Teses / dissertações sobre o tema "Global function optimization"
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1
Gutmann, H. M. "Radial basis function methods for global optimization". Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599804.
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In many real world optimization problems it is essential or desirable to determine the global minimum of the objective function. The subject of this dissertation is a new class of methods that tackle such problems. In particular, we have in mind problems where function evaluations are expensive and no additional information is available. The methods employ radial basis functions that have been proved to be useful for interpolation problems. Examples include thin plate splines and multiquadrics. Specifically, in each iteration, radial basis function interpolation is used to define a utility function. A maximizer of this function is chosen to be the next point where the objective function is evaluated. Relations to similar optimization methods are established, and a general framework is presented that combines these methods and our methods. A large part of the dissertation is devoted to the convergence theory. We show that convergence can be achieved for most types of basis functions without further assumptions on the objective function. For other types, however, a similar results could not be obtained. This is due to the properties of the so-called native space that is associated with a basis function. In particular, it is of interest whether this space contains sufficiently smooth functions with compact support. In order to address this question, we present two approaches. First, we establish a characterization of the native space in terms of generalized Fourier transforms. For many types, for example thin plate splines, this helps to derive conditions on the smoothness of a function that guarantee that it is in the native space. For other types, for example multiquadrics, however, we show that the native space does not contain a nonzero function with compact support. The second approach we present gives slightly weaker results, but it employs some new theory using interpolation on an infinite regular grid.
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Bastani, Spencer, e Olov Andersson. "Stochastic Optimization in Dynamic Environments : with applications in e-commerce". Thesis, Linköping University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8509.
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In this thesis we address the problem of how to construct an optimal algorithm for displaying banners (i.e advertisements shown on web sites). The optimization is based on the revenue each banner generates, with the aim of selecting those banners which maximize future total revenue. Banner optimality is of major importance in the e-commerce industry, in particular on web sites with heavy traffic. The 'micropayments' from showing banners add up to substantial profits due to the large volumes involved. We provide a broad, up-to-date and primarily theoretical treatment of this global optimization problem. Through a synthesis of mathematical modeling, statistical methodology and computer science we construct a stochastic 'planning algorithm'. The superiority of our algorithm is based on empirical analysis conducted by us on real internet-data at TradeDoubler AB, as well as test-results on a selection of stylized data-sets. The algorithm is flexible and adapts well to new environments.
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Hatton, Marc. "Requirements specification for the optimisation function of an electric utility's energy flow simulator". Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96956.
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Thesis (MEng)--Stellenbosch University, 2015.ENGLISH ABSTRACT: Efficient and reliable energy generation capability is vital to any country's economic growth. Many strategic, tactical and operational decisions take place along the energy supply chain. Shortcomings in South Africa's electricity production industry have led to the development of an energy ow simulator. The energy ow simulator is claimed to incorporate all significant factors involved in the energy ow process from primary energy to end-use consumption. The energy ow simulator thus provides a decision support system for electric utility planners. The original aim of this study was to develop a global optimisation model and integrate it into the existing energy ow simulator. After gaining an understanding of the architecture of the energy ow simulator and scrutinising a large number of variables, it was concluded that global optimisation was infeasible. The energy ow simulator is made up of four modules and is operated on a module-by-module basis, with inputs and outputs owing between modules. One of the modules, namely the primary energy module, lends itself well to optimisation. The primary energy module simulates coal stockpile levels through Monte Carlo simulation. Classic inventory management policies were adapted to fit the structure of the primary energy module, which is treated as a black box. The coal stockpile management policies that are introduced provide a prescriptive means to deal with the stochastic nature of the coal stockpiles. As the planning horizon continuously changes and the entire energy ow simulator has to be re-run, an efficient algorithm is required to optimise stockpile management policies. Optimisation is achieved through the rapidly converging cross-entropy method. By integrating the simulation and optimisation model, a prescriptive capability is added to the primary energy module. Furthermore, this study shows that coal stockpile management policies can be improved. An integrated solution is developed by nesting the primary energy module within the optimisation model. Scalability is incorporated into the optimisation model through a coding approach that automatically adjusts to an everchanging planning horizon as well as the commission and decommission of power stations. As this study is the first of several research projects to come, it paves the way for future research on the energy ow simulator by proposing future areas of investigation.
AFRIKAANSE OPSOMMING: Effektiewe en betroubare energie-opwekkingsvermoë is van kardinale belang in enige land se ekonomiese groei. Baie strategiese, taktiese en operasionele besluite word deurgaans in die energie-verskaffingsketting geneem. Tekortkominge in Suid-Afrika se elektrisiteitsopwekkingsindustrie het tot die ontwikkeling van 'n energie-vloei-simuleerder gelei. Die energie-vloei-simuleerder vervat na bewering al die belangrike faktore wat op die energie-vloei-proses betrekking het van primêre energieverbruik tot eindgebruik. Die energie-vloei-simuleerder verskaf dus 'n ondersteuningstelsel aan elektrisiteitsdiensbeplanners vir die neem van besluite. Die oorspronklike doel van hierdie studie was om 'n globale optimeringsmodel te ontwikkel en te integreer in die bestaande energie-vloeisimuleerder. Na 'n begrip aangaande die argitektuur van die energievloei- simuleerder gevorm is en 'n groot aantal veranderlikes ondersoek is, is die slotsom bereik dat globale optimering nie lewensvatbaar is nie. Die energie-vloei-simuleerder bestaan uit vier eenhede en werk op 'n eenheid-tot-eenheid basis met insette en uitsette wat tussen eenhede vloei. Een van die eenhede, naamlik die primêre energiemodel, leen dit goed tot optimering. Die primêre energiemodel boots steenkoolreserwevlakke deur Monte Carlo-simulering na. Tradisionele voorraadbestuursbeleide is aangepas om die primêre energiemodel se struktuur wat as 'n swartboks hanteer word, te pas. Die steenkoolreserwebestuursbeleide wat ingestel is, verskaf 'n voorgeskrewe middel om met die stogastiese aard van die steenkoolreserwes te werk. Aangesien die beplanningshorison deurgaans verander en die hele energie-vloei-simulering weer met die energie-vloei-simuleerder uitgevoer moet word, word 'n effektiewe algoritme benodig om die re-serwebestuursbeleide te optimeer. Optimering word bereik deur die vinnige konvergerende kruis-entropie-metode. 'n Geïntegreerde oplossing is ontwikkel deur die primêre energiemodel en die optimering funksie saam te voeg. Skalering word ingesluit in die optimeringsmodel deur 'n koderingsbenadering wat outomaties aanpas tot 'n altyd-veranderende beplanningshorison asook die ingebruikneem en uitgebruikstel van kragstasies. Aangesien hierdie studie die eerste van verskeie navorsingsprojekte is, baan dit die weg vir toekomstige navorsing oor die energie-vloeisimuleerder deur ondersoekareas vir die toekoms voor te stel.
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Al-Mharmah, Hisham. "Global optimization of stochastic functions". Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/25665.
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Sharikov, Evgenii. "Conditions for global minimum through abstract convexity". Thesis, University of Ballarat, 2008. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/45930.
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The theory of abstract convexity generalizes ideas of convex analysis by using the notion of global supports and the global definition of subdifferential. In order to apply this theory to optimization, we need to extend subdifferential calculus and separation properties into the area of abstract convexity.Doctor of Philosophy
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Andramonov, Mikhail. "Global minimization of some classes of generalized convex functions". Thesis, Federation University Australia, 2001. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/164850.
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Fowkes, Jaroslav Mrazek. "Bayesian numerical analysis : global optimization and other applications". Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:ab268fe7-f757-459e-b1fe-a4a9083c1cba.
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We present a unifying framework for the global optimization of functions which are expensive to evaluate. The framework is based on a Bayesian interpretation of radial basis function interpolation which incorporates existing methods such as Kriging, Gaussian process regression and neural networks. This viewpoint enables the application of Bayesian decision theory to derive a sequential global optimization algorithm which can be extended to include existing algorithms of this type in the literature. By posing the optimization problem as a sequence of sampling decisions, we optimize a general cost function at each stage of the algorithm. An extension to multi-stage decision processes is also discussed. The key idea of the framework is to replace the underlying expensive function by a cheap surrogate approximation. This enables the use of existing branch and bound techniques to globally optimize the cost function. We present a rigorous analysis of the canonical branch and bound algorithm in this setting as well as newly developed algorithms for other domains including convex sets. In particular, by making use of Lipschitz continuity of the surrogate approximation, we develop an entirely new algorithm based on overlapping balls. An application of the framework to the integration of expensive functions over rectangular domains and spherical surfaces in low dimensions is also considered. To assess performance of the framework, we apply it to canonical examples from the literature as well as an industrial model problem from oil reservoir simulation.
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Selassie, Abebe Geletu W. "A coarse solution of generalized semi-infinite optimization problems via robust analysis of marginal functions and global optimization". [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974862304.
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Sultanova, Nargiz. "A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard". Thesis, University of Ballarat, 2009. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44036.
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It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.Master of Mathematical Sciences (Research)
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Sultanova, Nargiz. "A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard". University of Ballarat, 2009. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/16160.
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It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.Master of Mathematical Sciences (Research)
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Cheon, Myun-Seok. "Global Optimization of Monotonic Programs: Applications in Polynomial and Stochastic Programming". Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-04152005-130317/unrestricted/Cheon%5FMyunSeok%5F200505%5Fphd.pdf.
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Thesis (Ph. D.)--Industrial & Systems Engineering, Georgia Institute of Technology, 2005.Barnes, Earl, Committee Member ; Shapiro, Alex, Committee Member ; Realff, Matthew, Committee Member ; Al-Khayyal, Faiz, Committee Chair ; Ahmed, Shabbir, Committee Co-Chair. Includes bibliographical references.
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Olofsson, Karl-Johan. "Black-box optimization of simulated light extraction efficiency from quantum dots in pyramidal gallium nitride structures". Thesis, Linköpings universitet, Matematiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-162235.
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Microsized hexagonal gallium nitride pyramids show promise as next generation Light Emitting Diodes (LEDs) due to certain quantum properties within the pyramids. One metric for evaluating the efficiency of a LED device is by studying its Light Extraction Efficiency (LEE). To calculate the LEE for different pyramid designs, simulations can be performed using the FDTD method. Maximizing the LEE is treated as a black-box optimization problem with an interpolation method that utilizes radial basis functions. A simple heuristic is implemented and tested for various pyramid parameters. The LEE is shown to be highly dependent on the pyramid size, the source position and the polarization. Under certain circumstances, a LEE over 17% is found above the pyramid. The results are however in some situations very sensitive to the simulation parameters, leading to results not converging properly. Establishing convergence for all simulation evaluations must be done with further care. The results imply a high LEE for the pyramids is possible, which motivates the need for further research.
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Niu, Yi Shuai. "Programmation DC et DCA en optimisation combinatoire et optimisation polynomiale via les techniques de SDP : codes et simulations numériques". Phd thesis, INSA de Rouen, 2010. http://tel.archives-ouvertes.fr/tel-00557911.
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L'objectif de cette thèse porte sur des recherches théoriques et algorithmiques d'optimisation locale et globale via les techniques de programmation DC & DCA, Séparation et Evaluation (SE) ainsi que les techniques de relaxation DC/SDP, pour résoudre plusieurs types de problèmes d'optimisation non convexe (notamment en Optimisation Combinatoire et Optimisation Polynomiale). La thèse comporte quatre parties :La première partie présente les outils fondamentaux et les techniques essentielles en programmation DC & l'Algorithme DC (DCA), ainsi que les techniques de relaxation SDP, et les méthodes de séparation et évaluation (SE).Dans la deuxième partie, nous nous intéressons à la résolution de problèmes de programmation quadratique et linéaire mixte en variables entières. Nous proposons de nouvelles approches locales et globales basées sur DCA, SE et SDP. L'implémentation de logiciel et des simulations numériques sont aussi étudiées.La troisième partie explore des approches de la programmation DC & DCA en les combinant aux techniques SE et SDP pour la résolution locale et globale de programmes polynomiaux. Le programme polynomial avec des fonctions polynomiales homogènes et son application à la gestion de portefeuille avec moments d'ordre supérieur en optimisation financière ont été discutés de manière approfondie dans cette partie.Enfin, nous étudions dans la dernière partie un programme d'optimisation sous contraintes de type matrices semi-définies via nos approches de la programmation DC. Nous nous consacrons à la résolution du problème de réalisabilité des contraintes BMI et QMI en contrôle optimal.L'ensemble de ces travaux a été implémenté avec MATLAB, C/C++ ... nous permettant de confirmer l'utilisation pratique et d'enrichir nos travaux de recherche.
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Stöcker, Martin. "Globale Optimierungsverfahren, garantiert globale Lösungen und energieeffiziente Fahrzeuggetriebe". Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-166805.
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Der Schwerpunkt der vorliegenden Arbeit liegt auf Methoden zur Lösung nichtlinearer Optimierungsprobleme mit der Anforderung, jedes globale Optimum garantiert zu finden und mit einer im Voraus festgesetzten Genauigkeit zu approximieren. Eng verbunden mit dieser deterministischen Optimierung ist die Berechnung von Schranken für den Wertebereich einer Funktion über einem gegebenen Hyperquader. Verschiedene Ansätze, z. B. auf Basis der Intervallarithmetik, werden vorgestellt und analysiert. Im Besonderen werden Methoden zur Schrankengenerierung für multivariate ganz- und gebrochenrationale Polynome mit Hilfe der Darstellung in der Basis der Bernsteinpolynome weiterentwickelt. Weiterhin werden in der Arbeit schrittweise die Bausteine eines deterministischen Optimierungsverfahrens unter Verwendung der berechneten Wertebereichsschranken beschrieben und Besonderheiten für die Optimierung polynomialer Aufgaben näher untersucht.
Die Analyse und Bearbeitung einer Aufgabenstellung aus dem Entwicklungsprozess für Fahrzeuggetriebe zeigt, wie die erarbeiteten Ansätze zur Lösung nichtlinearer Optimierungsprobleme die Suche nach energieeffizienten Getrieben mit einer optimalen Struktur unterstützen kann.
Kontakt zum Autor: [Nachname] [.] [Vorname] [@] gmx [.] de
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Rondina, Gustavo Garcia. "Novas ideias para o Método de Basin-Hopping Monte Carlo aplicado à otimização global de Clusters e Nanopartículas". Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/76/76132/tde-17012014-161604/.
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Neste trabalho é introduzido e avaliado um conjunto de novas ideias para aumentar a eficiência do método Basin-Hopping Monte Carlo (BHMC) aplicado à otimização global de clusters e nanopartículas, que resultou no método BHMC revisado. Dentro deste método, tomou-se o cuidado de manter as características fundamentais do método BHMC padrão, que consistem na transformação da superfície de energia potencial em um conjunto de basins de atração, e no emprego de amostragem de Monte Carlo utilizando o critério de Metropolis. As ideias por trás do método BHMC revisado incluem um grande conjunto de operadores locais e não locais construídos especificamente para clusters e nanopartículas e que permitem maior mobilidade sobre a superfície de energia potencial durante a busca pelo mínimo global, duas estratégias de seleção de operadores, e um operador de filtro estrutural para remover soluções não físicas. A eficiência do método apresentado foi avaliada através da sua aplicação a um grande número de clusters e nanopartículas de tamanhos variados, compreendendo sistemas descritos tanto por potenciais empíricos, quanto por primeiros princípios dentro do formalismo da teoria do funcional da densidade (DFT). Os sistemas investigados foram clusters de Lennard-Jones e Sutton-Chen contendo até 148 átomos, um conjunto de nanopartículas de Lennard-Jones com tamanhos variando entre 200 e 1500 átomos, clusters binários de Lennard-Jones com até 100 átomos, clusters binários de metais de transição (AgPd)55 descritos pelo potencial de Sutton-Chen, clusters de alumínio puros com até 30 átomos descritos por DFT, e clusters de alumínio com até 15 átomos dopados com um átomo de cobre, também descritos por DFT. Através da otimização global sem bias de todas essas partículas, o método BHMC revisado foi capaz de reproduzir com sucesso os mínimos globais putativos mais recentes disponíveis na literatura obtidos por diversas técnicas de otimização global, e também foi capaz de identificar mínimos globais previamente desconhecidos. Além disso, em comparação com o método BHMC padrão, o método RBHMC mostrou maior eficiência para muitos dos sistemas investigados. As ideias contidas na metodologia apresentada constituem uma ferramenta valiosa para auxiliar investigações teóricas visando uma melhor compreensão da estrutura atômica de clusters e nanopartículas.In this work it is introduced and evaluated a set of new ideas to increase the efficiency of the Basin-Hopping Monte Carlo (BHMC) method applied to the global optimization of clusters and nanoparticles, which resulted in the revised BHMC method. Within this method, care was taken to keep the main features of the standard BHMC method, which are the transformation of the potential energy surface into a set of basins of attraction, and the use of Monte Carlo sampling employing the Metropolis criterion. The ideas behind the revised BHMC method include a large set of local and non-local operators built specifically for clusters and nanoparticles which allow a greater mobility over the potential energy surface along of the search for the global minimum, two strategies for selecting the operators, and a structural filter operator to remove unphysical solutions. The efficiency of the presented method was evaluated by applying it to a large number of clusters and nanoparticles of various sizes, comprising systems described both by empirical potentials and by first-principles within the formalism of density functional theory (DFT). The systems that were investigated were Lennard-Jones and Sutton-Chen clusters with up to 148 atoms, a set of Lennard-Jones nanoparticles with sizes from 200 to 1500 atoms, binary Lennard-Jones clusters with up to 100 atoms, binary transition metal clusters (AgPd)55 described by the Sutton-Chen potential, pure aluminum clusters with up to 30 atoms described by DFT, and aluminum clusters with up to 15 atoms doped with a copper atom, also described by DFT. Through the unbiased global optimization of all those particles, the revised BHMC method was able to successfully reproduce the most recent putative global minima available in the literature obtained by several different global optimization techniques, and moreover, it was able to identify previously unkown global minima. Furthermore, in comparison with the standard BHMC method, the RBHMC method proved to be more efficient for many of the systems that were investigated. The ideas comprised within the presented methodology characterize a valuable tool for aiding theoretical investigations leading to a better understanding of the atomic structure of clusters and nanoparticles.
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Clausner, André. "Anwendung von Line-Search-Strategien zur Formoptimierung und Parameteridentifikation". Master's thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-114858.
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Die kontinuierliche Weiterentwicklung und Verbesserung technischer Prozesse erfolgt heute auf der Basis stochastischer und deterministischer Optimierungsstrategien in Kombination mit der numerischen Simulation dieser Abläufe. Da die FE-Simulation von Umformvorgängen in der Regel sehr zeitintensiv ist, bietet sich für die Optimierung solcher Prozesse der Einsatz deterministischer Methoden an, da hier weniger Optimierungsschritte und somit auch weniger FE-Simulationen notwendig sind. Eine wichtige Anforderung an solche Optimierungsverfahren ist globale Konvergenz zu lokalen Minima, da die optimalen Parametersätze nicht immer näherungsweise bekannt sind. Die zwei wichtigsten Strategien zum Ausdehnen des beschränkten Konvergenzradius der natürlichen Optimierungsverfahren (newtonschrittbasierte Verfahren und Gradientenverfahren) sind die Line-Search-Strategie und die Trust-Region-Strategie. Die Grundlagen der Line-Search-Strategie werden aufgearbeitet und die wichtigsten Teilalgorithmen implementiert. Danach wird dieses Verfahren auf eine effiziente Kombination der Teilalgorithmen und Verfahrensparameter hin untersucht. Im Anschluss wird die Leistung eines Optimierungsverfahrens mit Line-Search-Strategie verglichen mit der eines ebenfalls implementierten Optimierungsverfahrens mit skalierter Trust-Region-Strategie. Die Tests werden nach Einfügen der implementierten Verfahren in das Programm SPC-Opt anhand der Lösung eines Quadratmittelproblems aus der Materialparameteridentifikation sowie der Formoptimierung eines Umformwerkzeugs vorgenommen.
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Mokukcu, Mert. "Optimisation énergétique d'un véhicule hybride". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLC066/document.
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Les progrès technologiques augmentent la complexité des systèmes énergétiques, ce qui permet d'avoir variés sources et architectures possibles. Si le contexte économique et écologique est également pris en compte, l'industrie automobile est menée à aligner sa production sur des véhicules hybrides ou électriques qui disposent d'une gestion de l'énergie sophistiquée. Ainsi, les études pour la conception sont orientées à l'optimisation et à la gestion de l'énergie en tenant compte les tendances des constructeurs : i) augmenter les performances des véhicules, ii) avoir des véhicules moins polluants en réduisant la consommation de carburant et iii) diminuer le temps nécessaire à la conception et au processus de validation. Face à ces problèmes, une approche qui aide le concepteur à caractériser le système de gestion de l'énergie d'un VEH est proposée. Cette caractérisation consiste à : i) choisir l'architecture de la chaîne de traction, ii) le dimensionnement des composants (groupes) et iii) le contrôleur de gestion de l'énergie. Pour accomplir ces tâches, une méthode de modélisation énergétique fonctionnelle est proposée. Cette approche proposée à un niveau d'abstraction "juste nécessaire" qui permet d'avoir une analyse énergétique pour une série de cas d'utilisation. La méthode repose sur des boucles de contrôle locales, un contrôleur global et des équations de base et elle permet d'avoir une optimisation modulaire pour tout changement d'architecture. Prochaine étape de la validation est l'adaptation du modèle fonctionnel afin d'obtenir le contrôleur de haut niveau pour le niveau multi-physique avec deux étapes proposées : i) l'ajustement des paramètres des éléments fonctionnels et ii) l'interconnexion les modèles fonctionnels et multi-physiques. Après l'illustration du démonstrateur d'un VEH, trois stratégies de gestion de l'énergie sont proposées : i) fondée sur des règles, ii) fondée sur PFC avec fonctionnement de partage de besoin par priorisation et iii) fondée sur PFC avec fonctionnement boost. Les stratégies de gestion de l'énergie proposées sont ensuite comparées par indicateurs de performance (consommation de carburant, nombre de cycles marche/arrêt du groupe motopropulseur et consommation de carburant corrigée avec variation de l'état de charge du stockage électrique) avec des cas d'usages définisTechnology advancements increase the complexity of energy systems which bring additional varieties of sources and possible architectures to choose. If the economic and ecological context is also included, the automobile industry is in_uenced to align their production to hybrid or battery electric vehicles that have sophisticated energy management system. Thus, researchers and designers have oriented their studies for system design, optimisation and energy management that take into consideration the constructor tendencies : i) increasing vehicle performances, ii) having less polluting vehicles by reducing fuel consumption and iii) decreasing the time needed for design and validation process. Against these problematics, an approach that assists the system designer to fully characterize the energy management system of a HEV is proposed. This characterization consists : i) choosing powertrain architecture, ii) component (units) sizing and iii) energy management controller. In order to accomplish these tasks, a functional energetic modelling method is proposed. Proposed functional modelling level has a level of abstraction _just necessary_ which permits to have energetic analysis for a series of use case. This method relies on local control loops, a global controller and basic equations and it allows to have a modular optimisation for any architecture changes. The second-stage in the validation is completed by adapting the functional model in order to obtain the high-level controller for the multi-physical level with two offered steps : i) adjustment the functional elements' parameters and ii) interconnection the functional and multi-physical models. After the illustration of the demonstrator of a HEV, three strategies for energy management is proposed : i) based on rules, ii) based on PFC with power sharing function and iii) based on PFC with booster function. The proposed energy management strategies then compared by performance indicators (fuel consumption, number of on/off cycles of engine powertrain and corrected fuel consumption with variation of state of charge of electrical storage) with defined use cases
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Ben, Gharbia Ibtihel. "Résolution de problèmes de complémentarité. : Application à un écoulement diphasique dans un milieu poreux". Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00776617.
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Les problèmes de complémentarité interviennent dans de nombreux domaines scientifiques : économie, mécanique des solides, mécanique des fluides. Ce n'est que récemment qu'ils ont commencé d'intéresser les chercheurs étudiant les écoulements et le transport en milieu poreux. Les problèmes de complémentarité sont un cas particulier des inéquations variationnelles. Dans cette thèse, on offre plusieurs contributions aux méthodes numériques pour résoudre les problèmes de complémentarité. Dans la première partie de cette thèse, on étudie les problèmes de complémentarité linéaires 0 6 x ⊥ (Mx+q) > 0 où, x l'inconnue est dans Rn et où les données sont q, un vecteur de Rn, et M, une matrice d'ordre n. L'existence et l'unicité de ce problème est obtenue quand la matrice M est une P-matrice. Une méthode très efficace pour résoudre les problèmes de complémentarité est la méthode de Newton-min, une extension de la méthode de Newton aux problèmes non lisses.Dans cette thèse on montre d'abord, en construisant deux familles de contre-exemples, que la méthode de Newton-min ne converge pas pour la classe des P-matrices, sauf si n= 1 ou 2. Ensuite on caractérise algorithmiquement la classe des P-matrices : c'est la classe des matrices qui sont telles que quel que, soit le vecteur q, l'algorithme de Newton-min ne fait pas de cycle de deux points. Enfin ces résultats de non-convergence nous ont conduit à construire une méthode de globalisation de l'algorithme de Newton-min dont nous avons démontré la convergence globale pour les P-matrices. Des résultats numériques montrent l'efficacité de cet algorithme et sa convergence polynomiale pour les cas considérés. Dans la deuxième partie de cette thèse, nous nous sommes intéressés à un exemple de problème de complémentarité non linéaire concernant les écoulements en milieu poreux. Il s'agit d'un écoulement liquide-gaz à deux composants eau-hydrogène que l'on rencontre dans le cadre de l'étude du stockage des déchets radioactifs en milieu géologique. Nous présentons un modèle mathématique utilisant des conditions de complémentarité non linéaires décrivant ces écoulements. D'une part, nous proposons une méthode de résolution et un solveur pour ce problème. D'autre part, nous présentons les résultats numériques que nous avons obtenus suite à la simulation des cas-tests proposés par l'ANDRA (Agence Nationale pour la gestion des Déchets Radioactifs) et le GNR MoMaS. En particulier, ces résultats montrent l'efficacité de l'algorithme proposé et sa convergence quadratique pour ces cas-tests
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Cuko, Andi. "Modelling nano-oxide materials with technological and environmental relevance : silica, titania and titanosilicates Predicting size-dependent emergence of crystallinity in nanomaterials: titania nanoclusters versus nanocrystals Global optimisation of hydroxylated silica clusters: A cascade Monte Carlo Basin Hopping approach". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS368.
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Dans cette thèse, nous nous concentrons sur la modélisation des nano matériaux à base de titane, de silice et de titanosilicate en raison de leur importance technologique. Pour de tels systèmes, d'abord, nous avons identifiez les structures plus stables au moyen des méthodes d'optimisation global. Dans un deuxième temps, nous avons étudié les propriétés structurelles, énergétiques et électroniques de ces nanoparticules en fonction de leur taille, en extrapolant parfois jusqu'à l'échelle macroscopique. Pour une telle caractérisation, nous avons utilisé des méthodes quantiques basées sur la Théorie Fonctionnelle de la Densité. Des résultats obtenus, nous pouvons prédire que: (i) la cristallinité des nanoparticules d'oxyde de titane, qui est la propriété clé pour son activité photocatalytique, émergerait lorsque les nanoparticules atteignent une taille supérieure à 2,0-2,5 nm; (ii) le mélange d'oxyde de titane et de silice pour former des titanosilicates, se révèle thermodynamiquement favorable à l'échelle nanométrique, contrairement à l'échelle macroscopique; (iii) l'hydratation des nanoparticules de silice et de titane, qui joue un rôle important dans le processus d'agrégation et de nucléation pendant la synthèse de nanoparticules plus grandes, est contrôlée par les facteurs environnementaux tels que la température et la pression de vapeur d'eauIn this thesis we focus on modelling of titania, silica and titanosilicate based nano materials because of their technological importance as they are employed in heterogeneous (photo-)catalysis, in electronics gas-sensing etc. to cite a few. For such systems, we firstly performed global optimization studies in gas-phase and water containing environments in order to identify the structures of nanoparticles. Secondly, we studied structural, energetic and electronic size-dependent properties of such nanoparticles as well as their reducibility, extrapolating up to the bulk macroscopic level in some cases. For such characterization we use accurate quantum mechanical methods based on the Density Functional Theory (DFT). Our results point to a series of important predictions such us: i) the crystallinity of titania nanoparticles, which is the key property for the photoactivity, is predicted to emerge when nanoparticles become larger than 2.0-2.5 nm; ii) the mixing of titania and silica to form titanosilicates is found be thermodynamically favorable at the nanoscale, contrary to the bulk; iii) the hydration of silica and titania nanoclusters, which plays an important role in the aggregation and nucleation process during the synthesis of larger nanoparticles, is controlled by environmental factors such as temperature and water vapor pressure as predicted from calculated phase diagrams
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Kajee-Bagdadi, Zaakirah. "Differential evolution algorithms for constrained global optimization". Thesis, 2008. http://hdl.handle.net/10539/4733.
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In this thesis we propose four new methods for solving constrained global optimization problems.
The first proposed algorithm is a differential evolution (DE) algorithm using penalty
functions for constraint handling. The second algorithm is based on the first DE algorithm
but also incorporates a filter set as a diversification mechanism. The third algorithm is also
based on DE but includes an additional local refinement process in the form of the pattern
search (PS) technique. The last algorithm incorporates both the filter set and PS into the DE
algorithm for constrained global optimization. The superiority of feasible points (SFP) and
the parameter free penalty (PFP) schemes are used as constraint handling mechanisms.
The new algorithms were numerically tested using two sets of test problems and the
results where compared with those of the genetic algorithm (GA). The comparison shows
that the new algorithms outperformed GA. When the new methods are compared to each
other, the last three methods performed better than the first method i.e. the DE algorithm.
The new algorithms show promising results with potential for further research.
Keywords: constrained global optimization, differential evolution, pattern search, filter
method, penalty function, superiority of feasible points, parameter free penalty.
ii
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Hošala, Michal. "Riešenie problému globálnej optimalizácie využitím GPU". Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-336205.
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The global optimization problem -- i.e., the problem of finding global extreme points of given function on restricted domain of values -- often appears in many real-world applications. Improving efficiency of this task can reduce the latency of the application or provide more precise result since the task is usually solved by an approximative algorithm. This thesis focuses on the practical aspects of global optimization algorithms, especially in the domain of algorithmic trading data analysis. Successful implementations of the global optimization solver already exist for CPUs, but they are quite time demanding. The main objective of this thesis is to design a GO solver that utilizes the raw computational power of the GPU devices. Despite the fact that the GPUs have significantly more computational cores than the CPUs, the parallelization of a known serial algorithm is often quite challenging due to the specific execution model and the memory architecture constraints of the existing GPU architectures. Therefore, the thesis will explore multiple approaches to the problem and present their experimental results.
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Schomburg, Helen. "New Algorithms for Local and Global Fiber Tractography in Diffusion-Weighted Magnetic Resonance Imaging". Doctoral thesis, 2017. http://hdl.handle.net/11858/00-1735-0000-0023-3F8B-F.
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Yi-Yin, Chiu. "Modified Particle Swarm Optimization for Solving the Global Optimization of Continuous Multimodal Functions". 2004. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-0112200611323569.
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Yi-Yin, Chiu, e 邱怡瑛. "Modified Particle Swarm Optimization for Solving the Global Optimization of Continuous Multimodal Functions". Thesis, 2004. http://ndltd.ncl.edu.tw/handle/42490178787854981603.
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碩士元智大學
工業工程與管理學系
92
The development of the Particle Swarm Optimization (PSO) has been almost ten years since 1995. From that time on, a variety of modifications of the original PSO has been proposed by many PSO researchers. The evolutionary concept of PSO, simple in concept, easy to implement and computational efficient, is partly the motivation of this thesis. The performance of the original PSO on the solution quality and convergence speed becomes much aggravated while optimizing multimodal functions with higher dimension. This is the main objective of this research such that we would like to develop a modified PSO suitable for solving large-scale multimodal optimization problems. In this study, design of experiments (DOE) has been conducted to investigate the influences of each parameter in PSO. Based the computation results in the DOE stage, a modified PSO, termed Decreasing Weight Particle Swarm Optimization (DW-PSO), has been addressed. The success rate and number of function evaluation are considered performance measures. The experimental results show that the DW-PSO shows great promise in solving multimodal functions. The computational comparisons with PSO variants further reveal that DW-PSO has significant advantages, especially when it is performed to solve high dimension problems.
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Tian, Jing. "Global optimality conditions and optimization methods for polynomial programming problems and their applications". Thesis, 2014. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/94787.
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The polynomial programming problem which has a polynomial objective function, either with no constraints or with polynomial constraints occurs frequently in engineering design, investment science, control theory, network distribution, signal processing and locationallocation contexts. Moreover, the polynomial programming problem is known to be Nondeterministic Polynomial-time hard (NP-hard). The polynomial programming problem has attracted a lot of attention, including quadratic, cubic, homogenous or normal quartic programming problems as special cases. Existing methods for solving polynomial programming problems include algebraic methods and various convex relaxation methods. Especially, among these methods, semidefinite programming (SDP) and sum of squares (SOS) relaxations are very popular. Theoretically, SDP and SOS relaxation methods are very powerful and successful in solving the general polynomial programming problem with a compact feasible region. However, the solvability in practice depends on the size or the degree of the polynomial programming problem and the required accuracy. Hence, solving large scale SDP problems still remains a computational challenge. It is well-known that traditional local optimization methods are designed based on necessary local optimality conditions, i.e., Karush-Kuhn-Tucker (KKT) conditions. Motivated by this, some researchers proposed a necessary global optimality condition for a quadratic programming problem and designed a new local optimization method according to the necessary global optimality condition. In this thesis, we try to apply this idea to cubic and quatic programming problems, and further to general unconstrained and constrained polynomial programming problems. For these polynomial programming problems, we will investigate necessary global optimality conditions and design new local optimization methods according to these conditions. These necessary global optimality conditions are generally stronger than KKT conditions. Hence, the obtained new local minimizers by using the new local optimization methods may improve some KKT points. Our ultimate aim is to design global optimization methods for these polynomial programming problems. We notice that the filled function method is one of the well-known and practical auxiliary function methods used to achieve a global minimizer. In this thesis, we design global optimization methods by combining the new proposed local optimization methods and some auxiliary functions. The numerical examples illustrate the efficiency and stability of the optimization methods. Finally, we discuss some applications for solving some sensor network localization problems and systems of polynomial equations. It is worth mentioning that we apply the idea and the results for polynomial programming problems to nonlinear programming problems (NLP). We provide an optimality condition and design new local optimization methods according to the optimality condition and design global optimization methods for the problem (NLP) by combining the new local optimization methods and an auxiliary function. In order to test the performance of the global optimization methods, we compare them with two other heuristic methods. The results demonstrate our methods outperform the two other algorithms.Doctor of Philosophy
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Odat, Enas M. "Sequential Optimization of Global Sequence Alignments Relative to Different Cost Functions". Thesis, 2011. http://hdl.handle.net/10754/271672.
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The purpose of this dissertation is to present a methodology to model global sequence alignment problem as directed acyclic graph which helps to extract all possible optimal alignments. Moreover, a mechanism to sequentially optimize sequence alignment problem relative to different cost functions is suggested.
Sequence alignment is mostly important in computational biology. It is used to find evolutionary relationships between biological sequences. There are many algo- rithms that have been developed to solve this problem. The most famous algorithms are Needleman-Wunsch and Smith-Waterman that are based on dynamic program- ming. In dynamic programming, problem is divided into a set of overlapping sub- problems and then the solution of each subproblem is found. Finally, the solutions to these subproblems are combined into a final solution.
In this thesis it has been proved that for two sequences of length m and n over a fixed alphabet, the suggested optimization procedure requires O(mn) arithmetic operations per cost function on a single processor machine.
The algorithm has been simulated using C#.Net programming language and a number of experiments have been done to verify the proved statements. The results of these experiments show that the number of optimal alignments is reduced after each step of optimization. Furthermore, it has been verified that as the sequence length increased linearly then the number of optimal alignments increased exponentially which also depends on the cost function that is used. Finally, the number of executed operations increases polynomially as the sequence length increase linearly.
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Geletu, W. Selassie Abebe Weber Gerhard-Wilhelm. "A coarse solution of generalized semi-infinite optimization problems via robust analysis of marginal functions and global optimization /". 2004. http://www.gbv.de/dms/ilmenau/toc/476348986.PDF.
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Neilson, Daniel. "A Study of Match Cost Functions and Colour Use In Global Stereopsis". Phd thesis, 2009. http://hdl.handle.net/10048/449.
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Stereopsis is the process of inferring the distance to objects from two or more images. It has applications in areas such as: novel-view rendering, motion capture, autonomous navigation, and topographical mapping from remote sensing data. Although it sounds simple, in light of the effortlessness with which we are able to perform the task with our own eyes, a number of factors that make it quite challenging become apparent once one begins delving into computational methods of solving it. For example, occlusions that block part of the scene from being seen in one of the images, and changes in the appearance of objects between the two images due to: sensor noise, view dependent effects, and/or differences in the lighting/camera conditions between the two images.
Global stereopsis algorithms aim to solve this problem by making assumptions about the smoothness of the depth of surfaces in the scene, and formulating stereopsis as an optimization problem. As part of their formulation, these algorithms include a function that measures the similarity between pixels in different images to detect possible correspondences. Which of these match cost functions work better, when, and why is not well understood. Furthermore, in areas of computer vision such as segmentation, face detection, edge detection, texture analysis and classification, and optical flow, it is not uncommon to use colour spaces other than the well known RGB space to improve the accuracy of algorithms. However, the use of colour spaces other than RGB is quite rare in stereopsis research.
In this dissertation we present results from two, first of their kind, large scale studies on global stereopsis algorithms. In the first we compare the relative performance of a structured set of match cost cost functions in five different global stereopsis frameworks in such a way that we are able to infer some general rules to guide the choice of which match cost functions to use in these algorithms. In the second we investigate how much accuracy can be gained by simply changing the colour representation used in the input to global stereopsis algorithms.
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Geletu, Abebe [Verfasser]. "A coarse solution of generalized semi-infinite optimization problems via robust analysis of marginal functions and global optimization / vorgelegt von Abebe Geletu W. Selassie". 2004. http://d-nb.info/974862304/34.
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Stöcker, Martin. "Globale Optimierungsverfahren, garantiert globale Lösungen und energieeffiziente Fahrzeuggetriebe". Doctoral thesis, 2014. https://monarch.qucosa.de/id/qucosa%3A20243.
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Der Schwerpunkt der vorliegenden Arbeit liegt auf Methoden zur Lösung nichtlinearer Optimierungsprobleme mit der Anforderung, jedes globale Optimum garantiert zu finden und mit einer im Voraus festgesetzten Genauigkeit zu approximieren. Eng verbunden mit dieser deterministischen Optimierung ist die Berechnung von Schranken für den Wertebereich einer Funktion über einem gegebenen Hyperquader. Verschiedene Ansätze, z. B. auf Basis der Intervallarithmetik, werden vorgestellt und analysiert. Im Besonderen werden Methoden zur Schrankengenerierung für multivariate ganz- und gebrochenrationale Polynome mit Hilfe der Darstellung in der Basis der Bernsteinpolynome weiterentwickelt. Weiterhin werden in der Arbeit schrittweise die Bausteine eines deterministischen Optimierungsverfahrens unter Verwendung der berechneten Wertebereichsschranken beschrieben und Besonderheiten für die Optimierung polynomialer Aufgaben näher untersucht.
Die Analyse und Bearbeitung einer Aufgabenstellung aus dem Entwicklungsprozess für Fahrzeuggetriebe zeigt, wie die erarbeiteten Ansätze zur Lösung nichtlinearer Optimierungsprobleme die Suche nach energieeffizienten Getrieben mit einer optimalen Struktur unterstützen kann.
Kontakt zum Autor: [Nachname] [.] [Vorname] [@] gmx [.] de
31
Clausner, André. "Anwendung von Line-Search-Strategien zur Formoptimierung und Parameteridentifikation". Master's thesis, 2007. https://monarch.qucosa.de/id/qucosa%3A19910.
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Die kontinuierliche Weiterentwicklung und Verbesserung technischer Prozesse erfolgt heute auf der Basis stochastischer und deterministischer Optimierungsstrategien in Kombination mit der numerischen Simulation dieser Abläufe. Da die FE-Simulation von Umformvorgängen in der Regel sehr zeitintensiv ist, bietet sich für die Optimierung solcher Prozesse der Einsatz deterministischer Methoden an, da hier weniger Optimierungsschritte und somit auch weniger FE-Simulationen notwendig sind. Eine wichtige Anforderung an solche Optimierungsverfahren ist globale Konvergenz zu lokalen Minima, da die optimalen Parametersätze nicht immer näherungsweise bekannt sind. Die zwei wichtigsten Strategien zum Ausdehnen des beschränkten Konvergenzradius der natürlichen Optimierungsverfahren (newtonschrittbasierte Verfahren und Gradientenverfahren) sind die Line-Search-Strategie und die Trust-Region-Strategie. Die Grundlagen der Line-Search-Strategie werden aufgearbeitet und die wichtigsten Teilalgorithmen implementiert. Danach wird dieses Verfahren auf eine effiziente Kombination der Teilalgorithmen und Verfahrensparameter hin untersucht. Im Anschluss wird die Leistung eines Optimierungsverfahrens mit Line-Search-Strategie verglichen mit der eines ebenfalls implementierten Optimierungsverfahrens mit skalierter Trust-Region-Strategie. Die Tests werden nach Einfügen der implementierten Verfahren in das Programm SPC-Opt anhand der Lösung eines Quadratmittelproblems aus der Materialparameteridentifikation sowie der Formoptimierung eines Umformwerkzeugs vorgenommen.:1 Einleitung 7
2 Verfahren zur unrestringierten Optimierung 9
2.1 Vorbemerkungen 9
2.2 Der Schrittvektor sk 10
2.3 Natürliche Schrittweite und Konvergenz der Verfahren 11
2.4 Richtung des steilsten Abstiegs 12
2.5 Newtonschrittbasierte Verfahren 13
2.5.1 Newton-Verfahren 15
2.5.2 Quasi-Newton-Verfahren der Broyden-Klasse 15
2.5.3 Der BFGS-Auffrisch-Algorithmus 18
2.5.4 Die SR1-Auffrisch-Formel 19
2.5.5 Die DFP-Auffrisch-Formel 20
2.5.6 Gauß-Newton-Verfahren 20
2.6 Erzwingen der Bedingung der positiven Definitheit von Gk 21
3 Übersicht über die Verfahren zum Stabilisieren der natürlichen
Schrittweiten 24
3.1 Das Prinzip der Line-Search-Verfahren 24
3.2 Das Prinzip der Trust-Region-Verfahren 26
3.3 Vergleich der Trust-Region- und der Line-Search-Strategien 27
4 Line-Search-Strategien 30
4.1 Vorbemerkungen 30
4.2 Ein prinzipieller Line-Search-Algorithmus 33
5 Die Akzeptanzkriterien für die Line-Search-Strategien 36
5.1 Die exakte Schrittweite 37
5.2 Das Armijo-Kriterium, ein Abstiegskriterium 39
5.2.1 Das klassische Armijo-Kriterium 39
5.2.2 Armijo-Kriterium mit unterer Schranke fflo > 0 40
5.3 Die Goldstein-Kriterien 42
5.4 Die Wolfe-Kriterien 44
5.4.1 Die einfachen Wolfe-Kriterien 44
5.4.2 Die starken Wolfe-Kriterien 46
5.5 Näherungsweiser Line-Search basierend auf Armijo, ff-Methode 47
6 Ermittlung der nächsten Testschrittweite ffj+1 49
6.1 Die Startschrittweite ffj=1 51
6.2 Verfahren mit konstanten Faktoren 52
6.3 Verfahren mit konstanten Summanden 53
6.4 Verfahren mit quadratischen Polynomen 54
6.5 Verfahren mit kubischen Polynomen 56
6.6 Sektionssuche mit goldenem Schnitt 58
7 Absicherung und Abbruchbedingungen des Line-Search-Verfahrens 60
7.1 Die drei Konvergenzpunkte eines Line-Search-Verfahrens 60
7.1.1 Lokales Minimum in f 60
7.1.2 Algorithmus konvergiert gegen −1 61
7.1.3 Der Winkel zwischen sk und −rfk wird 90° 61
7.2 Weitere Absicherungen 62
7.2.1 Abstiegsrichtung 62
7.2.2 Der gradientenbezogene Schrittvektor 62
7.2.3 Zulässige Schrittweiten in der Extrapolationsphase 63
7.2.4 Intervalle bei der Interpolation 63
7.2.5 Maximale Durchlaufzahlen 63
8 Implementierung 65
8.1 Grundlegende Struktur der Implementierung 65
8.2 Anwendungsgebiete 67
8.2.1 Identifikation der Materialparameter der isotropen Verfestigung
und der HILLschen Fließbedingung 67
8.2.2 Optimierung der Form eines Umformwerkzeugs 70
8.3 Test des Programms anhand der Identifikation der Parameter der
isotropen Verfestigung und der HILLschen Fließbedingung 71
8.3.1 Einfluss der Funktionsumgebung 71
8.3.2 Test der Line-Search-Verfahrensparameter 74
8.3.3 Einfluss der Startwerte und der Qualität der Ableitungsermittlung 77
8.3.4 Test der Quasi-Newton-Strategien 77
8.3.5 Test der Trust-Region-Skalierung 79
8.3.6 Vergleich der Trust-Region- und der Line-Search-Strategie 80
8.3.7 Tests mit den HILLschen Anisotropieparametern und drei Vorwärtsrechnungen 81
9 Zusammenfassung und Ausblick 83
9.1 Zusammenfassung 83
9.2 Ausblick 84
Liste häufig verwendeter Formelzeichen 85
Literaturverzeichnis 88
A Zusätzliches zur Implementierung 90
A.1 Parametervorschläge für die Line-Search-Verfahren 90
A.2 Fehlercode-Liste 92
A.3 Programmablaufpläne 94
A.3.1 Ablauf in main.cpp 94
A.3.2 Ablauf in OneOptLoop 95
A.3.3 Ablauf während des Trust-Region-Verfahrens 96
A.3.4 Ablauf während des Line-Search-Verfahrens 97
A.4 Steuerung der Optimierungsoptionen über OptInputData.dat 98
A.4.1 Übergeordnete Algorithmen 98
A.4.1.1 Quasi-Newton-Verfahren 98
A.4.1.2 Absichern der positiven Definitheit von Gk 99
A.4.1.3 Auswahl des Optimierungsverfahrens, Auswahl der
Schrittweitensteuerung 100
A.4.1.4 Abbruchbedingungen für die Lösungsfindung 100
A.4.1.5 Wahl des Startvektors x0 101
A.4.2 Die Trust-Region-Algorithmen 102
A.4.2.1 Wahl des Anfangsradius 0 des Vertrauensbereichs 102
A.4.2.2 Wahl des Skalierungsverfahrens 102
A.4.2.3 Wahl des Startwertes l=0 für die Regularisierungsparameteriteration 103
A.4.2.4 Regularisierungsparameteriteration 103
A.4.2.5 Wahl des Verfahrens zum Auffrischen des Radius des
Vertrauensbereichs 103
A.4.2.6 Bedingungen für einen akzeptablen Schritt 104
A.4.2.7 Absicherungen des Trust-Region-Verfahrens 104
A.4.3 Die Line-Search-Algorithmen 105
A.4.3.1 Die Akzeptanzkriterien 105
A.4.3.2 Die Verfahren zur Extrapolation 105
A.4.3.3 Die Verfahren zur Interpolation 106
A.4.3.4 Verfahren zur Wahl von ffj=2 106
A.4.3.5 Absicherung des Line-Search-Verfahrens 106
B Testrechnungen 107
B.1 Ausgewählte Versuchsreihen 107
B.2 Bilder der Funktionsumgebung der Materialparameteridentifikation 109
B.3 Beschreibung der digitalen Anlagen 112
Eidesstattliche Erklärung und Aufgabenstellung 113
32
Nkwanyana, Thamsanqa Bongani. "Multi-input multi-output proportional integral derivative controller tuning based on improved particle swarm optimization". Diss., 2021. http://hdl.handle.net/10500/27692.
Texto completo da fonteResumo:
The PID controller is regarded as a dependable and reliable controller for process industry systems. Many researchers have devoted time and attention to PID controller tuning and they all agree that PID controllers are very important for control systems. A PID equation is very sensitive; its parameters must always be varied following the specific application to increase performance, such as by increasing the system’s responsiveness. PID controllers still have many problems despite their importance for control systems in industries. The problem of big overshoot on the conventional gain tuning is one of the serious problems. Researchers use the PSO algorithm to try and overcome those problems. The tuning of the MIMO PID controller based on the PSO algorithm shows many disadvantages such as high-quality control with a short settle time, steady-state error, and periodical step response. The traditional PSO algorithm is very sensitive and it sometimes affects the quality of good PID controller tuning.
This research has proposed a new equation for improving the PSO algorithm. The proposed algorithm is the combination of linearly decreasing inertia weight and chaotic inertia weight, after which a control factor was introduced as an exponential factor. This was very useful for simulations as it is adjustable. The Matlab simulation results of the experiments show that the simulations as it is adjustable. The Matlab simulation results of the experiments show that the new proposed equation converges faster and it gives the best fitness compared to linear inertia weight and oscillating inertia weight and other old equations. The MIMO PID controller system that consists of four plants was tuned based on the new proposed equation for the PSO algorithm (LCPSO). The optimized results show the best rise time, settling time, time delays, and steady-state compared to the systems that are tuned using the old equations. The exploration was directed at considering the impact of using the PSO calculation as an instrument for MIMO PID tuning. The results obtained in the examination reveal that the PSO tuning output improved reactions and can be applied to various system models in the measure control industry. The results for the MIMO PID controller tuned using PSO were assessed using integral square error (ISE), integral absolute error (IAE), and the integral of time expanded by absolute error (ITAE). The five well-known benchmark functions were also used to endorse the feasibility of the improved PSO and excellent results in terms of convergence and best fitness were attained.Electrical and Mining Engineering
M. Tech. (Electrical Engineering)