pathway may further limit productivity. I describe two methods for optimizing the host-enzyme interface, using an evolutionary approach to adapt an enzyme to its new host and a rational approach to modify the host in response. Using a synthetic RNA switch to screen for improvements in enzymatic activity in vivo, I increased the activity of a model enzyme more than 30-fold. I then used a systems-level analysis of the host to identify a stress, heme depletion, that the enzyme placed on its host. Alleviating that stress increased the activity of an optimized enzyme by a further 2.3-fold. These results highlight the advantages of combining systems and synthetic biology during the construction of a metabolic pathway. I also consider options for extending the uses of synthetic RNA switches both earlier and later in the pathway development process. An RNA switch could first be used in a functional screen for enzyme discovery and then be used to adapt the newly discovered enzyme to its production host. Finally, a variant of that switch could be used to dynamically regulate a biosynthetic pathway and improve the pathway reliability.
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13

Fernandes, Gustavo Nuno Vieira. "COSMO - Using error to optimize the city." Master's thesis, 2013. http://hdl.handle.net/10316/35543.

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Dissertação de Mestrado em Engenharia Informática apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Cities across the world are ghting a losing battle against the increasingly large tides of private and public transports that daily roam urban road networks. In an e ort to tackle this problem, we present a thorough research of the current tra c management and routing algorithm paradigm, and compare the available tra c simulator options. We also elaborate a plan of action by establishing goals, tasks and milestones. We propose an evolutionary approach to generate a behavior model, based on the inverted shortest path, to later use in SUMO (Simulator of Urban Mobility).
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14

Chou, Yanchuan, and 周彥全. "Using Evolutionary Algorithms to Optimize Execution Time and Code Size in Iterative Compilation." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/45985658286655008582.

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碩士
國立中正大學
資訊工程研究所
100
Modern compilers usually provide a large number of optimization options to aid users to fine tune their programs for the best performance. However, applying such optimization options involves complex knowledge about compiler optimization, so most users do not have the capability to utilize these optimization options. Iterative Compilation is currently the most common approach to searching for the optimal set of optimization options for a program. There are several interesting performance metrics in compiler optimization: execution time, compilation time, code size, memory space, power consumption, and other computing resources. This research investigates multi-objective optimization of execution time and code size in Iterative Compilation using the popular multi-objective evolutionary algorithms NSGA-II and MOEA/D. The experimental results show that the optimization sequences chosen by both algorithms are superior to the ones generated by the random search algorithm and the ones corresponding to the optimization levels provided by the compiler.
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15

Wilk, Piotr. "The use of evolutionary algorithms and finite element method to optimize the machine body." Rozprawa doktorska, 2011. https://repolis.bg.polsl.pl/dlibra/docmetadata?showContent=true&id=8229.

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16

Wilk, Piotr. "The use of evolutionary algorithms and finite element method to optimize the machine body." Rozprawa doktorska, 2011. https://delibra.bg.polsl.pl/dlibra/docmetadata?showContent=true&id=8229.

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17

LI, WEN-HSIUNG, and 李文雄. "Application of Bi-directional Evolutionary Structural Optimization to Optimize Two-dimensional Forging Preform Design." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/88646194763808408862.

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碩士
國立高雄應用科技大學
機械與精密工程研究所
104
Preform is a step between blanking and final forming. The design and optimization of the preforming step would affect the material flow, forming load, dimension accuracy and tool wear. Thus, the investigations of design and optimization of the preforming step play an important role in the metal forming operation. Conventional topology optimization focused on the field of structure design, in which little deformation was involved. However, the metal forming belong to a large amount of plastic deformation, in which the mesh distortion occur in the simulation process. Therefore, introducing the topology optimization into metal forming is a challenging work. In this study, the analysis and the simulation were carried out by utilizing MATLAB software as well as using DEFORM-2D finite element analysis software and CAD software as auxiliary tools. The research process were separated into five steps. In the first step, the effects of boundary fitting method on the evolution of preform were considered, then the differences of the changes of preform shape resulting from different fitting tolerance were compared. Thirdly, the consequences according to different addition/removal criterions in the optimization procedure were investigated. In the fourth step, we studied the influences of the different edge length of the background mesh. Finally, comparison between the results of algorithm modification and the results of the references was performed. The results of this study are as follows: using “Fit Curves”command in the CAD software and two times of reference length are the better option for the boundary fitting method. Performance index would oscillate and could not be convergent when using “evolutionary structural optimization” as removal method, but it could be significantly reduced by using “bi-directional evolutionary structural optimization”. Furthermore, the differences between using mean stress and normal pressure as addition criterion were considered. It shows that the results are quite similar. In the terms of strain, the average of effective strain is 0.643 and the standard deviation is 0.298 when using normal pressure as addition criterion. These values are slightly smaller than when using mean stress as addition criterion, in which the values are 0.674 and 0.308, respectively. In the terms of forming load, the value of the former is 70.616 tons. It is slightly bigger than the value of the latter that is 70.207 tons. Finally, in the terms of shape, the results from normal pressure are more complex than those from mean stress.
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18

Torabikalaki, Roham. "Development of an Algorithm to Control and Optimize the Charging Process of Group of Electric Vehicles." Master's thesis, 2014. http://hdl.handle.net/10316/39030.

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Dissertação de Mestrado em Energia para a Sustentabilidade apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
The increasing penetration of electric vehicles (EV) usage will require a control system to manage their recharging process. This work proposes the development of a locally decentralized EVs’ charging algorithm, which controls and optimizes the charging process of a group of EVs, based on a binary sequence. In this work the proposed method and the development of the charging algorithm are respectively explained. Then, by simulating various scenarios the performance of the algorithm is assessed. The algorithm controls the charging process in a coordinated way and it was designed to be implemented in a local distribution grid, allowing to accommodate all the EVs without needing to reinforce the grid infrastructure capacity. It considers users’ preferences, such as their desire state of charge, while takes their electricity tariffs into account. The optimization objective was set for the consumers, to minimize the deviation of the actual charging cost from the minimum charging cost. The integration of different EVs’ charging patterns and various types of electricity tariffs, leads to a realistic approach. It was concluded that, through the proposed method, charging a greater number of EVs is feasible without needing to invest in increasing the capacity of the grid infrastructure, while the charging cost for each and every user is kept close to the minimum one
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