Dissertations / Theses: 'Continuous global optimization problems'

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Ahmed, Abdel-Rahman Hedar A. "Studies on metaheuristics continuous global optimization problems." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/145313.

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Hirsch, Michael J. "Grasp-based heuristics for continuous global optimization problems." [Gainesville, Fla.] : University of Florida, 2006. http://purl.fcla.edu/fcla/etd/UFE0017140.

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Silva, Victor Billy da. "Otimização volumétrica de gemas de cor utilizadas para lapidação." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/90428.

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O Problema do Lapidário tem como objetivo encontrar o modelo de lapidação que resulte no maior aproveitamento volumétrico para uma dada gema bruta. Nesta dissertação apresentamos um Algoritmo Genético com variáveis de valores reais, e um GRASP Contínuo como heurísticas para resolução deste problema. Ambos os algoritmos maximizam o fator de escala do modelo de lapidação, sobre todas as posições de centro e ângulos de giro que o modelo pode assumir, buscando encontrar o modelo de maior volume inscrito no interior da gema, representada virtualmente por uma malha triangular. Propomos também um algoritmo de avaliação de uma instância do problema, o qual determina eficientemente o maior fator de escala, para um dado centro e orientação, que o modelo de lapidação pode assumir permanecendo completamente no interior da gema. Os algoritmos propostos foram avaliados em um conjunto de 50 gemas reais para o problema, utilizando como modelos base os cortes redondo e oval. Por fim, comparamos os resultados computacionais obtidos em relação a aproveitamento volumétrico e tempo de execução com os principais trabalhos relatados na literatura, demonstrando que as heurísticas propostas são competitivas com as demais abordagens. The goal of the gemstone cutting problem is to find the largest cutting design which fits inside a given rough gemstone. In this work, we propose a real-valued Genetic Algorithm and a Continuous GRASP heuristic to solve it. The algorithms determine the largest scaling factor, over all possibilities of centers and orientations which the cutting could assume, finding the cutting with the largest volume as possible inside a gemstone, represented by a triangular mesh. We also propose an algorithm to evaluate a problem instance. This method efficiently determines the greatest scaling factor, for a given center and orientation, such that the cutting fits inside the rough gemstone. The proposed algorithms are validated for an instance set of 50 real-world gemstones, using the round and oval cuttings. Finally, we compare our computational results, for volume yield and running time, with the state-of-art. Ours methods are proved be competitive with the previous approachs.

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Couetoux, Adrien. "Monte Carlo Tree Search for Continuous and Stochastic Sequential Decision Making Problems." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112192.

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Dans cette thèse, nous avons étudié les problèmes de décisions séquentielles, avec comme application la gestion de stocks d'énergie. Traditionnellement, ces problèmes sont résolus par programmation dynamique stochastique. Mais la grande dimension, et la non convexité du problème, amènent à faire des simplifications sur le modèle pour pouvoir faire fonctionner ces méthodes.Nous avons donc étudié une méthode alternative, qui ne requiert pas de simplifications du modèle: Monte Carlo Tree Search (MCTS). Nous avons commencé par étendre le MCTS classique (qui s’applique aux domaines finis et déterministes) aux domaines continus et stochastiques. Pour cela, nous avons utilisé la méthode de Double Progressive Widening (DPW), qui permet de gérer le ratio entre largeur et profondeur de l’arbre, à l’aide de deux méta paramètres. Nous avons aussi proposé une heuristique nommée Blind Value (BV) pour améliorer la recherche de nouvelles actions, en utilisant l’information donnée par les simulations passées. D’autre part, nous avons étendu l’heuristique RAVE aux domaines continus. Enfin, nous avons proposé deux nouvelles méthodes pour faire remonter l’information dans l’arbre, qui ont beaucoup amélioré la vitesse de convergence sur deux cas tests.Une part importante de notre travail a été de proposer une façon de mêler MCTS avec des heuristiques rapides pré-existantes. C’est une idée particulièrement intéressante dans le cas de la gestion d’énergie, car ces problèmes sont pour le moment résolus de manière approchée. Nous avons montré comment utiliser Direct Policy Search (DPS) pour rechercher une politique par défaut efficace, qui est ensuite utilisée à l’intérieur de MCTS. Les résultats expérimentaux sont très encourageants.Nous avons aussi appliqué MCTS à des processus markoviens partiellement observables (POMDP), avec comme exemple le jeu de démineur. Dans ce cas, les algorithmes actuels ne sont pas optimaux, et notre approche l’est, en transformant le POMDP en MDP, par un changement de vecteur d’état.Enfin, nous avons utilisé MCTS dans un cadre de méta-bandit, pour résoudre des problèmes d’investissement. Le choix d’investissement est fait par des algorithmes de bandits à bras multiples, tandis que l’évaluation de chaque bras est faite par MCTS.Une des conclusions importantes de ces travaux est que MCTS en continu a besoin de très peu d’hypothèses (uniquement un modèle génératif du problème), converge vers l’optimum, et peut facilement améliorer des méthodes suboptimales existantes In this thesis, we study sequential decision making problems, with a focus on the unit commitment problem. Traditionally solved by dynamic programming methods, this problem is still a challenge, due to its high dimension and to the sacrifices made on the accuracy of the model to apply state of the art methods. We investigate on the applicability of Monte Carlo Tree Search methods for this problem, and other problems that are single player, stochastic and continuous sequential decision making problems. We started by extending the traditional finite state MCTS to continuous domains, with a method called Double Progressive Widening (DPW). This method relies on two hyper parameters, and determines the ratio between width and depth in the nodes of the tree. We developed a heuristic called Blind Value (BV) to improve the exploration of new actions, using the information from past simulations. We also extended the RAVE heuristic to continuous domain. Finally, we proposed two new ways of backing up information through the tree, that improved the convergence speed considerably on two test cases.An important part of our work was to propose a way to mix MCTS with existing powerful heuristics, with the application to energy management in mind. We did so by proposing a framework that allows to learn a good default policy by Direct Policy Search (DPS), and to include it in MCTS. The experimental results are very positive.To extend the reach of MCTS, we showed how it could be used to solve Partially Observable Markovian Decision Processes, with an application to game of Mine Sweeper, for which no consistent method had been proposed before.Finally, we used MCTS in a meta-bandit framework to solve energy investment problems: the investment decision was handled by classical bandit algorithms, while the evaluation of each investment was done by MCTS.The most important take away is that continuous MCTS has almost no assumption (besides the need for a generative model), is consistent, and can easily improve existing suboptimal solvers by using a method similar to what we proposed with DPS

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Janiszewski, Szymon Pawel. "Optimization problems in discrete and continuous time." Thesis, University of Hull, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396087.

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Liao, Tianjun. "Population-based heuristic algorithms for continuous and mixed discrete-continuous optimization problems." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209439.

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Continuous optimization problems are optimization problems where all variableshave a domain that typically is a subset of the real numbers; mixed discrete-continuousoptimization problems have additionally other types of variables, sothat some variables are continuous and others are on an ordinal or categoricalscale. Continuous and mixed discrete-continuous problems have a wide rangeof applications in disciplines such as computer science, mechanical or electricalengineering, economics and bioinformatics. These problems are also often hard tosolve due to their inherent difficulties such as a large number of variables, manylocal optima or other factors making problems hard. Therefore, in this thesis ourfocus is on the design, engineering and configuration of high-performing heuristicoptimization algorithms.We tackle continuous and mixed discrete-continuous optimization problemswith two classes of population-based heuristic algorithms, ant colony optimization(ACO) algorithms and evolution strategies. In a nutshell, the main contributionsof this thesis are that (i) we advance the design and engineering of ACO algorithms to algorithms that are competitive or superior to recent state-of-the-artalgorithms for continuous and mixed discrete-continuous optimization problems,(ii) we improve upon a specific state-of-the-art evolution strategy, the covariancematrix adaptation evolution strategy (CMA-ES), and (iii) we extend CMA-ES totackle mixed discrete-continuous optimization problems.More in detail, we propose a unified ant colony optimization (ACO) frameworkfor continuous optimization (UACOR). This framework synthesizes algorithmiccomponents of two ACO algorithms that have been proposed in the literatureand an incremental ACO algorithm with local search for continuous optimization,which we have proposed during my doctoral research. The design of UACORallows the usage of automatic algorithm configuration techniques to automaticallyderive new, high-performing ACO algorithms for continuous optimization. We alsopropose iCMAES-ILS, a hybrid algorithm that loosely couples IPOP-CMA-ES, aCMA-ES variant that uses a restart schema coupled with an increasing populationsize, and a new iterated local search (ILS) algorithm for continuous optimization.The hybrid algorithm consists of an initial competition phase, in which IPOP-CMA-ES and the ILS algorithm compete for further deployment during a secondphase. A cooperative aspect of the hybrid algorithm is implemented in the formof some limited information exchange from IPOP-CMA-ES to the ILS algorithmduring the initial phase. Experimental studies on recent benchmark functionssuites show that UACOR and iCMAES-ILS are competitive or superior to otherstate-of-the-art algorithms.To tackle mixed discrete-continuous optimization problems, we extend ACOMV and propose CESMV, an ant colony optimization algorithm and a covariance matrix adaptation evolution strategy, respectively. In ACOMV and CESMV ,the decision variables of an optimization problem can be declared as continuous, ordinal, or categorical, which allows the algorithm to treat them adequately. ACOMV andCESMV include three solution generation mechanisms: a continuous optimizationmechanism, a continuous relaxation mechanism for ordinal variables, and a categorical optimization mechanism for categorical variables. Together, these mechanisms allow ACOMV and CESMV to tackle mixed variable optimization problems.We also propose a set of artificial, mixed-variable benchmark functions, which cansimulate discrete variables as ordered or categorical. We use them to automatically tune ACOMV and CESMV's parameters and benchmark their performance.Finally we test ACOMV and CESMV on various real-world continuous and mixed-variable engineering optimization problems. Comparisons with results from theliterature demonstrate the effectiveness and robustness of ACOMV and CESMVon mixed-variable optimization problems.Apart from these main contributions, during my doctoral research I have accomplished a number of additional contributions, which concern (i) a note on thebound constraints handling for the CEC'05 benchmark set, (ii) computational results for an automatically tuned IPOP-CMA-ES on the CEC'05 benchmark set and(iii) a study of artificial bee colonies for continuous optimization. These additionalcontributions are to be found in the appendix to this thesis. Doctorat en Sciences de l'ingénieur info:eu-repo/semantics/nonPublished

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Leon, Miguel. "Enhancing Differential Evolution Algorithm for Solving Continuous Optimization Problems." Licentiate thesis, Mälardalens högskola, Inbyggda system, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-33466.

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Differential Evolution (DE) has become one of the most important metaheuristics during the recent years, obtaining attractive results in solving many engineering optimization problems. However, the performance of DE is not always strong when seeking optimal solutions. It has two major problems in real world applications. First, it can easily get stuck in a local optimum or fail to generate better solutions before the population has converged. Secondly, its performance is significantly influenced by the control parameters, which are problem dependent and which vary in different regions of space under exploration. It usually entails a time consuming trial-and-error procedure to set suitable parameters for DE in a specific problem, particularly for those practioners with limited knowledge and experience of using this technique. This thesis aims to develop new DE algorithms to address the two aforementioned problems. To mitigate the first problem, we studied the hybridization of DE with local search techniques to enhance the efficiency of search. The main idea is to apply a local search mechanism to the best individual in each generation of DE to exploit the most promising regions during the evolutionary processs so as to speed up the convergence or increase the chance to scape from local optima. Four local search strategies have been integrated and tested in the global DE framework, leading to variants of the memetic DE algorithms with different properties concerning diversification and intensification. For tackling the second problem, we propose a greedy adaptation method for dynamic adjustment of the control parameters in DE. It is implemented by conducting greedy search repeatedly during the run of DE to reach better parameter assignments in the neighborhood of a current candidate. The candidates are assessed by considering both, the success rate and also fitness improvement of trial solutions against the target ones. The incorporation of this greedy parameter adaptation method into standard DE has led to a new adaptive DE algorithm, referred to as Greedy Adaptive Differential Evolution (GADE). The methods proposed in this thesis have been tested in different benchmark problems and compared with the state of the art algorithms, obtaining competitive results. Furthermore, the proposed GADE algorithm has been applied in an industrial scenario achieving more accurate results than those obtained by a standard DE algorithm. Differential Evolution (DE) har blivit en av de viktigaste metaheuristikerna under de senaste åren och har uppnått attraktiva resultat för att lösa många optimeringsproblem inom teknik. Dock är prestationen hos DE inte alltid framgångsrik när man söker optimala lösningar. Det finns två huvudsakliga problem för applikationer i den verkliga världen. Det första är att den lätt kan fastna i lokala optimum eller misslyckas att generera bättre lösningar före det att populationen (en grupp av lösningar) har hunnit konvergera. Det andra är att prestandan påverkas märkvärdigt av kontrollparametrar, vilkas optimala värden beror på problem som ska lösas och varierar mellan regioner i sökrymden. Detta innebär oftast ett tidskrävande trial-and-error förfarande för att hitta lämpliga parametrar till ett specifikt DE-problem, framför allt för utövare med begränsad kunskap och erfarenhet av DE. Syftet med denna licentiatavhandling är att utveckla nya DE-algoritmer för att behandla de ovannämnda problemen. För att möta det första problemet så studerades hybridisering av DE och lokala söktekniker för att effektivisera sökningen. Tanken är att använda en lokal sökmekanism på den bästa individen i varje generation i DE-algoritmen och utnyttja de mest lovande regionerna under evolutionsprocessen för att snabba på konvergensen eller öka chansen att undvika lokala optimum. Fyra lokala sökstrategier har integrerats och testats i det globala DE-ramverket vilket har lett till fyra varianter av DE-algoritmerna med olika egenskaper beträffande diversifiering och intensifiering. Till det andra problemet föreslås en greedy adaptation method för dynamisk justering av kontrollparametrarna i DE. Den implementeras genom att utföra greedy search upprepade gånger under körningen av DE för att hitta bättre värden till kontrollparametrarna. Utvärderingen av parameterval baseras på både success rate och fitness improvement av trial lösningar jämfört med target lösningar. Sammanslagningen av DE och denna greedy parameter adaptation har lett till en ny adaptiv DE-algoritm som kallas Greedy Adaptive Differential Evolution (GADE). Den föreslagna metoden i denna licentiatavhandling har testats i olika prestandamätningar och jämförts med state-of-the-art-algoritmer, med goda resultat. Dessutom har den föreslagna GADE-algoritmen använts i ett industriellt scenario och uppnådde då mer exakta resultat än den med en standard DE-algoritm.

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Schutte, Jaco Francois. "Applications of parallel global optimization to mechanics problems." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0012932.

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Koullias, Stefanos. "Methodology for global optimization of computationally expensive design problems." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49085.

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The design of unconventional aircraft requires early use of high-fidelity physics-based tools to search the unfamiliar design space for optimum designs. Current methods for incorporating high-fidelity tools into early design phases for the purpose of reducing uncertainty are inadequate due to the severely restricted budgets that are common in early design as well as the unfamiliar design space of advanced aircraft. This motivates the need for a robust and efficient global optimization algorithm. This research presents a novel surrogate model-based global optimization algorithm to efficiently search challenging design spaces for optimum designs. The algorithm searches the design space by constructing a fully Bayesian Gaussian process model through a set of observations and then using the model to make new observations in promising areas where the global minimum is likely to occur. The algorithm is incorporated into a methodology that reduces failed cases, infeasible designs, and provides large reductions in the objective function values of design problems. Results on four sets of algebraic test problems are presented and the methodology is applied to an airfoil section design problem and a conceptual aircraft design problem. The method is shown to solve more nonlinearly constrained algebraic test problems than state-of-the-art algorithms and obtains the largest reduction in the takeoff gross weight of a notional 70-passenger regional jet versus competing design methods.

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Pham, Viet. "A global optimization approach to pooling problems in refineries." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1445.

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Robertson, Blair Lennon. "Direct Search Methods for Nonsmooth Problems using Global Optimization Techniques." Thesis, University of Canterbury. Mathematics and Statistics, 2010. http://hdl.handle.net/10092/5060.

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This thesis considers the practical problem of constrained and unconstrained local optimization. This subject has been well studied when the objective function f is assumed to smooth. However, nonsmooth problems occur naturally and frequently in practice. Here f is assumed to be nonsmooth or discontinuous without forcing smoothness assumptions near, or at, a potential solution. Various methods have been presented by others to solve nonsmooth optimization problems, however only partial convergence results are possible for these methods. In this thesis, an optimization method which use a series of local and localized global optimization phases is proposed. The local phase searches for a local minimum and gives the methods numerical performance on parts of f which are smooth. The localized global phase exhaustively searches for points of descent in a neighborhood of cluster points. It is the localized global phase which provides strong theoretical convergence results on nonsmooth problems. Algorithms are presented for solving bound constrained, unconstrained and constrained nonlinear nonsmooth optimization problems. These algorithms use direct search methods in the local phase as they can be applied directly to nonsmooth problems because gradients are not explicitly required. The localized global optimization phase uses a new partitioning random search algorithm to direct random sampling into promising subsets of ℝⁿ. The partition is formed using classification and regression trees (CART) from statistical pattern recognition. The CART partition defines desirable subsets where f is relatively low, based on previous sampling, from which further samples are drawn directly. For each algorithm, convergence to an essential local minimizer of f is demonstrated under mild conditions. That is, a point x* for which the set of all feasible points with lower f values has Lebesgue measure zero for all sufficiently small neighborhoods of x*. Stopping rules are derived for each algorithm giving practical convergence to estimates of essential local minimizers. Numerical results are presented on a range of nonsmooth test problems for 2 to 10 dimensions showing the methods are effective in practice.

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Majig, Mend-Amar. "Studies on Global Optimization Approach for General Variational Inequality Problems." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/123852.

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Kumar, Manish. "Converting some global optimization problems to mixed integer linear problems using piecewise linear approximations." Diss., Rolla, Mo. : University of Missouri-Rolla, 2007. http://scholarsmine.umr.edu/thesis/pdf/Kumar_09007dcc803c8e68.pdf.

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Thesis (M.S.)--University of Missouri--Rolla, 2007. Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 7, 2007) Includes bibliographical references (p. 28).

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Stiglmayr, Michael [Verfasser]. "Discrete and Continuous Optimization Problems Arising in Medical Image Registration / Michael Stiglmayr." Aachen : Shaker, 2010. http://d-nb.info/1081887168/34.

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Tsoukalas, Angelos. "Global optimization algorithms for multi-level and generalized semi-infinite problems." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512078.

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Totzeck, Claudia [Verfasser]. "Asymptotic Analysis of Optimal Control Problems and Global Optimization / Claudia Totzeck." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126295876/34.

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Halstrup, Momchil Verfasser], Sonja [Akademischer Betreuer] [Kuhnt, and Claus [Gutachter] Weihs. "Black-box optimization of mixed discrete-continuous optimization problems / Momchil Halstrup ; Gutachter: Claus Weihs ; Betreuer: Sonja Kuhnt." Dortmund : Universitätsbibliothek Dortmund, 2016. http://d-nb.info/112468123X/34.

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Halstrup, Momchil [Verfasser], Sonja [Akademischer Betreuer] Kuhnt, and Claus [Gutachter] Weihs. "Black-box optimization of mixed discrete-continuous optimization problems / Momchil Halstrup ; Gutachter: Claus Weihs ; Betreuer: Sonja Kuhnt." Dortmund : Universitätsbibliothek Dortmund, 2016. http://d-nb.info/112468123X/34.

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Raber, Ulrich. "Nonconvex all-quadratic global optimization problems solution methods, application and related topics /." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=961036478.

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Wang, Hongjie. "Global Optimization of Nonconvex Factorable Programs with Applications to Engineering Design Problems." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36823.

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The primary objective of this thesis is to develop and implement a global optimization algorithm to solve a class of nonconvex programming problems, and to test it using a collection of engineering design problem applications.The class of problems we consider involves the optimization of a general nonconvex factorable objective function over a feasible region that is restricted by a set of constraints, each of which is defined in terms of nonconvex factorable functions. Such problems find widespread applications in production planning, location and allocation, chemical process design and control, VLSI chip design, and numerous engineering design problems. This thesis offers a first comprehensive methodological development and implementation for determining a global optimal solution to such factorable programming problems. To solve this class of problems, we propose a branch-and-bound approach based on linear programming (LP) relaxations generated through various approximation schemes that utilize, for example, the Mean-Value Theorem and Chebyshev interpolation polynomials, coordinated with a {em Reformulation-Linearization Technique} (RLT). The initial stage of the lower bounding step generates a tight, nonconvex polynomial programming relaxation for the given problem. Subsequently, an LP relaxation is constructed for the resulting polynomial program via a suitable RLT procedure. The underlying motivation for these two steps is to generate a tight outer approximation of the convex envelope of the objective function over the convex hull of the feasible region. The bounding step is thenintegrated into a general branch-and-bound framework. The construction of the bounding polynomials and the node partitioning schemes are specially designed so that the gaps resulting from these two levels of approximations approach zero in the limit, thereby ensuring convergence to a global optimum. Various implementation issues regarding the formulation of such tight bounding problems using both polynomial approximations and RLT constructs are discussed. Different practical strategies and guidelines relating to the design of the algorithm are presented within a general theoretical framework so that users can customize a suitable approach that takes advantage of any inherent special structures that their problems might possess. The algorithm is implemented in C++, an object-oriented programming language. The class modules developed for the software perform various functions that are useful not only for the proposed algorithm, but that can be readily extended and incorporated into other RLT based applications as well. Computational results are reported on a set of fifteen engineering process control and design test problems from various sources in the literature. It is shown that, for all the test problems, a very competitive computational performance is obtained. In most cases, the LP solution obtained for the initial node itself provides a very tight lower bound. Furthermore, for nine of these fifteen problems, the application of a local search heuristic based on initializing the nonlinear programming solver MINOS at the node zero LP solution produced the actual global optimum. Moreover, in finding a global optimum, our algorithm discovered better solutions than the ones previously reported in the literature for two of these test instances. Master of Science

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Morenko, Yana. "Continuous and discrete optimization techniques for some problems in industrial engineering and materials design." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1991.

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This work comprises several projects that involve optimization of physical systems. By a physical system we understand an object or a process that is governed by physical, mechanical, chemical, biological, etc., laws. Such objects and the related optimization problems are relatively rarely considered in operations research literature, where the traditional subjects of optimization methods are represented by schedules, assignments and allocations, sequences, and queues. The corresponding operations research and management sciences models result in optimization problems of relatively simple structure (for example, linear or quadratic optimization models), but whose difficulty comes from very large number (from hundreds to millions) of optimization variables and constraints. In contrast, in many optimization problems that arise in mechanical engineering, chemical engineering, biomedical engineering, the number of variables or constraints in relatively small (typically, in the range of dozens), but the objective function and constraints have very complex, nonlinear and nonconvex analytical form. In many problems, the analytical expressions for objective function and constraints may not be available, or are obtained as solutions of governing equations (e.g., PDE-onstrained optimization problems), or as results of external simulation runs (black-box optimization). In this dissertation we consider problems of classification of biomedical data, construction of optimal bounds on elastic tensor of composite materials, multiobjective (multi-property) optimization via connection to stochastic orderings, and black-box combinatorial optimization of crystal structures of organic molecules.

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Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.

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Lee, Haewon. "Nolinear Evolution Equations and Optimization Problems in Banach Spaces." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1127498683.

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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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Bryan, Jason M. "GLOBAL OPTIMIZATION OF MGA-DSM PROBLEMS USING THE INTERPLANETARY GRAVITY ASSIST TRAJECTORY OPTIMIZER (IGATO)." DigitalCommons@CalPoly, 2011. https://digitalcommons.calpoly.edu/theses/663.

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Interplanetary multiple gravity assist (MGA) trajectory optimization has long been a field of interest to space scientists and engineers. Gravity assist maneuvers alter a spacecraft's velocity vector and potentially allow spacecraft to achieve changes in velocity which would otherwise be unfeasible given our current technological limitations. Unfortunately, designing MGA trajectories is difficult and in order to find good solutions, deep space maneuvers (DSM) are often required which further increase the complexity of the problem. In addition, despite the active research in the field over the last 50 years, software for MGA trajectory optimization is scarce. A few good commercial, and even fewer open-source, options exist, but a majority of quality software remains proprietary. The intent of this thesis is twofold. The first part of this work explores the realm of global optimization applied to multiple gravity assist trajectories with deep space maneuvers (MGA-DSM). With the constant influx of new global optimization algorithms and heuristics being developed in the global optimization community, this work aims to be a high level optimization approach which makes use of those algorithms instead of trying to be one itself. Central to this approach is PaGMO, which is the open-source Parallel Multiobjective Global Optimizer created by ESA's Advanced Concepts Team (ACT). PaGMO is an implementation of the Island Model Paradigm which allows the parallelization of different global optimizers. The second part of this work introduces the IGATO software which improves PaGMO by complementing it with dynamic restart capabilities, a pruning algorithm which learns over time, subdomain decomposition, and other techniques to create a powerful optimization tool. IGATO aims to be an open-source platform independent C++ application with a robust graphical user interface (GUI). The application is equipped with 2D plotting and simulations, real time Porkchop Plot generation, and other useful features for analyzing various problems. The optimizer is tested on several challenging MGA-DSM problems and performs well: consistently performing as well or better than PaGMO on its own.

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Yamakawa, Yuya. "Studies on Optimization Methods for Nonlinear Semidefinite Programming Problems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199446.

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Barjhoux, Pierre-Jean. "Towards efficient solutions for large scale structural optimization problems with categorical and continuous mixed design variables." Thesis, Toulouse, ISAE, 2020. http://depozit.isae.fr/theses/2020/2020_Barjhoux_Pierre-Jean.pdf.

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Dans l’industrie aéronautique, les problèmes d’optimisation de structurepeuvent impliquer des changements de matériaux, de types de raidisseurs, et detailles d’éléments. Dans ce travail, il est ainsi proposé de résoudre des problèmes degrande taille (minimisation de masse) par rapport à des variables catégorielles et continues,sujets à des contraintes de stress et de déplacements. Trois algorithmes sontprésentés, discutés dans le manuscrit au regard de cas tests de plus en plus complexes.En tout premier lieu, un algorithme basé sur le "branch and bound" a été mis en place.Une formulation d’un problème dédié au calcul de minorants de la masse optimale estproposée. Bien que l’algorithme permette de trouver des solutions optimales, la tendancedu coût de calcul en fonction de l’augmentation du nombre d’éléments est exponentielle.Le second algorithme s’appuie sur une formulation bi-niveau du problème d’origine, oùle problème supérieur consiste à minimiser une approximation au premier ordre du résultatdu niveau inférieur. L’évolution du coût de calcul par rapport à l’augmentation dunombre d’éléments et de valeurs catégorielles est quasiment linéaire. Enfin, un troisièmealgorithme tire partie d’une reformulation du problème mixte catégoriel continu en unproblème bi-niveau mixte avec variables entières continûment relâchables. Les cas testsnumériques montrent la résolution d’un problème avec plus d’une centaine d’éléments.Également, le coût de calcul est quasi-indépendant du nombre de valeurs de variablescatégorielles disponibles par élément Nowadays in the aircraft industry, structural optimization problemscan be really complex and combine changes in choices of materials, stiffeners, orsizes/types of elements. In this work, it is proposed to solve large scale structural weightminimization problems with both categorical and continuous variables, subject to stressand displacements constraints. Three algorithms have been proposed. As a first attempt,an algorithm based on the branch and bound generic framework has been implemented.A specific formulation to compute lower bounds has been proposed. According to thenumerical tests, the algorithm returned the exact optima. However, the exponentialscalability of the computational cost with respect to the number of structural elementsprevents from an industrial application. The second algorithm relies on a bi-level formulationof the mixed categorical problem. The master full categorical problem consists ofminimizing a first order like approximation of the slave problem with respect to the categoricaldesign variables. The method offers a quasi-linear scaling of the computationalcost with respect to the number of elements and categorical values. Finally, in the thirdapproach the optimization problem is formulated as a bi-level mixed integer non-linearprogram with relaxable design variables. Numerical tests include an optimization casewith more than one hundred structural elements. Also, the computational cost scalingis quasi-independent from the number of available categorical values per element

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Fraticelli, Barbara M. P. "Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/27293.

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This dissertation develops efficient solution techniques for general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called semidefinite cuts. While these cuts are valid for any general problem for which RLT is applicable, we demonstrate their effectiveness in optimizing a nonconvex quadratic objective function over a simplex. Computational results indicate that on average, the semidefinite cuts have reduced the number of nodes in the branch-and-bound tree by a factor of 37.6, while decreasing solution time by a factor of 3.4. The semidefinite cuts have also led to a significant reduction in the optimality gap at termination, in some cases producing optimal solutions for problems that could not be solved using RLT alone. We then narrow our focus to the class of mixed-integer programming (MIP) problems, and develop a modification of Bendersâ decomposition method using concepts from RLT and lift-and-project cuts. This method is particularly motivated by the class of two-stage stochastic programs with integer recourse. The key idea is to design an RLT or lift-and-project cutting plane scheme for solving the subproblems where the cuts generated have right-hand sides that are functions of the first-stage variables. An illustrative example is provided to elucidate the proposed approach. The focus is on developing a first comprehensive finitely convergent extension of Bendersâ methodology for problems having 0-1 mixed-integer subproblems. We next address a specific challenging MIP application known as the facility layout problem, and we significantly improve its formulation through outer-linearization techniques and concepts from disjunctive programming. The enhancements produce a substantial increase in the accuracy of the layout produced, while at the same time, providing a dramatic reduction in computational effort. Overall, the maximum error in department size was reduced from about 6% to nearly zero, while solution time decreased by a factor of 110. Previously unsolved test problems from the literature that had defied even approximate solution methods have been solved to exact optimality using our proposed approach. Ph. D.

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Bucher, Max [Verfasser], Alexandra [Akademischer Betreuer] Schwartz, and Christian [Akademischer Betreuer] Kanzow. "Optimality Conditions and Numerical Methods for a Continuous Reformulation of Cardinality Constrained Optimization Problems / Max Bucher ; Alexandra Schwartz, Christian Kanzow." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2018. http://d-nb.info/1167926323/34.

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Hua, Xiaoqin. "Studies on block coordinate gradient methods for nonlinear optimization problems with separable structure." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199447.

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Garrigos, Guillaume. "Descent dynamical systems and algorithms for tame optimization, and multi-objective problems." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS191/document.

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Dans une première partie, nous nous intéressons aux systèmes dynamiques gradients gouvernés par des fonctions non lisses, mais aussi non convexes, satisfaisant l'inégalité de Kurdyka-Lojasiewicz. Après avoir obtenu quelques résultats préliminaires pour la dynamique de la plus grande pente continue, nous étudions un algorithme de descente général. Nous prouvons, sous une hypothèse de compacité, que tout suite générée par ce schéma général converge vers un point critique de la fonction. Nous obtenons aussi de nouveaux résultats sur la vitesse de convergence, tant pour les valeurs que pour les itérés. Ce schéma général couvre en particulier des versions parallélisées de la méthode forward-backward, autorisant une métrique variable et des erreurs relatives. Cela nous permet par exemple de proposer une version non convexe non lisse de l'algorithme Levenberg-Marquardt. Enfin, nous proposons quelques applications de ces algorithmes aux problèmes de faisabilité, et aux problèmes inverses. Dans une seconde partie, cette thèse développe une dynamique de descente associée à des problèmes d'optimisation vectoriels sous contrainte. Pour cela, nous adaptons la dynamique de la plus grande pente usuelle aux fonctions à valeurs dans un espace ordonné par un cône convexe fermé solide. Cette dynamique peut être vue comme l'analogue continu de nombreux algorithmes développés ces dernières années. Nous avons un intérêt particulier pour les problèmes de décision multi-objectifs, pour lesquels cette dynamique de descente fait décroitre toutes les fonctions objectif au cours du temps. Nous prouvons l'existence de trajectoires pour cette dynamique continue, ainsi que leur convergence vers des points faiblement efficients. Finalement, nous explorons une nouvelle dynamique inertielle pour les problèmes multi-objectif, avec l'ambition de développer des méthodes rapides convergeant vers des équilibres de Pareto In a first part, we focus on gradient dynamical systems governed by non-smooth but also non-convex functions, satisfying the so-called Kurdyka-Lojasiewicz inequality.After obtaining preliminary results for a continuous steepest descent dynamic, we study a general descent algorithm. We prove, under a compactness assumption, that any sequence generated by this general scheme converges to a critical point of the function.We also obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method, with variable metric and relative errors. As an example, a non-smooth and non-convex version of the Levenberg-Marquardt algorithm is detailed.Applications to non-convex feasibility problems, and to sparse inverse problems are discussed.In a second part, the thesis explores descent dynamics associated to constrained vector optimization problems. For this, we adapt the classic steepest descent dynamic to functions with values in a vector space ordered by a solid closed convex cone. It can be seen as the continuous analogue of various descent algorithms developed in the last years.We have a particular interest for multi-objective decision problems, for which the dynamic make decrease all the objective functions along time.We prove the existence of trajectories for this continuous dynamic, and show their convergence to weak efficient points.Then, we explore an inertial dynamic for multi-objective problems, with the aim to provide fast methods converging to Pareto points

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Viklands, Thomas. "Algorithms for the Weighted Orthogonal Procrustes Problem and other Least Squares Problems." Doctoral thesis, Umeå : Umeå universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-730.

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Andrade, Lisieux Marie Marinho dos Santos. "Novas Abordagens Sequencial e Paralela da meta-heurística C-GRASP Aplicadas à Otimização Global Contínua." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/6095.

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Made available in DSpace on 2015-05-14T12:36:40Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2336902 bytes, checksum: 41580878008a0f84da693637a48ceb33 (MD5) Previous issue date: 2013-08-08 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior The present work deals with the Continuous Global Optimization Problem, in its minimization form, by testing two approaches for the Continuous Greedy Randomized Adaptive Search Procedure (C-GRASP). The development of the first method - sequential and hybrid - comes from the deficiency of current approaches to provide a good neighborhood space exploration. Being constructed from the combination of two meta-heuristics, standard C-GRASP and Continuous General Variable Neighborhood Search (C-GVNS), as a strategy to achieving symmetric trades of neighborhood structures, it performed efficiently in the computational tests that were taken. The second procedure arises from the large consume of time when using high dimension functions with the standard C-GRASP construction procedure. As the optimization problems have a high dimensionality increase, it s preferable to have two parallel versions of the optimization method in order to handle bigger problems. Thus, for this new procedure developed, it was used the Compute Unified Device Architecture (CUDA), which provided promising acceleration regarding the processing time, based on the experiments performed. O presente trabalho aborda o Problema de Otimização Global Contínua, em sua forma de minimização, através de duas abordagens para o procedimento Continuous Greedy Randomized Adaptive Search Procedure (C-GRASP). A elaboração do primeiro método, sequencial e híbrido, parte da deficiência presente nas abordagens atuais, em promover boa exploração no espaço de vizinhança. Sendo constituída da combinação de duas meta-heurísticas, C-GRASP padrão e Continuous General Variable Neighborhood Search (C-GVNS). Como estratégia para a realização de trocas sistemática de estruturas de vizinhanças, mostrou-se eficiente aos testes computacionais realizados. O segundo procedimento elaborado parte do grande consumo de tempo ao utilizar funções com alta dimensão, pelo procedimento de construção do método C-GRASP padrão. Como os problemas de otimização possuem crescimento elevado de dimensionalidade, é desejável ter versões paralelas do método de otimização para lidar com os problemas maiores. Desta forma, para o novo procedimento elaborado foi empregado a plataforma de computação paralela Compute Unified Device Architecture (CUDA), que, conforme verificado nos experimentos realizados, promoveu promissora aceleração quanto ao tempo de processamento.

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Vasil, Timothy J. (Timothy James). "Forward thinking in reverse : design, implementation, and continuous monitoring of a closed-loop supply chain using optimization, simulation, and dashboard systems to maximize net recovery." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/66044.

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Thesis (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; in conjunction with the Leaders for Global Operations Program at MIT, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 197-199). Developed during our recent six-month engagement at Dell-a leading computer manufacturer and services provider with one of the world's leading supply chains--we discuss a network flow-based mixed-integer linear program (MILP) model to identify the critical factors in optimizing reverse supply chain design decisions to optimize profit. The model is fast, intuitive, flexible, and robust to uncertainty. Its outputs include specific design recommendations, financial impact estimates, dynamically generated product routing diagrams, and multi-scenario sensitivity analysis. Through two case studies, the first in U.S. smartphone returns and the second in Europe, Middle East and Africa (EMEA) Alienware-branded computer returns, we show how our model fosters standardized, robust strategic decision-making and serves as a platform upon which to build management systems for continuous improvement. We then discuss two such systems: a simulation-based reusable packaging cost-benefit analysis (CBA) calculator, and an automated dashboard for managing disassembly-for-parts decisions. by Timothy J. Vasil. S.M. M.B.A.

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Popov, Mikhail. "Analytic and Numerical Methods for the Solution of Electromagnetic Inverse Source Problems." Doctoral thesis, KTH, Electromagnetic Theory, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3134.

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Yu, Haofeng. "A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29095.

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This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space. The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions. Ph. D.

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Yerlikaya, Fatma. "A New Contribution To Nonlinear Robust Regression And Classification With Mars And Its Applications To Data Mining For Quality Control In Manufacturing." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12610037/index.pdf.

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Multivariate adaptive regression spline (MARS) denotes a modern methodology from statistical learning which is very important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. MARS is very useful for high dimensional problems and shows a great promise for fitting nonlinear multivariate functions. MARS technique does not impose any particular class of relationship between the predictor variables and outcome variable of interest. In other words, a special advantage of MARS lies in its ability to estimate the contribution of the basis functions so that both the additive and interaction effects of the predictors are allowed to determine the response variable. The function fitted by MARS is continuous, whereas the one fitted by classical classification methods (CART) is not. Herewith, MARS becomes an alternative to CART. The MARS algorithm for estimating the model function consists of two complementary algorithms: the forward and backward stepwise algorithms. In the first step, the model is built by adding basis functions until a maximum level of complexity is reached. On the other hand, the backward stepwise algorithm is began by removing the least significant basis functions from the model. In this study, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization problem, which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to become an important complementary technology and alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming which is an area of convex optimization that is very well-structured, herewith, resembling linear programming and, hence, permitting the use of interior point methods. The boundaries of this optimization problem are determined by the multiobjective optimization approach which provides us many alternative solutions. Based on these theoretical and algorithmical studies, this MSc thesis work also contains applications on the data investigated in a T&Uuml BiTAK project on quality control. By these applications, MARS and our new method are compared.

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Wagner, Andrea. "Locating a semi-obnoxious facility in the special case of Manhattan distances." Springer, 2019. http://dx.doi.org/10.1007/s00186-019-00671-z.

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The aim of thiswork is to locate a semi-obnoxious facility, i.e. tominimize the distances to a given set of customers in order to save transportation costs on the one hand and to avoid undesirable interactions with other facilities within the region by maximizing the distances to the corresponding facilities on the other hand. Hence, the goal is to satisfy economic and environmental issues simultaneously. Due to the contradicting character of these goals, we obtain a non-convex objective function. We assume that distances can be measured by rectilinear distances and exploit the structure of this norm to obtain a very efficient dual pair of algorithms.

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Excoffier, Mathilde. "Chance-Constrained Programming Approaches for Staffing and Shift-Scheduling Problems with Uncertain Forecasts : application to Call Centers." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112244/document.

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Le problème de dimensionnement et planification d'agents en centre d'appels consiste à déterminer sur une période le nombre d'interlocuteurs requis afin d'atteindre la qualité de service exigée et minimiser les coûts induits. Ce sujet fait l'objet d'un intérêt croissant pour son intérêt théorique mais aussi pour l'impact applicatif qu'il peut avoir. Le but de cette thèse est d'établir des approches en contraintes en probabilités en considérant l'incertitude de la demande.Tout d'abord, la thèse présente un modèle en problème d'optimisation stochastique avec contrainte en probabilité jointe traitant la problématique complète en une étape afin d'obtenir un programme facile à résoudre. Une approche basée sur l'idée de continuité est proposée grâce à des lois de probabilité continues, une nouvelle relation entre les taux d'arrivées et les besoins théoriques et la linéarisation de contraintes. La répartition du risque global est faite pendant le processus d'optimisation, permettant une solution au coût réduit. Ces solutions résultantes respectent le niveau de risque tout en diminuant le coût par rapport à d'autres approches.De plus, le modèle en une étape est étendu pour améliorer sa représentation de la réalité. D'une part, le modèle de file d'attente est amélioré et inclus la patience limitée des clients. D'autre part, une nouvelle expression de l'incertitude est proposée pour prendre la dépendance des périodes en compte.Enfin, une nouvelle représentation de l'incertitude est considérée. L'approche distributionally robust permet de modéliser le problème sous l'hypothèse que la loi de probabilité adéquate est inconnue et fait partie d'un ensemble de lois, défini par une moyenne et une variance données. Le problème est modélisé par une contrainte en probabilité jointe. Le risque à chaque période est définie par une variable à optimiser.Un problème déterministe équivalent est proposé et des approximations linéaires permettent d'obtenir une formulation d'optimisation linéaire The staffing and shift-scheduling problems in call centers consist in deciding how many agents handling the calls should be assigned to work during a given period in order to reach the required Quality of Service and minimize the costs. These problems are subject to a growing interest, both for their interesting theoritical formulation and their possible applicative effects. This thesis aims at proposing chance-constrained approaches considering uncertainty on demand forecasts.First, this thesis proposes a model solving the problems in one step through a joint chance-constrained stochastic program, providing a cost-reducing solution. A continuous-based approach leading to an easily-tractable optimization program is formulated with random variables following continuous distributions, a new continuous relation between arrival rates and theoritical real agent numbers and constraint linearizations. The global risk level is dynamically shared among the periods during the optimization process, providing reduced-cost solution. The resulting solutions respect the targeted risk level while reducing the cost compared to other approaches.Moreover, this model is extended so that it provides a better representation of real situations. First, the queuing system model is improved and consider the limited patience of customers. Second, another formulation of uncertainty is proposed so that the period correlation is considered.Finally, another uncertainty representation is proposed. The distributionally robust approach provides a formulation while assuming that the correct probability distribution is unknown and belongs to a set of possible distributions defined by given mean and variance. The problem is formulated with a joint chance constraint. The risk at each period is a decision variable to be optimized. A deterministic equivalent problem is proposed. An easily-tractable mixed-integer linear formulation is obtained through piecewise linearizations

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Lunday, Brian Joseph. "Resource Allocation on Networks: Nested Event Tree Optimization, Network Interdiction, and Game Theoretic Methods." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/77323.

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This dissertation addresses five fundamental resource allocation problems on networks, all of which have applications to support Homeland Security or industry challenges. In the first application, we model and solve the strategic problem of minimizing the expected loss inflicted by a hostile terrorist organization. An appropriate allocation of certain capability-related, intent-related, vulnerability-related, and consequence-related resources is used to reduce the probabilities of success in the respective attack-related actions, and to ameliorate losses in case of a successful attack. Given the disparate nature of prioritizing capital and material investments by federal, state, local, and private agencies to combat terrorism, our model and accompanying solution procedure represent an innovative, comprehensive, and quantitative approach to coordinate resource allocations from various agencies across the breadth of domains that deal with preventing attacks and mitigating their consequences. Adopting a nested event tree optimization framework, we present a novel formulation for the problem as a specially structured nonconvex factorable program, and develop two branch-and-bound schemes based respectively on utilizing a convex nonlinear relaxation and a linear outer-approximation, both of which are proven to converge to a global optimal solution. We also investigate a fundamental special-case variant for each of these schemes, and design an alternative direct mixed-integer programming model representation for this scenario. Several range reduction, partitioning, and branching strategies are proposed, and extensive computational results are presented to study the efficacy of different compositions of these algorithmic ingredients, including comparisons with the commercial software BARON. The developed set of algorithmic implementation strategies and enhancements are shown to outperform BARON over a set of simulated test instances, where the best proposed methodology produces an average optimality gap of 0.35% (compared to 4.29% for BARON) and reduces the required computational effort by a factor of 33. A sensitivity analysis is also conducted to explore the effect of certain key model parameters, whereupon we demonstrate that the prescribed algorithm can attain significantly tighter optimality gaps with only a near-linear corresponding increase in computational effort. In addition to enabling effective comprehensive resource allocations, this research permits coordinating agencies to conduct quantitative what-if studies on the impact of alternative resourcing priorities. The second application is motivated by the author's experience with the U.S. Army during a tour in Iraq, during which combined operations involving U.S. Army, Iraqi Army, and Iraqi Police forces sought to interdict the transport of selected materials used for the manufacture of specialized types of Improvised Explosive Devices, as well as to interdict the distribution of assembled devices to operatives in the field. In this application, we model and solve the problem of minimizing the maximum flow through a network from a given source node to a terminus node, integrating different forms of superadditive synergy with respect to the effect of resources applied to the arcs in the network. Herein, the superadditive synergy reflects the additional effectiveness of forces conducting combined operations, vis-Ã -vis unilateral efforts. We examine linear, concave, and general nonconcave superadditive synergistic relationships between resources, and accordingly develop and test effective solution procedures for the underlying nonlinear programs. For the linear case, we formulate an alternative model representation via Fourier-Motzkin elimination that reduces average computational effort by over 40% on a set of randomly generated test instances. This test is followed by extensive analyses of instance parameters to determine their effect on the levels of synergy attained using different specified metrics. For the case of concave synergy relationships, which yields a convex program, we design an inner-linearization procedure that attains solutions on average within 3% of optimality with a reduction in computational effort by a factor of 18 in comparison with the commercial codes SBB and BARON for small- and medium-sized problems; and outperforms these softwares on large-sized problems, where both solvers failed to attain an optimal solution (and often failed to detect a feasible solution) within 1800 CPU seconds. Examining a general nonlinear synergy relationship, we develop solution methods based on outer-linearizations, inner-linearizations, and mixed-integer approximations, and compare these against the commercial software BARON. Considering increased granularities for the outer-linearization and mixed-integer approximations, as well as different implementation variants for both these approaches, we conduct extensive computational experiments to reveal that, whereas both these techniques perform comparably with respect to BARON on small-sized problems, they significantly improve upon the performance for medium- and large-sized problems. Our superlative procedure reduces the computational effort by a factor of 461 for the subset of test problems for which the commercial global optimization software BARON could identify a feasible solution, while also achieving solutions of objective value 0.20% better than BARON. The third application is likewise motivated by the author's military experience in Iraq, both from several instances involving coalition forces attempting to interdict the transport of a kidnapping victim by a sectarian militia as well as, from the opposite perspective, instances involving coalition forces transporting detainees between interment facilities. For this application, we examine the network interdiction problem of minimizing the maximum probability of evasion by an entity traversing a network from a given source to a designated terminus, while incorporating novel forms of superadditive synergy between resources applied to arcs in the network. Our formulations examine either linear or concave (nonlinear) synergy relationships. Conformant with military strategies that frequently involve a combination of overt and covert operations to achieve an operational objective, we also propose an alternative model for sequential overt and covert deployment of subsets of interdiction resources, and conduct theoretical as well as empirical comparative analyses between models for purely overt (with or without synergy) and composite overt-covert strategies to provide insights into absolute and relative threshold criteria for recommended resource utilization. In contrast to existing static models, in a fourth application, we present a novel dynamic network interdiction model that improves realism by accounting for interactions between an interdictor deploying resources on arcs in a digraph and an evader traversing the network from a designated source to a known terminus, wherein the agents may modify strategies in selected subsequent periods according to respective decision and implementation cycles. We further enhance the realism of our model by considering a multi-component objective function, wherein the interdictor seeks to minimize the maximum value of a regret function that consists of the evader's net flow from the source to the terminus; the interdictor's procurement, deployment, and redeployment costs; and penalties incurred by the evader for misperceptions as to the interdicted state of the network. For the resulting minimax model, we use duality to develop a reformulation that facilitates a direct solution procedure using the commercial software BARON, and examine certain related stability and convergence issues. We demonstrate cases for convergence to a stable equilibrium of strategies for problem structures having a unique solution to minimize the maximum evader flow, as well as convergence to a region of bounded oscillation for structures yielding alternative interdictor strategies that minimize the maximum evader flow. We also provide insights into the computational performance of BARON for these two problem structures, yielding useful guidelines for other research involving similar non-convex optimization problems. For the fifth application, we examine the problem of apportioning railcars to car manufacturers and railroads participating in a pooling agreement for shipping automobiles, given a dynamically determined total fleet size. This study is motivated by the existence of such a consortium of automobile manufacturers and railroads, for which the collaborative fleet sizing and efforts to equitably allocate railcars amongst the participants are currently orchestrated by the \textit{TTX Company} in Chicago, Illinois. In our study, we first demonstrate potential inequities in the industry standard resulting either from failing to address disconnected transportation network components separately, or from utilizing the current manufacturer allocation technique that is based on average nodal empty transit time estimates. We next propose and illustrate four alternative schemes to apportion railcars to manufacturers, respectively based on total transit time that accounts for queuing; two marginal cost-induced methods; and a Shapley value approach. We also provide a game-theoretic insight into the existing procedure for apportioning railcars to railroads, and develop an alternative railroad allocation scheme based on capital plus operating costs. Extensive computational results are presented for the ten combinations of current and proposed allocation techniques for automobile manufacturers and railroads, using realistic instances derived from representative data of the current business environment. We conclude with recommendations for adopting an appropriate apportionment methodology for implementation by the industry. Ph. D.

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Ruiz, Manuel. "Une approche exacte de résolution de problèmes de pooling appliquée à la fabrication d'aliments." Phd thesis, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00992383.

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Cette thèse intitulée " Une approche exacte de résolution de problèmes de pooling appliquée à la fabrication d'aliments ", porte sur la résolution (par des méthodes exactes d'optimisation) de problèmes industriels liés à la fabrication d'aliments. Ces problèmes industriels traitent de l'aide à la décision pour la fabrication d'aliments pour des animaux et se rapprochent de problèmes biens connus de la littérature scientiﬁque, à savoir les problèmes de pooling. La méthode présentée dans cet exposé permet de résoudre les problèmes d'optimisation bilinéaires issus de cette problématique industrielle. Elle est basée un branch-and-bound résolvant des linéarisations. Une approche lagrangienne a aussi été explorée et testée pour calculer des bornes inférieures.

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Santos, Genasil Francisco dos. "Identificação de danos estruturais utilizando técnicas de otimização." Universidade do Estado do Rio de Janeiro, 2009. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=5647.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Sistemas estruturais em suas variadas aplicações incluindo-se veículos espaciais, automóveis e estruturas de engenharia civil tais como prédios, pontes e plataformas off-shore, acumulam dano durante suas vidas úteis. Em muitas situações, tal dano pode não ser visualmente observado. Do ponto de vista da segurança e da performance da estrutura, é desejável monitorar esta possível ocorrência, localizá-la e quantificá-la. Métodos de identificação de sistemas, que em geral, são classificados numa categoria de Técnicas de Avaliação Não-Destrutivas, podem ser utilizados para esta finalidade. Usando dados experimentais tais como frequências naturais, modos de vibração e deslocamentos estáticos, e um modelo analítico estrutural, parâmetros da estrutura podem ser identificados. As propriedades estruturais do modelo analítico são modificadas de modo a minimizar a diferença entre os dados obtidos por aquele modelo e a resposta medida. Isto pode ser definido como um problema inverso onde os parâmetros da estrutura são identificados. O problema inverso, descrito acima, foi resolvido usando métodos globais de otimização devido à provável presença de inúmeros mínimos locais e a não convexidade do espaço de projeto. Neste trabalho o método da Evolução Diferencial (Differential Evolution, DE) foi utilizado como ferramenta principal de otimização. Trata-se de uma meta-heurística inspirada numa população de soluções sucessivamente atualizada por operações aritméticas como mutações, recombinações e critérios de seleção dos melhores indivíduos até que um critério de convergência seja alcançado. O método da Evolução Diferencial foi desenvolvido como uma heurística para minimizar funções não diferenciáveis e foi aplicado a estruturas planas de treliças com diferentes níveis de danos. Structural systems in a variety of applications including aerospace vehicles, automobiles and civil engineering structures such as tall buildings, bridges and offshore platforms, accumulate damage during their service life. In several situations, such damage may not be visually observable. From the standpoint of both safety and performance, it is desirable to monitor the occurrence, location and extent of such damage.System identification methods, which may be classified in a general category of nondestructive evaluation techniques, can be employed for this purpose. Using experimental data, such as eigenmodes, eigenvectors and static displacements, and an analytical structural model, parameters of the structures can be identified. The approach used in the present work is one where the structural properties of the analytical model are varied to minimize the difference between the analytically predicted and empirically measured response. This is an inverse problem where the structural parameters are identified. In this work a reduced number of vibration modes were used as the measured response. For the damage assessment problem a close analytical model of the structural system is available and the model of the damaged structure will be identified. Damage will be represented by a reduction in the elastic stiffness properties of the structure.The problem described above was solved using global methods of optimization due to the fact that depending on the number of variables or the location of damage the resulting design space is nonconvex presenting several local minima. In the present work, the Differential Evolution Optimization Technique (DE) was used. It is a metaheuristic inspired by a population of solutions that is successively updated by arithmetic operations such as mutation and recombination, until convergence. The approach was applied to simple truss structures with different levels of damage.

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Soubies, Emmanuel. "Sur quelques problèmes de reconstruction en imagerie MA-TIRF et en optimisation parcimonieuse par relaxation continue exacte de critères pénalisés en norme-l0." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4082/document.

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Cette thèse s'intéresse à deux problèmes rencontrés en traitement du signal et des images. Le premierconcerne la reconstruction 3D de structures biologiques à partir d'acquisitions multi-angles enmicroscopie par réflexion totale interne (MA-TIRF). Dans ce contexte, nous proposons de résoudre leproblème inverse avec une approche variationnelle et étudions l'effet de la régularisation. Une batteried'expériences, simples à mettre en oeuvre, sont ensuite proposées pour étalonner le système et valider lemodèle utilisé. La méthode proposée s'est montrée être en mesure de reconstruire avec précision unéchantillon phantom de géométrie connue sur une épaisseur de 400 nm, de co-localiser deux moléculesfluorescentes marquant les mêmes structures biologiques et d'observer des phénomènes biologiquesconnus, le tout avec une résolution axiale de l'ordre de 20 nm. La deuxième partie de cette thèseconsidère plus précisément la régularisation l0 et la minimisation du critère moindres carrés pénalisé (l2-l0) dans le contexte des relaxations continues exactes de cette fonctionnelle. Nous proposons dans unpremier temps la pénalité CEL0 (Continuous Exact l0) résultant en une relaxation de la fonctionnelle l2-l0 préservant ses minimiseurs globaux et pour laquelle de tout minimiseur local on peut définir unminimiseur local de l2-l0 par un simple seuillage. Par ailleurs, nous montrons que cette relaxation éliminedes minimiseurs locaux de la fonctionnelle initiale. La minimisation de cette fonctionnelle avec desalgorithmes d'optimisation non-convexe est ensuite utilisée pour différentes applications montrantl'intérêt de la minimisation de la relaxation par rapport à une minimisation directe du critère l2-l0. Enfin,une vue unifiée des pénalités continues de la littérature est proposée dans ce contexte de reformulationexacte du problème This thesis is devoted to two problems encountered in signal and image processing. The first oneconcerns the 3D reconstruction of biological structures from multi-angle total interval reflectionfluorescence microscopy (MA-TIRF). Within this context, we propose to tackle the inverse problem byusing a variational approach and we analyze the effect of the regularization. A set of simple experimentsis then proposed to both calibrate the system and validate the used model. The proposed method hasbeen shown to be able to reconstruct precisely a phantom sample of known geometry on a 400 nmdepth layer, to co-localize two fluorescent molecules used to mark the same biological structures andalso to observe known biological phenomena, everything with an axial resolution of 20 nm. The secondpart of this thesis considers more precisely the l0 regularization and the minimization of the penalizedleast squares criteria (l2-l0) within the context of exact continuous relaxations of this functional. Firstly,we propose the Continuous Exact l0 (CEL0) penalty leading to a relaxation of the l2-l0 functional whichpreserves its global minimizers and for which from each local minimizer we can define a local minimizerof l2-l0 by a simple thresholding. Moreover, we show that this relaxed functional eliminates some localminimizers of the initial functional. The minimization of this functional with nonsmooth nonconvexalgorithms is then used on various applications showing the interest of minimizing the relaxation incontrast to a direct minimization of the l2-l0 criteria. Finally we propose a unified view of continuouspenalties of the literature within this exact problem reformulation framework

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Diouane, Youssef. "Globally convergent evolution strategies with application to Earth imaging problem in geophysics." Phd thesis, Toulouse, INPT, 2014. http://oatao.univ-toulouse.fr/12202/1/Diouane.pdf.

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In recent years, there has been significant and growing interest in Derivative-Free Optimization (DFO). This field can be divided into two categories: deterministic and stochastic. Despite addressing the same problem domain, only few interactions between the two DFO categories were established in the existing literature. In this thesis, we attempt to bridge this gap by showing how ideas from deterministic DFO can improve the efficiency and the rigorousness of one of the most successful class of stochastic algorithms, known as Evolution Strategies (ES’s). We propose to equip a class of ES’s with known techniques from deterministic DFO. The modified ES’s achieve rigorously a form of global convergence under reasonable assumptions. By global convergence, we mean convergence to first-order stationary points independently of the starting point. The modified ES’s are extended to handle general constrained optimization problems. Furthermore, we show how to significantly improve the numerical performance of ES’s by incorporating a search step at the beginning of each iteration. In this step, we build a quadratic model using the points where the objective function has been previously evaluated. Motivated by the recent growth of high performance computing resources and the parallel nature of ES’s, an application of our modified ES’s to Earth imaging Geophysics problem is proposed. The obtained results provide a great improvement for the problem resolution.

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Marzat, Julien. "Diagnostic des systèmes aéronautiques et réglage automatique pour la comparaison de méthodes." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00647333.

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Les travaux présentés dans ce mémoire contribuent à la définition de méthodes pour la détection et le diagnostic de défauts affectant les systèmes aéronautiques. Un système représentatif sert de support d'étude, constitué du modèle non linéaire à six degrés de liberté d'un missile intercepteur, de ses capteurs et actionneurs ainsi que d'une boucle de guidage-pilotage. La première partie est consacrée au développement de deux méthodes de diagnostic exploitant l'information de commande en boucle fermée et les caractéristiques des modèles aéronautiques. La première méthode utilise les objectifs de commande induits par les lois de guidage-pilotage pour générer des résidus indiquant la présence de défauts. Ceci permet la détection des défauts sur les actionneurs et les capteurs, ainsi que leur localisation pour ces derniers. La deuxième méthode exploite la mesure de dérivées des variables d'état (via une centrale inertielle) pour estimer la valeur de la commande réalisée par les actionneurs, sans intégration du modèle non linéaire du système. Le diagnostic est alors effectué en comparant cette estimée avec la valeur désirée, ce qui permet la détection, la localisation et l'identification de défauts multiples sur les actionneurs.La seconde partie propose une méthodologie de réglage automatique des paramètres internes (les hyperparamètres) de méthodes de diagnostic. Ceci permet une comparaison plus objective entre les méthodes en évaluant la meilleure performance de chacune. Le réglage est vu comme un problème d'optimisation globale, la fonction à optimiser étant calculée via la simulation numérique (potentiellement coûteuse) de cas test. La méthodologie proposée est fondée sur un métamodèle de krigeage et une procédure itérative d'optimisation bayésienne, qui permettent d'aborder ce problème à faible coût de calcul. Un nouvel algorithme est proposé afin d'optimiser les hyperparamètres d'une façon robuste vis à vis de la variabilité des cas test pertinents.Mots clés : détection et diagnostic de défauts, guidage-pilotage, krigeage, minimax continu, optimisation globale, redondance analytique, réglage automatique, systèmes aéronautiques.

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Li, Bo. "Supply Chain Inventory Management with Multiple Types of Customers: Motivated by Chinese Pharmaceutical Supply Chains among Others." University of Toledo / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1371136834.

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"High performance continuous/discrete global optimization methods." 2003. http://library.cuhk.edu.hk/record=b6073516.

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Ng, Chi Kong. "May 2003." Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. Includes bibliographical references (p. 175-187). Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. Mode of access: World Wide Web. Abstracts in English and Chinese.

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Juarez, Josue Rodolfo Cuevas, and 古定華. "Virus Optimization Algorithm (VOA): A Novel Metaheuristic for Continuous Optimization Problems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/70226177789162861524.

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碩士 元智大學 工業工程與管理學系 98 The virus, an infectious agent that can reproduce only inside a host cell can apparently spread without any control, but as we already know that the cells without any protection will tend to give better chances to the virus in the reproduction activity. In this thesis, we developed a novel metaheuristic, named Virus Optimization Algorithm (VOA) which imitates the behavior of the virus, this metaheuristic could be considered as a type of evolutionary algorithms (EA) since mechanisms that simulate reproduction and population maintenance are performed. The host cell represents the entire search space while the virus reproduction denotes the generation of new solutions. VOA is a population-based method that usually begins the search with a small set of solutions and the number of those solutions will grow at each iteration and a mechanism called antivirus will be in charge of maintain the population of viruses, the whole process will be repeated until the stopping criterion is reached. We compared this new metaheuristic with three widely known algorithms in the EA area such as Genetic Algorithm (GA), Harmony Search (HS), and Particle Swarm Optimization (PSO), where the problem solved was the continuous curve fitting by using generalized mixture gaussian models for nine stock index markets. As a conclusion from the tests performed the proposed VOA showed to be a competitive and robust tool for solving continuous optimization problems.

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Chou, Szu-Ting, and 周思婷. "Water Flow-like Optimization Algorithm for Multi-objective Continuous Optimization Problems." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/78366530328383888512.

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碩士 國立臺灣大學 工業工程學研究所 100 The newly developed optimization algorithm, Water Flow-like Algorithm, that is WFA, simulates a solution searching agent as a water flow traversing the lowest point of a terrain. The number of water flows is dynamically changed while water flows split into subflows against rough terrain and merge several flows into one single flow. Flow splitting and merging are mimicked by the WAF to conduct efficient optimum search in the solution space. In addition, water evaporation and precipitation are simulated in WFA to jump out of local optima or to broaden the searching area. This paper presents a WFA for Multi-objective Continuous Optimization Problems, namely WFA4MC. This paper presents three merging methods for different merging conditions. First, the location-based merging approach is frequently adopted in general optimization problems, either continuous or discrete ones. In addition to the location-based approach, we propose an objective-based merging approach for our multi-objective optimization problems, where a set of non-dominated solutions with objective values dispersedly distributed in the objective space is preferred. In order to prove WFA4MC performances precisely, this research proposes Correctness and Coverness to measure non-dominated solutions in ZDT functions. Besides, the Generational Distance is used in the comparison with other heuristic Algorithms. The result showed that based on the same limit of the number of objective function calls, the WFA4MC outperform than others.

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Wang, Chia-Chi, and 王佳琪. "Application of Soft Particle Swarm Optimization to Global Optimization Problems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/18592739685564108199.

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碩士 國立臺灣海洋大學 系統工程暨造船學系 96 Abstract Particle swarm optimization (PSO) is population-based and developed by imitating the swarm behavior of the natural world's creature for the global optimization problems. At first, the information about the effect of the parameters in PSO, such as inertia weight and learning constants is collected to investigate through two specific functions. The results show that the mathematical formula of inertia weight and learning constants about particle swarm’s convergence condition derived by the equation of dynamics can’t induce the high accuracy of searching performance. Furthermore, in the thesis, a switch type for inertia weight has been proposed and examined. The results show that the effect of searching performance for PSO is better than those of types of linearly decreasing and constant. Finally, in the thesis, a soft, neighborhood area concept has been proposed to modify the cognition-only model and social-only model and to enhance the particle’s searching ability. This algorithm is also called Soft Particle Swarm Optimization, S.PSO. Through a series of several benchmark function optimizations, the results indicate that the neighborhood area concept produce a powerful local searching ability when the extreme point of the testing function is located at origin of coordinate, but the diversing ability of particle swarm wild be weaken very much. Keyword：Particle Swarm Optimization, Soft Particle Swarm Optimization, Global optimization.

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Dissertations / Theses on the topic 'Continuous global optimization problems'

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