Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2001-02-17Bitstream added on 2014-06-13T19:07:26Z : No. of bitstreams: 1 fiorotto_dj_me_sjrp.pdf: 485977 bytes, checksum: 8cd2b3ba49a25a9c6a863795f27811c3 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O problema de dimensionamento de lotes é um problema de otimização da produção, em que o objetivo é planejar a quantidade de itens a ser produzida em várias, ou única, máquinas em cada período ao longo do horizonte de tempo, de modo a tender uma demanda e otimizar uma função objetivo. Este trabalho aborda o problema de dimensionamento de lotes em um único estágio em um ambiente com máquinas paralelas distintas. Cada item pode ser produzido em qualquer máquina, acarretando um tempo de preparação que é gasto antes de começar a produção. O objetivo do trabalho consiste em obter limitantes inferiores de boa qualidade para este problema. Para tanto, é desenvolvido um método de solução baseado numa reformulação do problema a e na relaxação lagrangiana de um conjunto de restrições. Alguns resultados computacionais são apresentados algumas propostas futuras para a continuidade do trabalho. / The lot-sizing problem is a production optimization problem, where the objective is to plan the quantity of items to be produced in multiple, or single, machines in each period over a time horizon, in order to satisfy a demand and optimize an objective function. This work addresses the single stage parallel machine lot-sizing problem. Each item can be produced on any machine, and incur a setup time before to start the production. The objective of this work is to lower bounds of good quality for this problem. A solution method is developed based on a reformulation of the problem and the Lagrangian relaxation of a set of constrainsts. Some computational results are presented comparing the proposed method with a method from the literature, and, some future researches are proposed.

The main goal of this thesis is to investigate the complexity of a variety of problems related to text indexing and text searching. We present new data structures that can be used as building blocks for full-text indices which occupies minute space (FM-indexes) and wavelet trees. These data structures also can be used to represent labeled trees and posting lists. Labeled trees are applied in XML documents, and posting lists in search engines. The main emphasis of this thesis is on lower bounds for time-space tradeoffs for the following problems: the rank/select problem, the problem of representing a string of balanced parentheses, the text retrieval problem, the problem of computing a permutation and its inverse, and the problem of representing a binary relation. These results are divided in two groups: lower bounds in the cell probe model and lower bounds in the indexing model. The cell probe model is the most natural and widely accepted framework for studying data structures. In this model, we are concerned with the total space used by a data structure and the total number of accesses (probes) it performs to memory, while computation is free of charge. The indexing model imposes an additional restriction on the storage: the object in question must be stored in its raw form together with a small index that facilitates an efficient implementation of a given set of queries, e.g. finding rank, select, matching parenthesis, or an occurrence of a given pattern in a given text (for the text retrieval problem). We propose a new technique for proving lower bounds in the indexing model and use it to obtain lower bounds for the rank/select problem and the balanced parentheses problem. We also improve the existing techniques of Demaine and Lopez-Ortiz using compression and present stronger lower bounds for the text retrieval problem in the indexing model. The most important result of this thesis is a new technique for cell probe lower bounds. We demonstrate its strength by proving new lower bounds for the problem of representing permutations, the text retrieval problem, and the problem of representing binary relations. (Previously, there were no non-trivial results known for these problems.) In addition, we note that the lower bounds for the permutations problem and the binary relations problem are tight for a wide range of parameters, e.g. the running time of queries, the size and density of the relation.

The main goal of this thesis is to investigate the complexity of a variety of problems related to text indexing and text searching. We present new data structures that can be used as building blocks for full-text indices which occupies minute space (FM-indexes) and wavelet trees. These data structures also can be used to represent labeled trees and posting lists. Labeled trees are applied in XML documents, and posting lists in search engines. The main emphasis of this thesis is on lower bounds for time-space tradeoffs for the following problems: the rank/select problem, the problem of representing a string of balanced parentheses, the text retrieval problem, the problem of computing a permutation and its inverse, and the problem of representing a binary relation. These results are divided in two groups: lower bounds in the cell probe model and lower bounds in the indexing model. The cell probe model is the most natural and widely accepted framework for studying data structures. In this model, we are concerned with the total space used by a data structure and the total number of accesses (probes) it performs to memory, while computation is free of charge. The indexing model imposes an additional restriction on the storage: the object in question must be stored in its raw form together with a small index that facilitates an efficient implementation of a given set of queries, e.g. finding rank, select, matching parenthesis, or an occurrence of a given pattern in a given text (for the text retrieval problem). We propose a new technique for proving lower bounds in the indexing model and use it to obtain lower bounds for the rank/select problem and the balanced parentheses problem. We also improve the existing techniques of Demaine and Lopez-Ortiz using compression and present stronger lower bounds for the text retrieval problem in the indexing model. The most important result of this thesis is a new technique for cell probe lower bounds. We demonstrate its strength by proving new lower bounds for the problem of representing permutations, the text retrieval problem, and the problem of representing binary relations. (Previously, there were no non-trivial results known for these problems.) In addition, we note that the lower bounds for the permutations problem and the binary relations problem are tight for a wide range of parameters, e.g. the running time of queries, the size and density of the relation.

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De nos jours, le problème de transport de marchandise occupe une place importante dans la vie économique des sociétés modernes. Le problème de ramassage et de livraison (pick-up and delivery problem) est l’un des problèmes dont une grande partie des chercheurs s’y est intéressée.Il s’agit de déterminer un circuit de plusieurs véhicules, de façon à servir à coût minimal un ensemble de clients et de fournisseurs répartis dans un réseau, satisfaisant certaines contraintes relatives aux véhicules, à leurs capacités et à des précédences entre les nœuds. Les travaux de recherche développés dans cette thèse portent sur le PDPTW (Pickup and Delivery Problem with Time Windows) à plusieurs véhicules (m-PDPTW). Ce dernier a été traité dans les deux cas : statique et dynamique. Nous avons proposé plusieurs approches de résolution du m-PDPTW basées sur les algorithmes génétiques, l’optimisation multicritère et le calcul des bornes inférieures, et ceci pour minimiser un certain nombre de critères comme : le nombre de véhicules utilisés, la somme des retards ou le coût total de transport. Ces approches ont donné de bons résultats, principalement au niveau de la minimisation de la somme des retards où nous avons obtenu, dans plusieurs cas, un retard nul avec un coût de transport tolérable / Nowadays, the transport goods problem occupies an important place in the economic life of modern societies. The PDPTW (Pickup and delivery problem with Time Windows) is one which a large part of researchers was interested. This is an optimization vehicles routing problem which must meet requests for transport between suppliers and customers satisfying precedence and capacity.Researchers developed in this thesis concerns the resolution of the PDPTW with multiple vehicles (m-PDPTW). The latter was treated in two cases: static and dynamic.We have proposed some approaches to solving the m- PDPTW, based on genetic algorithms, multicriteria optimization and the lower bounds, and this to minimize a number of criteria such as: the vehicles number, the total travel cost, and the total tardiness time.Computational results indicate that the proposed approach gives good results with a total tardiness equal to zero with a tolerable cost

Orientador: Silvio Alexandrede Araujo / Banca: Bernardo Sobrinho Simões de Almada Lobo / Banca: Franklina Maria Bragion Toledo / Resumo: O problema de dimensionamento de lotes é um problema de otimização da produção, em que o objetivo é planejar a quantidade de itens a ser produzida em várias, ou única, máquinas em cada período ao longo do horizonte de tempo, de modo a tender uma demanda e otimizar uma função objetivo. Este trabalho aborda o problema de dimensionamento de lotes em um único estágio em um ambiente com máquinas paralelas distintas. Cada item pode ser produzido em qualquer máquina, acarretando um tempo de preparação que é gasto antes de começar a produção. O objetivo do trabalho consiste em obter limitantes inferiores de boa qualidade para este problema. Para tanto, é desenvolvido um método de solução baseado numa reformulação do problema a e na relaxação lagrangiana de um conjunto de restrições. Alguns resultados computacionais são apresentados algumas propostas futuras para a continuidade do trabalho. / Abstract: The lot-sizing problem is a production optimization problem, where the objective is to plan the quantity of items to be produced in multiple, or single, machines in each period over a time horizon, in order to satisfy a demand and optimize an objective function. This work addresses the single stage parallel machine lot-sizing problem. Each item can be produced on any machine, and incur a setup time before to start the production. The objective of this work is to lower bounds of good quality for this problem. A solution method is developed based on a reformulation of the problem and the Lagrangian relaxation of a set of constrainsts. Some computational results are presented comparing the proposed method with a method from the literature, and, some future researches are proposed. / Mestre

Title: Complexity Theory in Feasible Mathematics Author: Ján Pich Department: Department of Algebra Supervisor: Prof. RNDr. Jan Krajíček, DrSc., MAE Abstract: We study the provability of statements and conjectures from Complex- ity Theory in Bounded Arithmetic. First, modulo a hardness assumption, we show that theories weaker in terms of provably total functions than Buss's theory S1 2 cannot prove nk -size circuit lower bounds for SAT formalized as a Σb 2-formula LB(SAT, nk ). In particular, the true universal first-order theory in the language containing names for all uniform NC1 algorithms denoted TNC1 does not prove LB(SAT, n4kc ) where k ≥ 1, c ≥ 2 unless each function f ∈ SIZE(nk ) can be approximated by formulas Fn of subexponential size 2O(n1/c) with subexponential advantage: Px∈{0,1}n [Fn(x) = f(x)] ≥ 1/2 + 1/2O(n1/c) . Unconditionally, V 0 does not prove quasipolynomial nlog n -size circuit lower bounds for SAT. Considering upper bounds, we prove the PCP theorem in Cook's theory PV1. This includes a formalization of the (n, d, λ)-graphs in PV1. A consequence of the result is that Extended Frege proof system admits p-size proofs of tautologies encoding the PCP theorem. Keywords: Circuit Lower Bounds, Bounded Arithmetic, The PCP theorem

Les travaux de cette thèse réalisée sous contrat CIFRE portent sur des problématiques d’ordonnancement de projets mufti-compétences. Définis en collaboration avec des experts de gestion de projet au sein de la société Néréide, deux modèles d’ordonnancement de projet font l’objet de cette étude. Dans le premier modèle, une tâche est définie par l’ensemble des compétences dont elle a besoin, la charge nécessaire de chaque compétence ainsi que la possibilité d’être interrompue ou non. Pour l’élaboration d’un planning prédictif respectant toutes les contraintes et minimisant la date de fin du projet, nous proposons des heuristiques de liste et métaheuristiques. Un modèle mathématique linéaire en nombres entiers ainsi que des bornes inférieures sont également développés. Dans un second temps, nous proposons, à partir d’un planning prédéfini, des méthodes pour ajuster le planning et répondre aux aléas survenus lors du déroulement du projet. Pour résoudre ce problème réactif, nous proposons une approche exacte itérative basée sur une formulation linéaire en nombres entiers ainsi qu’un algorithme génétique de type NSGA-II. Il s’agit donc d’une approche réactive bicritère où les solutions calculées doivent minimiser à la fois la date d’achèvement du projet et le nombre maximum de changements d’affectation de tâches aux employés. Dans le deuxième modèle, un cas particulier du modèle préemptif précédent est étudié. Nous nous intéressons au cas où une tâche nécessite une seule compétence avec possibilité de préemption seulement si les ressources ne sont pas disponibles (absence, congés, etc.). Dans ce modèle, une tâche est définie également par sa date de disponibilité et une date de fin souhaitée. Un coût d’utilisation personne/compétence est introduit. Pour ce dernier modèle, il s’agit d’un problème d’ordonnancement de projet bicritère, pour lequel les solutions calculées doivent minimiser le retard maximum et le coût global d’affectation des personnes aux tâches. Des heuristiques et métaheuristiques sont proposées pour ce modèle. Certaines méthodes de résolution proposées ont été implémentées sous forme d’add-ons intégrables au framework OFBiz. / The work presented in this thesis deals with multi-skill project scheduling problems. We have studied two models of project scheduling which are defined in collaboration with project management experts in Néréide company. In the first model, a task is defined by a set of required skills, the load needed for each skill as welI as the possibility of preemption. To build a predictive planning which respects aIl problem constraints and minimize the project completion time (makespan), we propose heuristics and meta-heuristics methods. A mixed integer mathematical linear programming model and lower bounds are also proposed. From a predefined planning, we propose an exact method based on a mathematical program as weIl as a genetic algorithm of type NSGA-II allowing to deal with disruptions occurred during the project realization. It is, therefore, a reactive approach in which we look for feasible solutions minimizing both the project completion date and the maximum number of resources assignment changes. In the second studied model, we focus on a case where a task exactly requires one skill with preemption possibility only in case of resources unavailability. In this model, a task is also characterized by its release and due date. A cost per person/skill is given. It is, therefore, a bi-objective problem in which the computed solutions must minimize both the maximum tardiness and the project global cost. Heuristics and meta-heuristics are proposed for solving this problem. Some proposed methods are integrated in the framework OFBiz as add-ons.

Os problemas de corte e empacotamento são muito comuns nas indústrias e na logística. Dado um conjunto de N itens com diferentes pesos e um conjunto de M contentores com capacidade C, o problema de empacotamento unidimensional consiste em determinar o menor número de contentores a serem utilizados para alocar todos os itens respeitando a restrição de capacidade dos contentores. Nesse estudo pretende-se resolver o problema com instâncias benchmark da literatura, por meio de sessenta heurísticas diferentes, que são comparadas a quatro limitantes inferiores propostos na literatura com o intuito de avaliar a qualidade da solução heurística. Quatro limitantes inferiores e dez heurísticas construtivas diferentes foram programados em C++ num mesmo ambiente computacional, permitindo sua comparação tanto em termos de qualidade das soluções, quanto em termos dos tempos de processamento. Uma heurística simples de troca de itens entre contentores chamada Diferença-de-Quadrados foi proposta para melhorar as soluções iniciais do problema. A metaheurística simulated annealing foi acionada para melhorar a solução inicial quando o limitante inferior não foi atingido. Os parâmetros dos simulated annealing foram determinados com os dados das instâncias de forma diferente da utilizada na literatura. As combinações entre as dez soluções iniciais, a heurística Diferença-de-Quadrados e o simulated annealing geraram um conjunto de sessenta heurísticas diferentes. Os resultados mostraram que o algoritmo proposto é eficiente para resolver o problema com tempos de processamento adequados a tomada de decisão. / Cutting and packing problems are very common in industries and logistics. Given a set of N items with different weights and a set of M bins with full capacity C, the one-dimensional bin packing problem consists of determining the smallest number of bins capable to allocate all items respecting the capacity constraint of the bins. that impose that the sum of the weights of the items allocated to the bin is less than or equal to their capacity. In this study we intend to solve the problem with benchmark instances of the literature, by means of sixty different heuristics, which are compared to four lower bounds proposed in the literature in order to evaluate the quality of the heuristic solution. Four lower bounds and ten different constructive heuristics were programmed in C++ in the same computational environment, allowing their comparison both in terms of the quality of the solutions and in terms of processing times. A simple heuristic of item exchange between bins called Difference-of-Squares was proposed to improve the initial solutions of the problem. The simulated annealing metaheuristic was triggered to improve the initial solution when the lower bounds was not reached. The parameters of the simulated annealing were determined with the data of the instances differently from that used in the literature. The combinations of the ten initial solutions, the Difference-of-Squares heuristic and the simulated annealing generated a set of sixty different heuristics. The results showed that the proposed algorithm is efficient to solve the problem with adequate processing times for decision making.

This thesis consists of two parts. In part I, a group of combinatorial problems pertaining to strings, boolean matrices and graphs is studied. For given two strings x and y, their edit distance is the minimum number of character insertions, deletions and substitutions required to convert x into y. In this thesis we provide an algorithm that computes a constant approximation of edit distance in truly sub-quadratic time. Based on the provided ideas, we construct a separate sub- quadratic time algorithm that can find an occurrence of a pattern P in a given text T while allowing a few edit errors. Afterwards we study the boolean matrix multiplication (BMM) problem where given two boolean matrices, the aim is to find their product over boolean semi-ring. For this problem, we present two combinatorial models and show in these models BMM requires Ω(n3 /2O( √ log n) ) and Ω(n7/3 /2O( √ log n) ) work respectively. Furthermore, we also give a construction of a sparse sub-graph that preserves the distance between a designated source and any other vertex as long as the total weight increment of all the edges is bounded by some constant. In part II, we study the efficient construction of quasi-Gray codes. We give a construction of space optimal quasi-Gray codes over odd sized alphabets with read complexity 4...