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Darbe apžvelgiama trimačio pakavimo problemos tipologija. Nagrinėjama trimečio konteinerių pakavimo problema ir jos sprendimo būdai. Pateikiama šakos ir ribos, bei tabu paieškos algoritmų formulavimas ir jų rezultatų analizė. / The paper gives an overview of three-dimensional packing problem typology. There are investigating issue of container packing problem and its solutions. Branch and bound, TSpack algorithms formulation and analysis of their results.

In this paper, we minimize the holding cost of the safety stock in the supply chain subject to linear constraints on the service times between the nodes of the network. In the problem, the objective function is concave as we assume the demand to be bounded by a concave function. The optimal solutions of the problem belong to the set of extreme points of the polyhedron, specified by the constraints of the problem. We first characterize the extreme points for the two-layer networks and then provide bounds to use in a branch and bound algorithm. / Singapore-MIT Alliance (SMA)

Monotonic optimization consists of minimizing or maximizing a monotonic objective function over a set of constraints defined by monotonic functions. Many optimization problems in economics and engineering often have monotonicity while lacking other useful properties, such as convexity. This thesis is concerned with the development and application of global optimization algorithms for monotonic optimization problems. First, we propose enhancements to an existing outer-approximation algorithm | called the Polyblock Algorithm | for monotonic optimization problems. The enhancements are shown to significantly improve the computational performance of the algorithm while retaining the convergence properties. Next, we develop a generic branch-and-bound algorithm for monotonic optimization problems. A computational study is carried out for comparing the performance of the Polyblock Algorithm and variants of the proposed branch-and-bound scheme on a family of separable polynomial programming problems. Finally, we study an important class of monotonic optimization problems | probabilistically constrained linear programs. We develop a branch-and-bound algorithm that searches for a global solution to the problem. The basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partitions and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires the solution of only linear programming subproblems. We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions are presented.

In this thesis, we consider the Multi Resource Agent Bottleneck Generalized Assignment Problem. We aim to minimize the maximum load over all agents. We study the Linear Programming (LP) relaxation of the problem. We use the optimal LP relaxation solutions in our Branch and Bound algorithm while defining lower and upper bounds and branching schemes. We find that our Branch and Bound algorithm returns optimal solutions to the problems with up to 60 jobs when the number of agents is 5, and up to 30 jobs when the number of agents is 10, in less than 20 minutes. To find approximate solutions, we define a tabu search algorithm and an &amp / #945 / approximation algorithm. Our computational results have revealed that these procedures can find high quality solutions to large sized instances very quickly.

Dans cette thèse, nous étudions trois problèmes d'ordonnancement de la chaîne logistique dans le modèle de production à la demande. Le premier problème est un problème d'ordonnancement de production et de distribution intermédiaire dans une chaîne logistique avec un producteur et un prestataire logistique. Le deuxième problème est un problème d'ordonnancement de production et de distribution aval avec des dates de début au plus tôt et des dates limites de livraison dans une chaîne logistique avec un producteur, un prestataire logistique et un client. Le troisième problème est un problème d'ordonnancement de production et de distribution aval avec des temps de réglage et des fenêtres de temps de livraison dans une chaîne logistique avec un producteur, un prestataire logistique et plusieurs clients. Pour les trois problèmes, nous étudions les problèmes d'ordonnancement individuels et les problèmes d'ordonnancement coordonnés. Nous proposons des algorithmes polynomiaux ou prouvons la NP-Complétude de ces problèmes, et développons des algorithmes exacts ou heuristiques pour résoudre les problèmes NP-Difficiles. Nous proposons des mécanismes de coordination et évaluons le bénéfice de la coordination. / In this dissertation, we aim at investigating three supply chain scheduling problems in the make-To-Order business model. The first problem is a production and interstage distribution scheduling problem in a supply chain with a manufacturer and a third-Party logistics (3PL) provider. The second problem is a production and outbound distribution scheduling problem with release dates and deadlines in a supply chain with a manufacturer, a 3PL provider and a customer. The third problem is a production and outbound distribution scheduling problem with setup times and delivery time windows in a supply chain with a manufacturer, a 3PL provider and several customers. For the three problems, we study their individual scheduling problems and coordinated scheduling problems: we propose polynomial-Time algorithms or prove the intractability of these problems, and develop exact algorithms or heuristics to solve the NP-Hard problems. We establish mechanisms of coordination and evaluate the benefits of coordination.

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.

Submitted by Miriam Lucas (miriam.lucas@unioeste.br) on 2018-02-22T16:42:27Z No. of bitstreams: 2 Miguel_Angel_Sanchez_Cuno_2016.pdf: 1159111 bytes, checksum: 5e8f5e6fcd310a19270e2164cb09c3e3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-02-22T16:42:27Z (GMT). No. of bitstreams: 2 Miguel_Angel_Sanchez_Cuno_2016.pdf: 1159111 bytes, checksum: 5e8f5e6fcd310a19270e2164cb09c3e3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-16 / Fundação Parque Tecnológico de Itaipu / This work presents the development of a Hybrid Algorithm to solve the problem of Planning the Expansion of Medium Voltage Overhead Networks. The Hybrid Algorithm uses two strategies to solve the problem. First uses a Constructive Heuristic Algorithm that tries to work with parameters instead of working with variables, with the objective of reducing the convergence time to the research process trying not to impair the quality of the solution. The second strategy is based in a Branch and Bound Algorithm, that uses the solution of the problem obtained as a starting point while the first strategy is running. Thus, this solution is used like incumbent in the second process. In this context the hybrid algorithm developed and implemented in this work, takes advantage of reducing the convergence time of the Constructive Heuristic Algorithm and the advantage of guarantee that the solution has the best quality, which are the solutions produced by algorithms type Branch and Bound. The Algorithm has been tested in three test systems, being established a plan to expand overhead medium voltage networks for each system. / Neste trabalho é apresentado um Algoritmo Híbrido para resolver o problema de Planejamento da Expansão de Redes Aéreas de Média Tensão. O Algoritmo Híbrido utiliza duas estratégias para resolver o problema. A primeira utiliza um Algoritmo Heurístico Construtivo que procura trabalhar com parâmetros ao invés de trabalhar com variáveis, com o objetivo de reduzir o tempo de convergência do processo de busca procurando não prejudicar a qualidade da solução. A segunda estratégia é baseada em um Algoritmo do tipo Branch and Bound, que utiliza a solução do problema obtida durante a execução da primeira estratégia como um ponto de partida. Assim, esta solução é usada como incumbente neste segundo processo. Neste contexto, o Algoritmo Híbrido desenvolvido e implementado neste trabalho, aproveita a vantagem de reduzir o tempo de convergência do Algoritmo Heurístico Construtivo e a vantagem de garantir que a solução seja a de melhor qualidade, que são as soluções produzidas por algoritmos do tipo Branch and Bound. O Algoritmo foi testado em três sistemas testes, sendo estabelecido um plano para a expansão de redes aéreas de média tensão para cada sistema

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Dans ces travaux, nous présentons des méthodes d'optimisation théoriques et numériques pour la conception optimale de circuits magnétiques pour propulseurs à effet Hall. Ces problèmes de conception sont des problèmes inverses très difficiles à résoudre que nous formulons sous forme de problèmes d'optimisation topologique. Les problèmes resultant sont non convexes avec des contraintes aux équations différentielles de Maxwell. Au cours de ces travaux, des approches originales ont été proposées afin de résoudre efficacement ces problèmes d'optimisation topologique. L'approche de densité de matériaux SIMP (Solid Isotropic Material with Penalization) qui est une variante de la méthode d'homogénéisation a été privilégiées. De plus, les travaux de ma thèse ont permis la mise en place de codes d'optimisation dénommé ATOP (Algorithm To Optimize Propulsion) utilisant en parallèle les logiciels de calculs scientifiques Matlab et d'élément finis FEMM (Finite Element Method Magnetics). Dans ATOP, nous utilisant à la fois des algorithmes d'optimisation locale de type descente basés sur une analyse de la sensibilité du problème et des algorithmes d'optimisation globale principalement de type Branch and Bound basés sur l'Arithmétique des Intervals. ATOP permettra d'optimiser à la fois la forme topologique des circuits magnétiques mais aussi le temps et le coût de production de nouvelles génération de propulseurs électriques. / In this work, we present theoretical and numerical optimization method for designing magnetic circuits for Hall effect thrusters. These design problems are very difficult inverse ones that we formulate under the form of topology optimization problems. Then, the obtained problems are non convex subject to Maxwell equations like constraints. Some original approaches have been proposed to solve efficiently these topology optimization problems. These approaches are based on the material density model called SIMP approach (Solid Isotropic Material with Penalization) which is a variante of the homogenization method. The results in my thesis allowed to provide optimization source code named ATOP (Algorithm To Optimize Propulsion) unsung in parallel two scientific computing softwares namely Matlab and FEMM (Finite Element Method Magnetics). In ATOP, we use both local optimization algorithms based on sensitivity analysis of the design problem; and global optimization algorithms mainly of type Branch and Bound based on Interval Arithmetic analysis. ATOP will help to optimize both the topological shape of the magnetic circuits and the time and cost of production (design process) of new generations of electrical thrusters.