Dans un graphe orienté contenant un nœud appelé racine, un sous ensemble de nœuds appelés terminaux et une pondération sur les arcs, le problème de l’arborescence de Steiner (DST) consiste en la recherche d’une arborescence de poids minimum contenant pour chaque terminal un chemin de la racine vers ce terminal. Ce problème est NP-Complet. Cette thèse se penche sur l’étude de l’approximabilité de ce problème. Sauf si P=NP, il n’existe pas pour ce problème d’approximation de rapport constant ou logarithmique en k, oú k est le nombre de terminaux. Le plus petit rapport d’approximation connu est O (k") où " est un réel strictement positif. Dans la première partie, nous donnons trois algorithmes d’approximation : un algorithme glouton efficace qui associe deux techniques d’approximations connues pour DST, un algorithme dans le cas des graphes structurés en paliers qui étudie l’approximabilité du problème quand les terminaux sont éloignés de la racine, et un algorithme exponentiel qui combine un algorithme d’approximation et un algorithme exact, dont le rapport d’approximation et la complexité temporelle sont paramétrés par le nombre de terminaux couverts par l’algorithme exact. Dans la seconde partie, nous étudions deux problèmes issus de DST auquel est ajoutée une contrainte sur les nœuds de branchement. Cette contrainte réduit le nombre de solutions réalisables et peut faciliter la recherche d’une solution optimale parmi ce sous-ensemble de solutions. En fonction de la contrainte, nous étudions la possibilité de la trouver en temps polynomial et quel est le rapport d’approximation entre cette solution et la solution du problème non contraint / The directed Steiner tree problem (DST) asks, considering a directed weighted graph, a node r called root and a set of nodes X called terminals, for a minimum cost directed tree rooted in r spanning X. DST is an NP-complete problem. We are interested in the search for polynomial approximations for DST. Unless P = NP, DST can not be approximated neither within a constant ratio nor a logarithmic ratio with respected to k, where k is the number of terminals. The smallest known approximation ratio is O(kԑ)$ where ԑ is a positive real.In the first part, we provide three new approximation algorithms : a practical greedy algorithm merging two of the main approximation techniques for DST, an algorithm for the case where the graph is layered and where the distance between the terminals and the root is high, and an exponential approximation algorithm combining an approximation algorithm and an exact algorithm, parameterized with the number of terminals the exact algorithm must cover.In the last part we study DST with two branching constraints. With this technique, we are able to reduce the number of feasible solutions, and possibly facilitate the search for an optimal solution of the constraint problem. We study how it is possible to build such a solution in polynomial time and if this solution is a good approximation of an optimal solution of the non-constraint problem

Orientador: Rafael Santos Mendes / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-07T23:46:24Z (GMT). No. of bitstreams: 1 Portugal_DeniseSoderoVinhas_D.pdf: 1731980 bytes, checksum: 98f3bdce8b6d0d6e00e2c6c96ba968f7 (MD5) Previous issue date: 2006 / Resumo: Uma metodologia para obter um escalonamento cíclico em Sistemas a Eventos Discretos é proposta neste trabalho. Esta metodologia parte de uma rede de Petri que modela minimamente um sistema a eventos discretos funcionando em regime periódico. O método identifica quais são as redes que podem ser tratadas por ele. As redes de Petri tratáveis serão decompostas em subredes identificadas por processos, que são classificados de acordo com suas topologias, o que permite a modelagemdo escalonamento cíclico do sistema através de uma modelagem em programação linear inteira mista. Este modelo em MILP será implementado no software GAMS. Alguns exemplos tirados da literatura serão usados para mostrar e testar a aplicação desta metodologia / Abstract: A methodology to obtain a cyclic scheduling in Discrete Events Systems is proposed in this work. This methodology initializes with a Petri netmodeling a discrete events system functioning with periodic processing. The method identifieswhich are the nets that can be treaties by him. The ¿tractable¿ Petri nets will be decomposed in subnets identified by process, which are classified according to its topologies, that permits us tomodel the cyclic scheduling of the systemby amixed integer linear programming model. This model in MILP will be implemented using software GAMS. Some examples from the literature will be used to show and to test the application of this methodology / Doutorado / Automação Industrial / Doutor em Engenharia Elétrica

O problema de corte consiste no corte de objetos maiores para produção de peças menores, de modo que uma certa função objetivo seja otimizada, por exemplo, a perda seja minimizada. O problema de empacotamento pode também ser visto como um problema de corte, onde as peças menores são arranjadas dentro dos objetos. Uma abordagem em grafo E/OU para a resolução de problemas de corte e empacotamento foi proposta inicialmente por Morabito (1989) para problemas de corte bidimensionais e, mais tarde, estendida para problemas tridimensionais (Morabito, 1992). Nesta abordagem foi utilizada uma técnica de busca híbrida, onde se combinou a busca em profundidade primeiro com limite de profundidade e a busca hill-climbing, utilizando-se heurísticas baseadas nos limitantes superiores e inferiores. Experiências computacionais mostraram a viabilidade de uso na prática desta abordagem. Mais tarde, Arenales (1993) generalizou esta a abordagem em grafo E/OU mostrando como diferentes problemas de corte poderiam ser resolvidos, independentemente da dimensão, formas dos objetos e itens, baseado em simples hipóteses, sem realizar, entretanto, estudos computacionais. O presente trabalho tem por objetivo estender a abordagem em grafo E/OU para tratar outros casos não analisados pelos trabalhos anteriores, tais como situações envolvendo diferentes processos de corte, bem como a implementação computacional de métodos baseados na abordagem em grafo E/OU, mostrando, assim, a versatilidade da abordagem para tratar diversas situações práticas de problemas de corte e sua viabilidade computacional. / The cutting problem consists of cutting larger objects in order to produce smaller pieces, in such a way as to optimizing a given objective function, for example, minimizing the waste. The packing problem can also be seen as a cutting problem, where the position that each smaller piece is arranged inside of the objects can be seen as the place it was cut from. An AND/OR-graph approach to solve cutting and packing problems was initially proposed by Morabito (1989) for two-dimensional cutting problem and, later, extended to threedimensional problems (Morabito, 1992). That approach uses a hybrid search, which combines depth-first search under depth bound and hill-climbing strategy. Heuristics were devised based on upper and lower bounds. Computational experiences demonstrated its practical feasibility. The AND/OR-graph approach was later generalized by Arenales (1993) based on simple hypothesis. He showed that different cutting problems Gould be solved using the AND/ORgraph approach, independently of the dimension and shapes. The main objective of this thesis is the practical extension of the AND/OR-graph approach to handle other cases not considered by previous works. It was considered different cutting processes, as well as the analysis of computational implementation, showing how can it be adapted to many classes of practical cutting and packing problems.

Nesta dissertação estudamos --- do ponto de vista algorítmico --- o seguinte problema, conhecido como problema da partição conexa balanceada. Dado um grafo conexo G com pesos atribuídos a seus vértices, e um inteiro q >= 2, encontrar uma partição dos vértices de G em q classes, de forma que cada classe da partição induza um grafo conexo e que, ao considerar as somas dos pesos dos vértices de cada classe, a menor das somas seja o maior possível. Em outras palavras, o objetivo é encontrar q classes cujos pesos sejam tão balanceados quanto possível. Sabe-se que este problema é NP-difícil. Mencionamos alguns resultados sobre complexidade computacional e algoritmos que são conhecidos para este problema. Apresentamos algumas heurísticas que desenvolvemos, todas elas baseadas no uso do algoritmo polinomial para árvores, devido a Perl e Schach, que apresentamos com detalhe. Implementamos quatro heurísticas e um algoritmo de 3/4-aproximação conhecido para o caso q=2. Exibimos os resultados obtidos com os vários testes computacionais conduzidos com instâncias aleatórias, com grafos de diferentes pesos e densidades. Os resultados computacionais indicam que o desempenho dessas heurísticas --- todas elas polinomiais --- é bem satisfatório. No caso especial em que q=2, observamos que a heurística mais onerosa sistematicamente produziu soluções melhores ou iguais às do algoritmo de aproximação / In this dissertation we study algorithmic aspects of the following problem, known as the balanced connected partition. Given a connected graph G with weights defined on its vertices, and an integer q >= 2, find a partition of the vertices of G into q classes such that each class induces a connected graph, and furthermore, when we consider the sum of the weights of the vertices in each class, the smallest sum is as large as possible. In other words, the q classes must have weights that are as balanced as possible. This problem is known to be NP-hard. We mention some computational complexity and algorithmic results that are known for this problem. We present some heuristics that we designed, all of them based on the use of the polynomial algorithm for trees, due to Perl and Schach, which we show in detail. We implemented four heuristics and a 3/4-approximation algorithm that is known for q=2. We run tests on many random instances, of graphs with different weights and densities. The computational results indicate that the performance of these heuristics --- all of polynomial time complexity --- are very satisfactory. For q=2, we observed that the most expensive heuristic produced solutions with values which are systematically better or equal to those produced by the approximation algorithm.

A capacidade das células para responder corretamente a sinais externos e perceber mudanças no seu microambiente é a base do desenvolvimento, reparação de tecidos e de imunidade, bem como a homeostase do tecido normal. Transdução de sinal é o principal meio pelo qual as células respondem a sinais externos de seu ambiente e coordenam alterações celulares complexas. O estudo das vias de sinalização molecular permite-nos tentar compreender o funcionamento dessas transduções de sinais e, consequentemente, as respostas celulares a estímulos externos. Uma abordagem adequada para tais estudos é o uso de modelos matemáticos para simular a cinética das reações químicas que descrevem uma dada via de sinalização, o que nos permite gerar predições testáveis de processos celulares. Construir modelos cinéticos preditivos de vias de sinalização molecular através de dados de alto rendimento produzidos utilizando técnicas ômicas (i.e., genômica, transcriptômica, (fosfo-)proteômica) constitui um dos atuais desafios enfrentados pelos pesquisadores na área de Biologia Molecular. Recentemente, para lidar com este desafio, o arcabouço de e-Science SigNetSim foi introduzido pelo Grupo de Biologia Computacional e de Bioinformática do Instituto Butantan. Esse arcabouço permite fazer a descrição de vias de sinalização molecular através da descrição da estrutura de um modelo através de um conjunto de reações químicas, que por sua vez é mapeado para um sistema de Equações Diferencias Ordinárias (EDOs), numericamente simuladas e avaliadas. Todavia, modificações na estrutura das vias precisam ser feitas manualmente, o qual restringe severamente o número de estruturas da via que precisam ser testadas, especialmente no caso de modelos grandes. Portanto, diante desse panorama, este trabalho propõe o desenvolvimento de um método para modificar vias de sinalização molecular. Esse método se baseia no uso de bancos de dados de interatomas para fornecer um conjunto de espécies químicas candidatas para serem incluídas na via de sinalização. Um componente integrado ao arcabouço SigNetSim capaz de testar diferentes hipóteses de modificação de vias foi desenvolvido neste projeto utilizando a metodologia de heurística incremental. Para avaliar a eficiência do componente implementado, utilizamos como estudo de caso um modelo de vias sinalização de MAPKs e PI3K/Akt para realizar testes experimentais e analisar os resultados obtidos. / The ability of cells to respond correctly external signals and to perceive changes in their microenvironment is the basis for development, tissue repair and immunity as well as normal tissue homeostasis. Signal transduction is the primary means by which cells respond to external signals from their environment and coordinate complex cellular changes. The study of molecular signaling pathways allows us to understand the operation of each process of cellular signal transduction. The use of mathematical models to simulate the kinetics of chemical reactions that describe a given signaling pathway, allow us to generate testable predictions of the cell processos. To Build Kinetic predictive models to molecular signaling pathways through massive data omics produced using modern techniques, Genomics, transcriptomics, (Phospho) proteomics, is one of the current challenges faced by researchers in the field of molecular biology. Recently, the \\textit SigNetSim e-Science was introduced by the Biological Computacional and Bioinformatical Group from the Butantan Institute to face this challenge. This \\textit makes the description of molecular signaling pathways through a set of chemical reactions, which are mapped into a system of ordinary differential equations, this system will be numerically simulated and evaluated . However, changes in the structure of the pathways need to be updated manually presented in this work, which severely restricts the number of track structures that need to be tested, especially for the large models. Therefore, given this background, we present the method to modify the molecular signaling pathways. This method relies on the use of interactome database to provide a set of chemical species candidates to be included in the signaling pathway. An component integrated to SigNetSim framework able to test different hypotheses of pathways modification was developed in this project using the incremental heuristic methodology. To evaluate the implemented component, we used the MAPKs and PI3K/Akt pathways model as case study, in order to perform experimental tests and to analyze the obtained results.

Dans la collaboration entre transporteurs, plusieurs transporteurs forment une alliance pour échanger leurs demandes de transport dans le but d'améliorer la rentabilité. Dans cette thèse, nous avons étudié la planification collaborative de transport entre transporteurs de charges partielles. Plus concrètement, nous avons étudié trois sous-problèmes soulevés dans cette planification collaborative: le problème de ramassage et de livraison avec fenêtres de temps, profits et demandes réservées, le problème de détermination de gagnants dans l'échange combinatoire, et le problème de génération d'enchère.Ces trois sous-problèmes sont les problèmes clés pour la planification collaborative de transport parmi des transporteurs, et ils sont peu étudiés dans la littérature. Nous avons établi les nouveaux modèles de programmation mathématique pour ces problèmes et développé des heuristiques efficaces pour trouver des solutions très proches de leurs optimums dans un temps de calcul raisonnable. Les heuristiques proposées sont plus performantes que les solveurs commerciaux (GUROBI, CPLEX) non seulement en termes de la qualité de solution, mais aussi en termes du temps de calcul. / In carrier collaboration, multiple carriers form an alliance to exchange their delivery requests for the purpose of improving profitability. In this thesis, we have studied the collaborative transportation planning (CTP) among less-than-truckload (LTL) carriers. More concretely, we have studied three sub-problems raised in this collaborative planning: the pickup and delivery problem with time windows, profits, and reserved requests (PDPTWPR), the winner determination problem (WDP) in carrier collaboration via combinatorial exchange (CE), and the bid generation problem (BGP).These sub-problems are the key issues for collaborative transportation planning among carriers, and they are rarely studied in the literature. We have established new mathematical programming models for these problems and developed efficient heuristics to find solutions close to their optimums in a reasonable computational time. The heuristics proposed are more efficient than commercial solvers (GUROBI, CPLEX) not only in terms of solution quality, but also in terms of computation time.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22588号 / 情博第725号 / 新制||情||124(附属図書館) / 京都大学大学院情報学研究科通信情報システム専攻 / (主査)教授 湊 真一, 教授 五十嵐 淳, 教授 山本 章博 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

La structure de projet se retrouve dans de nombreux contextes de l'industrie et des services. Il s'agit de réaliser un ensemble d'activités pouvant être connectées par des liens logiques de séquence (antériorité), en faisant appel à des ressources disponibles en quantité limitée. L'objectif est la minimisation d'un critère généralement lié à la durée ou au coût du projet. La plupart des problèmes d'ordonnancement de projet dans la littérature considèrent une unité de temps commune pour la détermination des dates d'exécution des activités et pour l'évaluation instantanée du respect des capacités des ressources qu'elles utilisent. Or, s'il est souvent nécessaire en pratique d'obtenir un calendrier détaillé des plages d'exécution des activités, l'utilisation des ressources peut être évaluée sur un horizon plus agrégé, comme par exemple les quarts de travail des employés. Dans cette thèse, un nouveau modèle intégrant ces deux échelles de temps est présenté afin de définir le problème d'ordonnancement de projet avec agrégation périodique des contraintes de ressources (PARCPSP). Ce problème est étudié du point de vue de la théorie de la complexité et des propriétés structurelles sont établies, mettant notamment en évidence des différences majeures avec le problème classique d'ordonnancement de projet sous contraintes de ressources (RCPSP). De ces propriétés sont dérivées des formulations exactes basées sur la programmation linéaire en nombres entiers, comparées en termes de qualité de la relaxation linéaire. Par ailleurs, plusieurs heuristiques, telles que des algorithmes de liste, ou une méthode approchée basée sur une résolution itérative qui exploite différentes échelles de temps, sont proposées. Les résultats expérimentaux montrent l'intérêt de ces différentes méthodes et illustrent la difficulté du problème. / The project structure arises in many fields of industry and services. It consists in performing a set of activities that may be linked by precedence relations, and use resources whose capacity is limited. The objective is to minimize a criterion usually linked to the duration or the cost of the project. Most of project scheduling problems in the literature assume that the same time scale should be used to determine activity start and completion dates and check resource constraints at each time. However, although it is often required in practice to build a precise schedule specifying the execution range of each activity, the resource usage can be evaluated on an aggregated basis, like worker shifts. In this thesis, a new model that enables the integration of these two time scales is presented in order to define the periodically aggregated resource-constrained project scheduling problem (PARCPSP). This problem is studied within the framework of complexity theory and several structural properties are established, highlighting major differences with the standard resource-constrained project scheduling problem (RCPSP). These properties allow deriving exact formulations based on integer linear programming, whose linear relaxations are compared. Moreover, several heuristics, such as schedule generations schemes, or an approached method based on a multi time scale iterative process, are proposed. Experimental results show the interest of these different methods and point out the intractability of the problem.

In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties. The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the university-wide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this large-size problem. A facility layout problem involving arbitrary-shaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitrary-shaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitrary-shaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitrary-shaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixed-integer programming model that maintains the arbitrary shapes of the departments. We use a meta-heuristic to solve the large-size instances of the ASFLP in a reasonable amount of time. The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the single-customer problem, we present a polynomial-time algorithm to solve it to optimality. For the multiple-customer problem, we prove that this problem is NP-hard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branch-and-bound-based methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

Le crowdsourcing est une pratique permettant aux entreprises de faire appel à l’intelligence humaine à grande échelle afin d’apporter des solutions à des problématiques qu’elles souhaitent externaliser. Les problématiques externalisées sont de plus en plus complexes et ne peuvent être résolues individuellement. Nous proposons dans cette thèse une approche appelée SocialCrowd, contribuant à améliorer la qualité des résultats de crowdsourcing. Elle consiste à faire collaborer les participants afin d’unir leur capacité de résolution et apporter des solutions aux problèmes externalisés de plus en plus complexes. Les groupes collaboratifs sont mis en compétition, via des rétributions attrayantes, afin d’obtenir de meilleures résolutions. Par ailleurs, il est nécessaire de protéger les données privées des groupes en compétition. Nous utilisons les réseaux sociaux comme support de fuite de données. Nous proposons une approche basée sur l’algorithme Dijkstra pour estimer la probabilité de propagation de données privées d’un membre sur le réseau social. Ce calcul est complexe étant donné la taille des réseaux sociaux. Une parallélisation du calcul est proposée suivant le modèle MapReduce. Un algorithme de classification basé sur le calcul de propagation dans les réseaux sociaux est proposé permettant de regrouper les participants en groupes collaboratifs et compétitifs tout en minimisant les fuites de données d’un groupe vers l’autre. Comme ce problème de classification est d’une complexité combinatoire, nous avons proposé un algorithme de classification basé sur les algorithmes d’optimisation combinatoires tels que le recuit simulé et les algorithmes génétiques. Etant donnée le nombre important de solutions possible, une approche basée sur le modèle du Soft Constraint Satisfaction Problem (SCSP) est proposée pour classer les différentes solutions. / Crowdsourcing is the practice of allowing companies to use human intelligence scale to provide solutions to issues they want to outsource. Outsourced issues are increasingly complex and cannot be resolved individually. We propose in this thesis an approach called SocialCrowd, helping to improve the quality of the results of crowdsourcing. It compromise to collaborate participants to unite solving ability and provide solutions to outsourced problems more and more complex. Collaborative groups are put in competition through attractive remuneration, in order to obtain better resolution. Furthermore, it is necessary to protect the private information of competing groups. We use social media as a support for data leakage. We propose an approach based on Dijkstra algorithm to estimate the propagation probability of private data member in the social network. Given the size of social networks, this computation is complex. Parallelization of computing is proposed according to the MapReduce model. A classification algorithm based on the calculation of propagations in social networks is proposed for grouping participants in collaborative and competitive groups while minimizing data leaks from one group to another. As this classification problem is a combinatorial complexity, we proposed a classification algorithm based on combinatorial optimization algorithms such as simulated annealing and genetic algorithms. Given the large number of feasible solutions, an approach based on the model of Soft Constraint Satisfaction Problem (SCSP) is proposed to classify the different solutions.