Thesis (M.S.)--University of Nevada, Reno, 2008. / "May, 2008." Includes bibliographical references (leaves 63-64). Online version available on the World Wide Web.

Typically, design is approached as a sequence of decisions in which designers select what they believe to be the best alternative in each decision. While this approach can be used to arrive at a final solution quickly, it is unlikely to result in the most-preferred solution. The reason for this is that all the decisions in the design process are coupled. To determine the most preferred alternative in the current decision, the designer would need to know the outcomes of all future decisions, information that is currently unavailable or indeterminate. Since the designer cannot select a single alternative because of this indeterminate (interval-based) uncertainty, a set-based design approach is introduced. The approach is motivated by the engineering practices at Toyota and is based on the structure of the Branch and Bound Algorithm. Instead of selecting a single design alternative that is perceived as being the most preferred at the time of the decision, the proposed set-based design approach eliminates dominated design alternatives: rather than selecting the best, eliminate the worst. Starting from a large initial design space, the approach sequentially reduces the set of non-dominated design alternatives until no further reduction is possible ??e remaining set cannot be rationally differentiated based on the available information. A single alternative is then selected from the remaining set of non-dominated designs. In this thesis, the focus is on the elimination step of the set-based design method: A criterion for rational elimination under interval-based uncertainty is derived. To be efficient, the criterion takes into account shared uncertainty ??certainty shared between design alternatives. In taking this uncertainty into account, one is able to eliminate significantly more design alternatives, improving the efficiency of the set-based design approach. Additionally, the criterion uses a detailed reference design to allow more elimination of inferior design sets without evaluating each alternative in that set. The effectiveness of this elimination is demonstrated in two examples: a beam design and a gearbox design.

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. Dimitri N. Mavris; Committee Member: Dr. Brian J. German; Committee Member: Dr. Daniel P. Schrage; Committee Member: Dr. Frederic Villeneuve; Committee Member: Dr. Michelle R. Kirby; Committee Member: Ms. Antje Lembcke. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 121-128).

Thesis (M.S.) -- Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.

Orientador: Francisco de Assis Magalhães Gomes Neto / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T16:09:04Z (GMT). No. of bitstreams: 1 Villela_PedroFerraz_M.pdf: 727069 bytes, checksum: d87d64ae49bfc1a53017a463cf10b453 (MD5) Previous issue date: 2008 / Resumo: Neste trabalho, propomos um método exato para a resolução de problemas de programação quadrática que envolvem restrições de cardinalidade. Como aplicação, empregamos o método para a obtenção da fronteira eficiente de um problema (bi-objetivo) de otimização de carteiras de investimento. Nosso algoritmo é baseado no método Branch-and-Bound. A chave de seu sucesso, entretanto, reside no uso do método de Lemke, que é aplicado para a resolução dos subproblemas associados aos nós da árvore gerada pelo Branch-and-Bound. Ao longo do texto, algumas heurísticas também são introduzidas, com o propósito de acelerar a convergência do método. Os resultados computacionais obtidos comprovam que o algoritmo proposto é eficiente. / Abstract: In this work, we propose an exact method for the resolution of quadratic programming problems involving cardinality restrictions. As an application, the algorithm is used to generate the effective Pareto frontier of a (bi-objective) portfolio optimization problem. This algorithm is based on the Branch-and-Bound method. The key to its success, however, resides in the application of Lemke's method to the resolution of the subproblems associated to the nodes of the tree generated by the Branch-and-Bound algorithm. Throughout the text, some heuristics are also introduced as a way to accelerate the performance of the method. The computational results acquired show that the proposed algorithm is efficient. / Mestrado / Otimização / Mestre em Matemática Aplicada

Several techniques were studied to select and prioritize technologies for a complex system. Based on the findings, a method called Pareto Optimization and Selection of Technologies (POST) was formulated to efficiently explore the combinatorial technology space. A knapsack problem was selected as a benchmark problem to test-run various algorithms and techniques of POST. A Monte Carlo simulation using the surrogate models was used for uncertainty quantification. The concepts of graph theory were used to model and analyze compatibility constraints among technologies. A probabilistic Pareto optimization, based on the concepts of Strength Pareto Evolutionary Algorithm II (SPEA2), was formulated for Pareto optimization in an uncertain objective space. As a result, multiple Pareto hyper-surfaces were obtained in a multi-dimensional objective space; each hyper-surface representing a specific probability level. These Pareto layers enabled the probabilistic comparison of various non-dominated technology combinations. POST was implemented on a technology exploration problem for a 300 passenger commercial aircraft. The problem had 29 identified technologies with uncertainties in their impacts on the system. The distributions for these uncertainties were defined using beta distributions. Surrogate system models in the form of Response Surface Equations (RSE) were used to map the technology impacts on the system responses. Computational complexity of technology graph was evaluated and it was decided to use evolutionary algorithm for probabilistic Pareto optimization. The dimensionality of the objective space was reduced using a dominance structure preserving approach. Probabilistic Pareto optimization was implemented with reduced number of objectives. Most of the technologies were found to be active on the Pareto layers. These layers were exported to a dynamic visualization environment enabled by a statistical analysis and visualization software called JMP. The technology combinations on these Pareto layers are explored using various visualization tools and one combination is selected. The main outcome of this research is a method based on consistent analytical foundation to create a dynamic tradeoff environment in which decision makers can interactively explore and select technology combinations.

Orientador: Cid Carvalho de Souza / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-15T07:24:38Z (GMT). No. of bitstreams: 1 Piva_Breno_M.pdf: 1251793 bytes, checksum: bf559620a7bdefeec032b5c87d196b5b (MD5) Previous issue date: 2009 / Resumo: O problema do Máximo Subgrafo Induzido Comum (MSIC) pertence a classe NP-difícil e possui aplicações em diversas áreas. Apesar de sua complexidade, ainda é importante conhecer soluções exatas para instâncias deste problema. Os algoritmos exatos encontrados na literatura buscam resolvê-lo através de técnicas de backtracking ou através de sua redução para o problema da Clique Máxima. Neste trabalho procuramos dar uma solução exata para o MSIC, tratando-o diretamente através da utilização de modelos de Programação Linear Inteira (PLI) e técnicas de combinatória poliédrica. Assim, realizamos um estudo teórico do poliedro do MSIC e fomos capazes de encontrar algumas desigualdades válidas fortes, inclusive com provas de que algumas delas representam facetas daquele poliedro. Adicionalmente, provamos que existe uma equivalâencia entre o modelo PLI aqui apresentado para o MSIC e uma formulação bem conhecida para o problema da Clique Máxima. Posteriormente, foram implementados algoritmos de Branch-and-Bound (B&B) e Branch-and-Cut (B&C) utilizando as desigualdades encontradas e algumas técnicas para tentar tornar os algoritmos mais eficientes. Experimentos foram executados com os algoritmos implementados neste trabalho e, também, com um algoritmo já existente para resolver o problema da Clique, chamado Cliquer. Os resultados foram comparados e, dentre os algoritmos de PLI, constatamos que o mais eficiente foi aquele que utilizou uma formulação para o MSIC que chamamos de Clique-IS, utilizando B&B e técnicas mais básicas que outros algoritmos. Este algoritmo mostrou-se mais eficiente, inclusive, que um algoritmo PLI com um modelo baseado no problema da Clique Máaxima. Este fato sugere que para uma abordagem baseada em PLI, vale a pena utilizar uma formulação do MSIC diretamente, ao invés de uma que se apóie na redução deste para o problema da Clique Máxima. Ja a comparaçao do melhor algoritmo desenvolvido neste trabalho com o Cliquer, mostrou que este último é mais eficiente. Para que um algoritmo baseado em PLI (utilizando uma formulação com as mesmas variáveis usadas por nós) tivesse alguma chance de vencer um algoritmo combinatório como o Cliquer, seria necessário conhecer mais desigualdades que estivessem ativas na solução ótima do problema / Abstract: The Maximum Common Subgraph problem (MSIC) is in MV-hard and has applications in several fields. Despite its complexity, it is still important to know exact solutions for instances of this problem. The exact algorithms found in literature try to solve it through backtracking techniques or through its reduction to the Maximum Clique problem. In this work we try to give an exact solution to MSIC by addressing it directly, using Linear Integer Programming (PLI) and polyhedral combinatorics techniques. So, we performed a study of the MSIC polyhedron and we were able to find some strong valid inequalities, including some that were proven to define facets of that polyhedron. Additionally, we proved that an equivalence between the PLI model presented here for MSIC and a well known formulation for the Maximum Clique problem exists. Later, Branch-and-Bound (B&B) and Branch-and-Cut (B&C) algorithms were implemented using the inequalities found and some techniques to try to render the algorithms more efficient. Experiments were performed with the algorithms implemented in this work and, also, with an already existing algorithm to solve the Maximum Clique problem, called Cliquer. The results were compared and, among the PLI algorithms, we found that the most efficient was the one that used the formulation which we called Clique-IS, using B&B and more basic techniques than other algorithms. This algorithm was even more efficient than a PLI algorithm with a Clique-based model. This fact suggests that for a PLI approach it is worth to use a formulation based on the MSIC polyhedron instead of one based on its reduction to the Maximum Clique problem. The comparison of the best algorithm developed in this work with Cliquer, though, showed that the latest is more efficient. In order to some PLI-based algorithm (using a formulation with the same variables used by us) to have any chance of outperforming a combinatorial algorithm like Cliquer, it would be necessary to know more inequalities that are active in the problem's optimal solution / Mestrado / Otimização Combinatoria / Mestre em Ciência da Computação

On s'attache dans cette thèse à plusieurs aspects liés à la résolution de problèmes multi-objectifs, sans se limiter au cas biobjectif. Nous considérons la résolution exacte, dans le sens de la détermination de l'ensemble des points non dominés, ainsi que la résolution approchée dans laquelle on cherche une approximation de cet ensemble dont la qualité est garantie a priori.Nous nous intéressons d'abord au problème de la détermination d'une représentation explicite de la région de recherche. La région de recherche, étant donné un ensemble de points réalisables connus, exclut la partie de l'espace des objectifs que dominent ces points et constitue donc la partie de l'espace des objectifs où les efforts futurs doivent être concentrés dans la perspective de déterminer tous les points non dominés.Puis nous considérons le recours aux algorithmes de séparation et évaluation ainsi qu'aux algorithmes de ranking afin de proposer une nouvelle méthode hybride de détermination de l'ensemble des points non dominés. Nous montrons que celle-ci peut également servir à obtenir une approximation de l'ensemble des points non dominés. Cette méthode est implantée pour le problème de l'arbre couvrant de poids minimal. Les quelques propriétés de ce problème que nous passons en revue nous permettent de spécialiser certaines procédures et d'intégrer des prétraitements spécifiques. L'intérêt de cette approche est alors soutenu à l'aide de résultats expérimentaux. / This thesis deals with several aspects related to solving multi-objective problems, without restriction to the bi-objective case. We consider exact solving, which generates the nondominated set, and approximate solving, which computes an approximation of the nondominated set with a priori guarantee on the quality.We first consider the determination of an explicit representation of the search region. The search region, defined with respect to a set of known feasible points, excludes from the objective space the part which is dominated by these points. Future efforts to find all nondominated points should therefore be concentrated on the search region.Then we review branch and bound and ranking algorithms and we propose a new hybrid approach for the determination of the nondominated set. We show how the proposed method can be adapted to generate an approximation of the nondominated set. This approach is instantiated on the minimum spanning tree problem. We review several properties of this problem which enable us to specialize some procedures of the proposed approach and integrate specific preprocessing rules. This approach is finally supported through experimental results.

Les enjeux du développement durable, le réchauffement climatique, la pollution dans les grandes villes, la congestion et les nuisances sonores, l'augmentation des prix de carburants, sont parmi des nombreux facteurs qui incitent les pays développés à l'innovation dans les transports publics. Dans ce contexte, l'introduction des systèmes de vélos en libre-service, au cours de ces dernières années, est une des solutions adoptées par de nombreuses grandes villes. Malgré leur succès fulgurant dans le monde entier, il existe peu d'études fondamentales sur ce type transport urbain. Pourtant, leur exploitation et leur management par des opérateurs soulèvent de nombreuses questions notamment d'ordre opérationnel. Dans ce contexte, cette thèse s'adresse aux problèmes d'ordonnancement et de rééquilibrage des stations de vélos en libre-service. Ce sont des problèmes cruciaux pour la qualité de service et la viabilité économique de tels systèmes. Le rééquilibrage consiste à redistribuer le nombre de vélos entre les différentes stations afin de satisfaire au mieux les demandes des usagers. Cette régulation se fait souvent par le biais de véhicules spécifiques qui font des tournées autour des différentes stations. Ainsi, deux problèmes d'optimisation difficiles se posent : la recherche de la meilleure tournée du véhicule de régulation (ordonnancement de la tournée) et la détermination des nombres de véhicules à utiliser (rééquilibrage des stations). Dans cette optique, les travaux de cette thèse constituent une contribution à la modélisation et à l'optimisation de performances des systèmes de vélos en libre-service en vue de leur rééquilibrage et leur ordonnancement. Plusieurs méthodes d'optimisation et ont été développées et testées. De telles méthodes incorporent différentes approches de simulation ou d'optimisation comme les réseaux de Petri, les algorithmes génétiques, les algorithmes gloutons, les algorithmes de recherche par voisinage, la méthode arborescente de branch-and-bound, l'élaboration des bornes supérieures et inférieures, etc. Différentes facettes du problème ont été étudiées : le cas statique, le cas dynamique, l'ordonnancement et le rééquilibrage avec un seul (ou multiple) véhicule(s). Afin de montrer la pertinence de nos approches, la thèse comporte également plusieurs applications réelles et expérimentations / In our days, developed countries have to face many public transport problems, including traffic congestion, air pollution, global oil prices and global warming. In this context, Public Bike sharing systems are one of the solutions that have been recently implemented in many big cities around the world. Despite their apparent success, the exploitation and management of such transportation systems imply crucial operational challenges that confronting the operators while few scientific works are available to support such complex dynamical systems. In this context, this thesis addresses the scheduling and balancing in public bicycle-sharing systems. These problems are the most crucial questions for their operational efficiency and economic viability. Bike sharing systems are balanced by distributing bicycles from one station to another. This procedure is generally ensured by using specific redistribution vehicles. Therefore, two hard optimization problems can be considered: finding a best tour for the redistribution vehicles (scheduling) and the determination of the numbers of bicycles to be assigned and of the vehicles to be used (balancing of the stations). In this context, this thesis constitutes a contribution to modelling and optimizing the bicycle sharing systems' performances in order to ensure a coherent scheduling and balancing strategies. Several optimization methods have been proposed and tested. Such methods incorporate different approaches of simulation or optimization like the Petri nets, the genetic algorithms, the greedy search algorithms, the local search algorithms, the arborescent branch-and-bound algorithms, the elaboration of upper and lower bounds, ... Different variants of the problem have been studied: the static mode, the dynamic mode, the scheduling and the balancing by using a single or multiple vehicle(s). In order to demonstrate the coherence and the suitability of our approaches, the thesis contains several real applications and experimentations