Dissertations / Theses on the topic 'Combinatorial optimization Computer algorithms'

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.
Includes bibliographical references (p. 87-90).
Combinatorial optimization problems arise in many fields of industry and technology, where they are frequently used in production planning, transportation, and communication network design. Whereas in the context of classical discrete optimization it is usually assumed that the problem inputs are known, in many real-world applications some of the data may be subject to an uncertainty, often because it represents information about the future. In the field of stochastic optimization uncertain parameters are usually represented as random variables that have known probability distributions. In this thesis we study a number of different scenarios of planning under uncertainty motivated by applications from robotics, communication network design and other areas. We develop approximation algorithms for several NP-hard stochastic combinatorial optimization problems in which the input is uncertain - modeled by probability distribution - and the goal is to design a solution in advance so as to minimize expected future costs or maximize expected future profits. We develop techniques for dealing with certain probabilistic cost functions making it possible to derive combinatorial properties of an optimum solution. This enables us to make connections with already well-studied combinatorial optimization problems and apply some of the tools developed for them. The first problem we consider is motivated by an application from AI, in which a mobile robot delivers packages to various locations. The goal is to design a route for robot to follow so as to maximize the value of packages successfully delivered subject to an uncertainty in the robot's lifetime.
(cont.) We model this problem as an extension of the well-studied Prize-Collecting Traveling Salesman problem, and develop a constant factor approximation algorithm for it, solving an open question along the way. Next we examine several classical combinatorial optimization problems such as bin-packing, vertex cover, and shortest path in the context of a "preplanning" framework, in which one can "plan ahead" based on limited information about the problem input, or "wait and see" until the entire input becomes known, albeit incurring additional expense. We study this time-information tradeoff, and show how to approximately optimize the choice of what to purchase in advance and what to defer. The last problem studied, called maybecast is concerned with designing a routing network under a probabilistic distribution of clients using locally available information. This problem can be modeled as a stochastic version of the Steiner tree problem. However probabilistic objective function turns it into an instance of a challenging optimization problem with concave costs.
by Maria Minkoff.
Ph.D.

We consider several combinatorial optimization problems in a geometric set- ting. The first problem we consider is the problem of clustering to minimize the sum of radii. Given a positive integer k and a set of points with interpoint distances that satisfy the definition of being a "metric", we define a ball centered at some input point and having some radius as the set of all input points that are at a distance smaller than the radius of the ball from its center. We want to cover all input points using at most k balls so that the sum of the radii of the balls chosen is minimized. We show that when the points lie in some Euclidean space and the distance measure is the standard Euclidean metric, we can find an exact solution in polynomial time under standard assumptions about the model of computation. The second problem we consider is the Network Spanner Topology Design problem. In this problem, given a set of nodes in the network, represented by points in some geometric setting - either a plane or a 1.5-D terrain, we want to compute a height assignment function h that assigns a height to a tower at every node such that the set of pairs of nodes that can form a direct link with each other under this height function forms a connected spanner. A pair of nodes can form a direct link if they are within a bounded distance B of each other and the heights of towers at the two nodes are sufficient to achieve Line-of-Sight connectivity - i.e. the straight line connecting the top of the towers lies above any obstacles. In the planar setting where the obstacles are modeled as having a certain maximum height and minimum clearance distance, we give a constant factor approximation algorithm. In the case where the points lie on a 1.5-D terrain we illustrate that it might be hard to use Computational Geometry to achieve efficient approximations. The final problem we consider is the Multiway Barrier Cut problem. Here, given a set of points in the plane and a set of unit disk sensors also in the plane such that any path in the plane between any pair of input points hits at least one of the given sensor disks we consider the problem of finding the minimum size subset of these disks that still achieves this separation. We give a constant factor approximation algorithm for this problem.

Genetic algorithms are stochastic search techniques based on the mechanics of natural selection and natural genetics. Genetic algorithms differ from traditional analytical methods by using genetic operators and historic cumulative information to prune the search space and generate plausible solutions. Recent research has shown that genetic algorithms have a large range and growing number of applications. The research presented in this thesis is that of using genetic algorithms to solve some typical combinatorial optimization problems, namely the Clique, Vertex Cover and Max Cut problems. All of these are NP-Complete problems. The empirical results show that genetic algorithms can provide efficient search heuristics for solving these combinatorial optimization problems. Genetic algorithms are inherently parallel. The Connection Machine system makes parallel implementation of these inherently parallel algorithms possible. Both sequential genetic algorithms and parallel genetic algorithms for Clique, Vertex Cover and Max Cut problems have been developed and implemented on the SUN4 and the Connection Machine systems respectively.

The focus of this thesis is on the design and analysis of algorithms for basic problems in Stochastic Optimization, specifically a class of fundamental combinatorial optimization problems where there is some form of uncertainty in the input. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. However, a common assumption in traditional algorithms is that the exact input is known in advance. What if this is not the case? What if there is uncertainty in the input? With the growing size of input data and their typically distributed nature (e.g., cloud computing), it has become imperative for algorithms to handle varying forms of input uncertainty. Current techniques, however, are not robust enough to deal with many of these problems, thus necessitating the need for new algorithmic tools. Answering such questions, and more generally identifying the tools for solving such problems, is the focus of this thesis. The exact problems we study in this thesis are the following: (a) the Survivable Network Design problem where the collection of (source,sink) pairs is drawn randomly from a known distribution, (b) the Stochastic Knapsack problem with random sizes/rewards for jobs, (c) the Multi-Armed Bandits problem, where the individual Markov Chains make random transitions, and finally (d) the Stochastic Orienteering problem, where the random tasks/jobs are located at different vertices on a metric. We explore different techniques for solving these problems and present algorithms for all the above problems with near-optimal approximation guarantees. We also believe that the techniques are fairly general and have wider applicability than the context in which they are used in this thesis.

Games on graphs have become an indispensable tool in modern computer science. They provide powerful and expressive models for numerous phenomena and are extensively used in computer- aided verification, automata theory, logic, complexity theory, computational biology, etc.

The infinite games on finite graphs we study in this thesis have their primary applications in verification, but are also of fundamental importance from the complexity-theoretic point of view. They include parity, mean payoff, and simple stochastic games.

We focus on solving graph games by using iterative strategy improvement and methods from linear programming and combinatorial optimization. To this end we consider old strategy evaluation functions, construct new ones, and show how all of them, due to their structural similarities, fit into a unifying combinatorial framework. This allows us to employ randomized optimization methods from combinatorial linear programming to solve the games in expected subexponential time.

We introduce and study the concept of a controlled optimization problem, capturing the essential features of many graph games, and provide sufficent conditions for solvability of such problems in expected subexponential time.

The discrete strategy evaluation function for mean payoff games we derive from the new controlled longest-shortest path problem, leads to improvement algorithms that are considerably more efficient than the previously known ones, and also improves the efficiency of algorithms for parity games.

We also define the controlled linear programming problem, and show how the games are translated into this setting. Subclasses of the problem, more general than the games considered, are shown to belong to NP intersection coNP, or even to be solvable by subexponential algorithms.

Finally, we take the first steps in investigating the fixed-parameter complexity of parity, Rabin, Streett, and Muller games.

This thesis makes a number of contributions to the theory of approximation algorithm design for multi-agent systems. In particular, we focus on two research directions. The first direction is to generalize the classical framework of combinatorial optimization to the submodular setting, where we assume that each agent has a submodular cost function. We show hardness results from both the information-theoretic and computational aspects for several fundamental optimization problems in the submodular setting, and provide matching approximation algorithms for most of them. The second direction is to introduce game-theoretic issues to approximation algorithm design. Towards this direction, we study the application of approximation algorithms in the theory of truthful mechanism design. We study both the standard objectives of revenue and social welfare, by designing efficient algorithms that satisfy the requirement of truthfulness and guarantee approximate optimality.

In recent years, evolving technology has provided a wide range of resources for Military forces. However, that wideness also caused resource management difficulties in combat missions. Air Tasking Order (ATO) is prepared for various missions of air combats in order to reach objectives by an optimized resource management. Considering combinatorial military aspects with dynamic objectives and various constraints
computer support became inevitable for optimizing the resource management in air force operations. In this thesis, we study different optimization approaches for resource allocation problem of ATO preparation and analyze their performance. We proposed a genetic algorithm formulation with customized encoding, crossover and fitness calculation mechanisms by using the domain knowledge. A linear programming formulation of the problem is developed by integer decision variables and it is used for effectivity and efficiency analysis of genetic algorithm formulations.

Stochastic combinatorial optimization problems are combinatorial optimization problems where part of the problem data are probabilistic. The focus of this thesis is on stochastic routing problems, a class of stochastic combinatorial optimization problems that arise in distribution management. Stochastic routing problems involve finding the best solution to distribute goods across a logistic network. In the problems we tackle, we consider a setting in which the cost of a solution is described by a random variable; the goal is to find the solution that minimizes the expected cost. Solving such stochastic routing problems is a challenging task because of two main factors. First, the number of possible solutions grows exponentially with the instance size. Second, computing the expected cost of a solution is computationally very expensive.

To tackle stochastic routing problems, stochastic local search algorithms such as iterative improvement algorithms and metaheuristics are quite promising because they offer effective strategies to tackle the combinatorial nature of these problems. However, a crucial factor that determines the success of these algorithms in stochastic settings is the trade-off between the computation time needed to search for high quality solutions in a large search space and the computation time spent in computing the expected cost of solutions obtained during the search.

To compute the expected cost of solutions in stochastic routing problems, two classes of approaches have been proposed in the literature: analytical computation and empirical estimation. The former exactly computes the expected cost using closed-form expressions; the latter estimates the expected cost through Monte Carlo simulation.

Many previously proposed metaheuristics for stochastic routing problems use the analytical computation approach. However, in a large number of practical stochastic routing problems, due to the presence of complex constraints, the use of the analytical computation approach is difficult, time consuming or even impossible. Even for the prototypical stochastic routing problems that we consider in this thesis, the adoption of the analytical computation approach is computationally expensive. Notwithstanding the fact that the empirical estimation approach can address the issues posed by the analytical computation approach, its adoption in metaheuristics to tackle stochastic routing problems has never been thoroughly investigated.

In this thesis, we study two classical stochastic routing problems: the probabilistic traveling salesman problem (PTSP) and the vehicle routing problem with stochastic demands and customers (VRPSDC). The goal of the thesis is to design, implement, and analyze effective metaheuristics that use the empirical estimation approach to tackle these two problems. The main results of this thesis are:

1) The empirical estimation approach is a viable alternative to the widely-adopted analytical computation approach for the PTSP and the VRPSDC;

2) A principled adoption of the empirical estimation approach in metaheuristics results in high performing algorithms for tackling the PTSP and the VRPSDC. The estimation-based metaheuristics developed in this thesis for these two problems define the new state-of-the-art.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Combinatorial optimization problems are of high academical as well as practical importance. Many instances of relevant combinatorial optimization problems are, due to their dimensions, intractable for complete methods such as branch and bound. Therefore, approximate algorithms such as metaheuristics received much attention in the past 20 years. Examples of metaheuristics are simulated annealing, tabu search, and evolutionary computation. One of the most recent metaheuristics is ant colony optimization (ACO), which was developed by Prof. M. Dorigo (who is the supervisor of this thesis) and colleagues. This thesis deals with theoretical as well as practical aspects of ant colony optimization.

* A survey of metaheuristics. Chapter 1 gives an extensive overview on the nowadays most important metaheuristics. This overview points out the importance of two important concepts in metaheuristics: intensification and diversification.

* The hyper-cube framework. Chapter 2 introduces a new framework for implementing ACO algorithms. This framework brings two main benefits to ACO researchers. First, from the point of view of the theoretician: we prove that Ant System (the first ACO algorithm to be proposed in the literature) in the hyper-cube framework generates solutions whose expected quality monotonically increases with the number of algorithm iterations when applied to unconstrained problems. Second, from the point of view of the experimental researcher, we show through examples that the implementation of ACO algorithms in the hyper-cube framework increases their robustness and makes the handling of the pheromone values easier.

* Deception. In the first part of Chapter 3 we formally define the notions of first and second order deception in ant colony optimization. Hereby, first order deception corresponds to deception as defined in the field of evolutionary computation and is therefore a bias introduced by the problem (instance) to be solved. Second order deception is an ACO-specific phenomenon. It describes the observation that the quality of the solutions generated by ACO algorithms may decrease over time in certain settings. In the second part of Chapter 3 we propose different ways of avoiding second order deception.

* ACO for the KCT problem. In Chapter 4 we outline an ACO algorithm for the edge-weighted k-cardinality tree (KCT) problem. This algorithm is implemented in the hyper-cube framework and uses a pheromone model that was determined to be well-working in Chapter 3. Together with the evolutionary computation and the tabu search approaches that we develop in Chapter 4, this ACO algorithm belongs to the current state-of-the-art algorithms for the KCT problem.

* ACO for the GSS problem. Chapter 5 describes a new ACO algorithm for the group shop scheduling (GSS) problem, which is a general shop scheduling problem that includes among others the well-known job shop scheduling (JSS) and the open shop scheduling (OSS) problems. This ACO algorithm, which is implemented in the hyper-cube framework and which uses a new pheromone model that was experimentally tested in Chapter 3, is currently the best ACO algorithm for the JSS as well as the OSS problem. In particular when applied to OSS problem instances, this algorithm obtains excellent results, improving the best known solution for several OSS benchmark instances. A final contribution of this thesis is the development of a general method for the solution of combinatorial optimization problems which we refer to as Beam-ACO. This method is a hybrid between ACO and a tree search technique known as beam search. We show that Beam-ACO is currently a state-of-the-art method for the application to the existing open shop scheduling (OSS) problem instances.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

Context. Train re-scheduling during disturbances is a time-consuming task. Modified schedules need to be found, so that trains can meet in suitable locations and delays minimized. Domino effects are difficult to manage. Commercial optimization software has been shown to find optimal solutions, but modied schedules need to be found quickly. Therefore, greedy depth-first algorithms have been designed to find solutions within a limited time-frame. Modern GPUs have a high computational capacity, and have become easier to use for computations unrelated to computer graphics with the development of technologies such as CUDA and OpenCL. Objectives. We explore the feasibility of running a re-scheduling algorithm developed specifically for this problem on a GPU using the CUDA toolkit. The main objective is to find a way of exploiting the computational capacity of modern GPUs to find better re-scheduling solutions within a limited time-frame. Methods. We develop and adapt a sequential algorithm for use on a GPU and run multiple experiments using 16 disturbance scenarios on the single-tracked iron ore line in northern Sweden. Results. Our implementation succeeds in finding re-scheduling solutions without conflicts for all 16 scenarios. The algorithm visits on average 7 times more nodes per time unit than the sequential CPU algorithm when branching at depth 50, and 4 times more when branching at depth 200. Conclusions. The computational performance of our parallel algorithm is promising but the approach is not complete. Our experiments only show that multiple solution branches can be explored fast in parallel, but not how to construct a high level algorithm that systematically searches for better schedules within a certain time limit. Further research is needed for that. We also find that multiple threads explore redundant solutions in our approach.

Indoor Positioning Systems (IPS) using the existing WLAN have won growing interest in the last years, it can be a perfect supplement to provide location information of users in indoor environments where other positioning techniques such as GPS, are not much effective. The thesis manuscript proposes a new approach to define a WLAN-based indoor positioning system (WLAN-IPS) as a combinatorial optimization problem to guarantee the requested communication quality while optimizing the positioning error. This approach is characterised by several difficult issues we tackled in three steps.At first, we designed a WLAN-IPS and implemented it as a test framework. Using this framework, we looked at the system performance under various experimental constraints. Through these experiments, we went as far as possible in analysing the relationships between the positioning error and the external environmental factors. These relationships were considered as evaluation indicators of the positioning error. Secondly, we proposed a model that defines all major parameters met in the WLAN-IPS from the literature. As the original purpose of the WLAN infrastructures is to provide radio communication access, we introduced an additional purpose which is to minimize the location error within IPS context. Two main indicators were defined in order to evaluate the network Quality of Service (QoS) and the positioning error for Location-Based Service (LBS). Thirdly, after defining the mathematical formulation of the optimisation problem and the key performance indicators, we proposed a mono-objective algorithm and a multi-objective algorithm which are based on Tabu Search metaheuristic to provide good solutions within a reasonable amount of time. The simulations demonstrate that these two algorithms are highly efficient for the indoor positioning optimization problem.

Thesis (MSc) - Information and Communication Technology, Swinburne University of Technology, 2007.
Submitted in partial fulfilment of the requirements for the degree of Master of Science (IT), [Information and Communication Technology], Swinburne University of Technology - 2007. Typescript. Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 1999.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 206-211). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9948016.

The traveling salesman problem (TSP) has become a classic in the field of combinatorial optimization. Attracting computer scientists and mathematicians, the problem involves finding a minimum cost Hamiltonian cycle in a weighted graph.

Orientadores: Flavio Keidi Miyazawa, Mauricio Guilherme de Carvalho Resende
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Nos últimos anos, as redes de telecomunicação tem experienciado um grande aumento no fluxo de dados. Desde a utilização massiva de vídeo sob demanda até o incontável número de dispositivos móveis trocando texto e vídeo, o tráfego alcançou uma escala capaz de superar a capacidade das redes atuais. Portanto, as companhias de telecomunicação ao redor do mundo tem sido forçadas a aumentar a capacidade de suas redes para servir esta crescente demanda. Como o custo de instalar uma infraestrutura de rede é geralmente muito grande, o projeto de redes usa fortemente ferramentas de otimização para manter os custos tão baixos quanto possível. Nesta tese, nós analisamos vários aspectos do projeto e implementação de redes de telecomunicação. Primeiramente, nós apresentamos um novo problema de projeto de redes usado para servir demandas sem fio de dispositivos móveis e rotear tal tráfego para a rede principal. Tais redes de acesso são baseadas em tecnologias sem fio modernos como Wi-Fi, LTE e HSPA. Este problema consideramos várias restrições reais e é difícil de ser resolvido. Nós estudamos casos reais nas vizinhanças de uma grande cidade nos Estados Unidos. Em seguida, nós apresentamos uma variação do problema de localização de hubs usado para modelar as redes principais (backbones ou laços centrais). Este problema também pode ser utilizado para modelar redes de transporte de cargas e passageiros. Nós também estudamos o problema de clusterização correlacionada com sobreposições usado para modelar o comportamento dos usuários quando utilizam seus equipamentos móveis. Neste problema, nós podemos rotular um objeto usando múltiplos rótulos e analisar a conexão entre eles. Este problema é adequado para análise de mobilidade de equipamentos que pode ser usada para estimar o tráfego em uma dada região. E finalmente, nós analisamos o licenciamento de espectro sobre uma perspectiva governamental. Nestes casos, uma agência do governo deseja vender licenças para companhias de telecomunicação para que operem em uma dada faixa de espectro. Este processo usualmente é conduzido usando leilões combinatoriais. Para todos problemas, nós propomos algoritmos genéticos de chaves aleatórias viciadas e modelos de programação linear inteira mista para resolvê-los (exceto para o problema de clusterização correlacionada com sobreposição, devido sua natureza não-linear). Os algoritmos que propusemos foram capazes de superar algoritmos do estado da arte para todos problemas
Abstract: Cutting and packing problems are common problems that occur in many industry and business process. Their optimized resolution leads to great profits in several sectors. A common problem, that occur in textil and paper industries, is to cut a strip of some material to obtain several small items, using the minimum length of material. This problem, known by Two Dimensional Strip Packing Problem (2SP), is a hard combinatorial optimization problem. In this work, we present an exact algorithm to 2SP, restricted to two staged cuts (known by Two Dimensional Level Strip Packing, 2LSP). The algorithm uses the branch-and-price technique, and heuristics based on approximation algorithms to obtain upper bounds. The algorithm obtained optimal or almost optimal for small and moderate sized instances
Abstract: In last twenty years, telecommunication networks have experienced a huge increase in data utilization. From massive on-demand video to uncountable mobile devices exchanging text and video, traffic reached scales that overcame the network capacities. Therefore, telecommunication companies around the world have been forced to increase their capacity to serve this increasing demand. As the cost to deploy network infrastructure is usually very large, the design of a network heavily uses optimization tools to keep costs as low as possible. In this thesis, we analyze several aspects of the design and deployment of communication networks. First, we present a new network design problem used to serve wireless demands from mobile devices and route the traffic to the core network. Such access networks are based on modern wireless access technologies such as Wi-Fi, LTE, and HSPA. This problem has several real world constraints and it is hard to solve. We study real cases of the vicinity of a large city in the United States. Following, we present a variation of the hub-location problem used to model these core networks. Such problem is also suitable to model transportation networks. We also study the overlapping correlation clustering problem used to model the user's behavior when using their mobile devices. In such problem, one can label an object with multiple labels and analyzes the connections between them. Although this problem is very generic, it is suitable to analyze device mobility which can be used to estimate traffic in geographical regions. Finally, we analyze spectrum licensing from a governmental perspective. In these cases, a governmental agency wants to sell rights for telecommunication companies to operate over a given spectrum range. This process usually is conducted using combinatorial auctions. For all problems we propose biased random-key genetic algorithms and mixed integer linear programming models (except in the case of the overlapping correlation clustering problem due its non-linear nature). Our algorithms were able to overcome the state of the art algorithms for all problems
Doutorado
Ciência da Computação
Doutor em Ciência da Computação

Orientador: Flavio Keidi Miyazawa
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Neste trabalho estudamos a interação entre duas áreas: otimização combinatória e compartilhamento de custos (cost-sharing), que é a arte de dividir os custos associados a construção e manutenção de uma solução a qual um grupo de usuários é beneficiado. Apresentamos algoritmos para problemas de projeto de redes, tendo como objetivo principal os problemas ¿Connected Facility Location¿ e ¿Rent-or-Buy¿. Estes dois problemas são NP-difíceis, pois têm como caso particular o problema da arvore mínima de Steiner, que tambem é NP-dificil. Na primeira parte do trabalho, temos a seguinte questão como motivação: ¿Como projetar uma boa rede, ou seja, uma rede que satisfaça todas as propriedades do problema e ao mesmo tempo minimize o custo de construção desta rede?¿ 'E nesta parte que os algoritmos de aproximação entram em ação. Uma vez que esse custo for determinado, na segunda parte do trabalho, uma outra questão surge: ¿Como dividir esse custo entre todos os usuários que participam da rede de uma maneira ¿justa¿? Nesta parte, usaremos o compartilhamento de custos juntamente com as tecnicas de algoritmos de aproximação para responder a essa questão
Abstract: We consider the interplay of two areas: combinatorial optimization and cost-sharing in network design problems. In the first, we are interested to find a solution with small cost. In the second we would like to share the solution cost between its users. We present algorithms for the problems ¿Connected Facility Location¿ and ¿Rent-or-Buy¿. These two problems are NP-hard, since they have as a particular case the minimum Steiner tree problem, which is a known NP-hard problem. In the first part of this work, we have the following question as motivation: ¿how to design a good network, i.e., one that satisfies all problem requirements and minimize the overall network construction cost?¿ In this part, approximation algorithms takes action. Once this cost is determinated, in the second part of the work, another question arises: ¿How to distribute this cost among all users that participate in the network in a ¿fair¿ way? In this part, we will use cost-sharing together with approximation algorithms techniques to answer this question
Mestrado
Teoria da Computação
Mestre em Ciência da Computação

Orientador: Cid Carvalho de Souza
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Aplicações desse problema incluem: máquina de controle numérico, inspeção automática e roteamento. Esta dissertação estuda soluções para o problema do recorte. Propomos um modelo de programação linear inteira e a partir deste desenvolvemos um algoritmo exato. Descrevemos um algoritmo 3.75 aproximado da literatura e propomos algumas melhorias heurísticas para o mesmo. Abandonando as garantias teóricas, projetamos duas heurísticas: a primeira utiliza uma ideia gulosa bastante simples complementada por técnicas da meta-heurística GRASP, especificamente aleatorização e busca local; e a segunda resolve um problema de cobertura mais simples e cuja sua solução pode ser adaptada para o problema original. Por fim propomos uma série de vizinhanças executadas em uma fase de busca local, que dada uma solução, faz mudanças locais que reduzem o custo do tour. As implementações dos algoritmos descritos são analisadas experimentalmente utilizando um benchmark de instâncias que construímos e deixamos público para comparações futuras
Abstract: In the orthogonal milling with turn costs problem is given an orthogonal polygon P that may contain holes. Our goal is to find a closed polygonal curve made of horizontal and vertical segments which when traversed by a unit square, the covered area is exactly P. Turn costs are assigned to direction changes and the objective is to minimize the sum of turn costs. This problem arises in many applications including: numerically controlled (NC) machining, automatic inspection and routing. This dissertation studies solutions for the milling problem. We propose an integer linear programming model and from which an exact algorithm is proposed. A 3.75- approximate algorithm from the literature is described for which heuristic improvements are proposed. Lifting the theoretical guarantees we project two heuristics: the first is based in a simple greedy idea supplemented with techniques of the GRASP meta-heuristic, specifically, randomization and local search; the latter solves a simpler covering problem whose its solution is adapted for the original problem. Finally, we propose a series of neighborhoods run in a local search step where, local changes are made to the solution such that the tour cost is reduced. All described algorithms are implemented and evaluated experimentally using a benchmark of instances that we built and made public for future comparisons
Mestrado
Ciência da Computação
Mestre em Ciência da Computação

Orientador: Flavio Keidi Miyazawa
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Em um problema de classificação tradicional temos um conjunto de n objetos e um conjunto de m classes e queremos classificar cada objeto como pertencente a uma classe, de modo que esta classificação seja consistente com alguns dados que temos sobre o problema. Este trabalho apresenta um estudo do problema de classificação métrica através de algoritmos aproximados. Os algoritmos aproximados conhecidos para este problema são baseados na solução de grandes programas lineares e são impraticáveis para instâncias de tamanho moderado e grande. Apresentamos um algoritmo 8 log n-aproximado, analisado pela técnica primal-dual, que apesar de possuir fator de aproximação maior que os algoritmos anteriores, pode ser aplicado a grandes instâncias. Mostramos também que este fator de aproximação é justo, exceto por um fator constante. Obtivemos resultados experimentais usando instâncias geradas computacionalmente e instâncias de processamento de imagens com o novo algoritmo e com outros dois algoritmos baseados na resolução de programas lineares. Para estas instâncias o algoritmo proposto apresentou soluções de boa qualidade com um ganho considerável no tempo computacional
Abstract: In a traditional classification problem, we have a set of n objects and a set of m labels (or classes). We wish to assign one of m labels (or classes) to each one of n objects, in a way that is consistent with some observed data that we have about the problem. In this work we present a study of approximation algorithms for the metric labeling problem. The known approximation algorithms for this problem are based on solutions of large linear programs and are impractical for moderate and large size instances. We present an 8 log n-approximation algorithm analyzed by a primal-dual technique which, although has a factor greater than the previous algorithms, can be applied to large sized instances. We also show that the analysis is tight, up to a constant factor. We obtained experimental results on computational generated and image processing instances with the new algorithm and two other LP-based approximation algorithms. For these instances our algorithm presents good quality solutions with a considerable gain of computational time
Mestrado
Ciência da Computação
Mestre em Ciência da Computação

Orientador: Cid Carvalho de Souza
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Esta dissertação tem como foco a investigação experimental de algoritmos exatos, aproximativos e heurísticos aplicados na resolução do chamado problema do corredor de comprimento mínimo (PCCM). No PCCM recebemos um polígono retilinear P e um conjunto de polígonos retilineares menores formando uma subdivisão S planar conexa de P. Uma solução para este problema, também chamada de corredor, é formada por um conjunto conexo de arestas de S, e tal que cada face interna em S possui pelo menos um ponto em sua borda que pertence a alguma aresta deste conjunto. O objetivo então é encontrar um corredor tal que a soma total dos comprimentos das arestas seja a menor possível. Trata-se de um problema NP-difícil com aplicações em áreas diversas, tais como telecomunicações, engenharia civil e projeto de circuitos VLSI. O PCCM pode ser reduzido polinomialmente a um problema em grafos denominado problema da árvore de Steiner com grupos (PASG). Considerando esta transformação, estudamos e implementamos dois métodos aproximativos, um método exato de branch-and-cut, e um método heurístico baseado na metaheurística GRASP combinada com um evolutionary path relinking (GRASP+EPR). Além disso, propomos três heurísticas de busca local que visam melhorar a qualidade de soluções do PASG. Instâncias do PCCM foram geradas aleatoriamente, nas quais aplicamos os métodos implementados. Analisamos os resultados, e apresentamos as situações onde é interessante utilizar cada método. Verificamos que o método branch-and-cut foi capaz de encontrar soluções ótimas para instâncias que julgamos ser de grande porte em tempos computacionalmente aceitáveis. O melhor algoritmo aproximativo obteve corredores que na média têm comprimento 17% maior que o comprimento ótimo. Se combinarmos este algoritmo com as heurísticas de melhoria propostas este percentual cai para a média de 3,5%. Finalmente, o GRASP+EPR consome mais tempo que este algoritmo aproximativo, entretanto, o comprimento dos corredores obtidos por ele é em média 0,9% maior que o comprimento ótimo
Abstract: This dissertation focuses on the experimental investigation of exact, approximation and heuristic algorithms applied to solve the so-called minimum length corridor problem (MLCP). In the MLCP we receive a rectilinear polygon P and a set of minor rectilinear polygons forming a connected planar subdivision S of P. A solution for this problem, also called corridor, is formed by a set of connected edges of S, and such that each inner face of S has at least one point on its your border which belongs to an edge in this set. The goal is to find a corridor such that the sum of lengths of the edges is as small as possible. This is an NP-hard problem with applications in several areas such as telecommunications, civil engineering and design of VLSI circuits. The MLCP can be polynomially reduced to a graph problem known as group Steiner tree problem (GSTP). Based on this transformation, we studied and implemented two approximation methods, an exact branch-and-cut method, and a heuristic method based on the metaheuristic GRASP combined with an evolutionary path relinking (GRASP+EPR). Furthermore, we propose three local search heuristics to improve the quality of GSTP solutions. MLCP instances were randomly generated, in which we apply the methods implemented. We analyzed the results, and present situations where it is interesting to use each method. We found that the branch-and-cut has been able to find optimal solutions for instances that we consider to be large in acceptable computational times. The best approximation algorithm obtained corridors having average length 17% higher than the optimum length. If we combine this algorithm with the improvement heuristics proposed this percentage drops to an average of 3.5%. Finally, the GRASP+EPR spent more time than this approximation algorithm, however, the length of the corridors obtained by the method is, on average, 0.9% higher than the optimum length
Mestrado
Ciência da Computação
Mestre em Ciência da Computação

Orientador: Orlando Lee
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
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Resumo: Nesta dissertação consideramos o problema do k-Servidor. Neste problema temos k servidores em um espaço métrico e nosso objetivo e atender a uma seqüência de requisições, de modo a minimizar a distancia total percorrida pelos servidores. Dedicamos especial atenção a conjectura do k-Servidor: qualquer espaço métrico admite um algoritmo k-competitivo para o problema do k-Servidor. Este e um dos problemas mais importantes em aberto da area de computação online. O algoritmo da função trabalho, proposto por Chrobak e Larmore, e especialmente relevante para a conjectura. Isto porque foi provado que este algoritmo e k-competitivo para diversos casos particulares do problema do k-Servidor. Alem disso, acredita-se que este algoritmo e de fato k-competitivo para todo espaço métrico. Por isto, o entendimento deste algoritmo e central neste trabalho. Para analisar o algoritmo da função trabalho são utilizados diversos resultados auxiliares desenvolvidos por vários autores. Neste trabalho tentamos apresentar de forma coesa uma coletânea destes resultados. A partir desta mostramos uma prova do teorema de Koutsoupias e Papadimitriou: o algoritmo da função trabalho e (2k - 1)-competitivo para todo espaço métrico. Este e o resultado mais importante relacionado ao problema do k-Servidor. Alem disso, mostramos que a conjectura do k-Servidor vale para alguns casos particulares do problema
Abstract: In this work we study the k-server problem. In this problem, we have k servers on a metric space that must attend a sequence of requests with the goal of minimizing the total distance moved by the servers. We dedicate special attention to the k-server conjecture: any metric space allows for a k-competitive k-server algorithm. This is one of the most important open problems in online computing. The work function algorithm, proposed by Chrobak and Larmore, is very relevant to the conjecture. It has been proved that this algorithm is k-competitive for several special cases of the k-server problem. Furthermore, most researchers believe that the algorithm is indeed k-competitive for any metric space. Thus, a deeper understanding of this algorithm plays a special role in this work. To analyze the work function algorithm, we use many auxiliary results developed by several authors. In this work we tried to present a collection of these results in a concise way. From this, we present a proof of Koutsoupias and Papadimitriou's theorem: the work function algorithm is (2k - 1)-competitive for any metric space. This is the most important result related to the k-server problem. Moreover, we show that the k-server conjecture holds in some special cases
Mestrado
Otimização Combinatoria
Mestre em Ciência da Computação

In this work, we present a way to extend Ant Colony Optimization (ACO), so that it can be applied to both continuous and mixed-variable optimization problems. We demonstrate, first, how ACO may be extended to continuous domains. We describe the algorithm proposed, discuss the different design decisions made, and we position it among other metaheuristics.

Following this, we present the results of numerous simulations and testing. We compare the results obtained by the proposed algorithm on typical benchmark problems with those obtained by other methods used for tackling continuous optimization problems in the literature. Finally, we investigate how our algorithm performs on a real-world problem coming from the medical field—we use our algorithm for training neural network used for pattern classification in disease recognition.

Following an extensive analysis of the performance of ACO extended to continuous domains, we present how it may be further adapted to handle both continuous and discrete variables simultaneously. We thus introduce the first native mixed-variable version of an ACO algorithm. Then, we analyze and compare the performance of both continuous and mixed-variable

ACO algorithms on different benchmark problems from the literature. Through the research performed, we gain some insight into the relationship between the formulation of mixed-variable problems, and the best methods to tackle them. Furthermore, we demonstrate that the performance of ACO on various real-world mixed-variable optimization problems coming from the mechanical engineering field is comparable to the state of the art.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Electrical Engineering
M.S.E.
Redundancy Allocation Problem (RAP) is a well known mathematical problem for modeling series-parallel systems. It is a combinatorial optimization problem which focuses on determining an optimal assignment of components in a system design. Due to the diverse possible selection of components, the RAP is proved to be NP-hard. Therefore, many algorithms, especially heuristic algorithms were proposed and implemented in the past several decades, committed to provide innovative methods or better solutions. In recent years, multi-agent system (MAS) is proposed for modeling complex systems and solving large scale problems. It is a relatively new programming concept with the ability of self-organizing, self-adaptive, autonomous administrating, etc. These features of MAS inspire us to look at the RAP from another point of view. An RAP can be divided into multiple smaller problems that are solved by multiple agents. The agents can collaboratively solve optimal RAP solutions quickly and efficiently. In this research, we proposed to solve RAP using MAS. This novel approach, to the best of our knowledge, has not been proposed before, although multi-agent approaches have been widely used for solving other large and complex nonlinear problems. To demonstrate that, we analyzed and evaluated four benchmark RAP problems in the literature. From the results, the MAS approach is shown as an effective and extendable method for solving the RAP problems.
Temple University--Theses

A teoria dos grafos é uma ferramenta matemática muito utilizada na resolução de problemas algorítmicos e computacionais em que se quer modelar conjuntos de elementos e relações entre estes elementos. Sistemas naturais e tecnológicos de diversos domínios podem ser representados matematicamente por grafos que possuem propriedades estatísticas bem conhecidas, sendo uma destas propriedades a distribuição de graus dos vértices do grafo seguindo a lei de potência (power law). Exemplos destes grafos, conhecidos como grafos power law são a internet, World-Wide Web, as redes sociais, redes biológicas. No contexto de problemas algorítmicos em grafos, estamos interessados em problemas computacionalmente difíceis de serem resolvidos que pertencem à classe NP-Difícil (ou NP-Hard), mais especificamente no problema de cobertura por vértices. Neste trabalho será estudado experimentalmente o comportamento de um algoritmo baseado em uma estratégia gulosa para o problema de cobertura de vértices e compararemos com outro algoritmo de aproximação e com a solução exponencial ótima. Em particular esta solução será aplicada e analisada em redes complexas.
Graph theory is a mathematical tool used in solving many algorithmic and computational problems in that both sets of model elements and relationships between these elements. Most natural and technological systems can be mathematically modeled by graph having many well known properties, in particular the power law distribution of the vertex degree sequence. Examples of such graphs, called power law graphs are the Internet, World-Wide Web, social networks, biological networks. In the context of algorithmic problems on graphs, we are interested in problems in class NP-Hard, more specifically in the vertex cover problem. This work will be studied experimentally the behavior of an algorithm based on a greedy strategy for the vertex cover problem and compare with other approximation algorithms and with the exponential optimal solution. In particular this solution will be applied and analyzed in complex networks.

La résolution efficace de problèmes d'optimisation a permutation de grande taille nécessite le développement de méthodes hybrides complexes combinant différentes classes d'algorithmes d'optimisation. L'hybridation des metaheuristiques avec les méthodes exactes arborescentes, tel que l'algorithme du branch-and-bound (B&B), engendre une nouvelle classe d'algorithmes plus efficace que ces deux classes de méthodes utilisées séparément. Le défi principal dans le développement de telles méthodes consiste a trouver des liens ou connections entre les stratégies de recherches divergentes utilisées dans les deux classes de méthodes. Les Algorithmes Genetiques (AGs) sont des metaheuristiques, a base de population, tr'es populaires bas'es sur des op'erateurs stochastiques inspirés de la théorie de l'évolution. Contrairement aux AGs et aux m'etaheuristiques généralement, les algorithmes de B&B sont basées sur l'énumération implicite de l'espace de recherche représente par le moyen d'un arbre, dit arbre de recherche. Notre approche d'hybridation consiste a définir un codage commun des solutions et de l'espace de recherche ainsi que des opérateurs de recherche ad'equats afin de permettre un couplage efficace de bas niveau entre les deux classes de méthodes AGs et B&B. La représentation de l'espace de recherche par le moyen d'arbres est traditionnellement utilis'ee dans les algorithmes de B&B. Dans cette thèse, cette représentation a été adaptée aux metaheuristiques. L'encodage des permutations au moyen de nombres naturels faisant référence a l'ordre d'énumération lexicographique des permutations dans l'arbre du B&B, est proposé comme une nouvelle manière de représenter l'espace de recherche des problèmes 'a permutations dans les metaheuristiques. Cette méthode de codage est basée sur les propriétés mathématiques des permutations, 'a savoir les codes de Lehmer et les tables d'inversions ainsi que les système d'énumération factoriels. Des fonctions de transformation permettant le passage entre les deux représentations (permutations et nombres) ainsi que des opérateurs de recherche adaptes au codage, sont définis pour les problèmes 'a permutations généralisés. Cette représentation, désormais commune aux metaheuristiques et aux algorithmes de B&B, nous a permis de concevoir des stratégies d'hybridation et de collaboration efficaces entre les AGs et le B&B. En effet, deux approches d'hybridation entre les AGs et les algorithmes de B&B (HGABB et COBBIGA) bas'es sur cette représentation commune ont été proposées dans cette thèse. Pour validation, une implémentation a été réalisée pour le problème d'affectation quadratique 'a trois dimension (Q3AP). Afin de résoudre de larges instances de ce problème, nous avons aussi propose une parallélisation pour les deux algorithme hybrides, basée sur des techniques de décomposition d'espace (décomposition par intervalle) utilisées auparavant pour la parallélisation des algorithmes de B&B. Du point de vue implémentation, afin de faciliter de futurs conceptions et implémentations de méthodes hybrides combinant metaheuristiques et méthodes exacte arborescentes, nous avons développe une plateforme d'hybridation intégrée au logiciel pour metaheuristiques, ParadisEO. La nouvelle plateforme a été utilisée pour réaliser des expérimentations intensives sur la grille de calcul Grid'5000.

A metaheuristic is a generic algorithmic template that, once properly instantiated, can be used for finding high quality solutions of combinatorial optimization problems.

For obtaining a fully functioning algorithm, a metaheuristic needs to be configured: typically some modules need to be instantiated and some parameters need to be tuned. For the sake of precision, we use the expression parametric tuning for referring to the tuning of numerical parameters, either continuous or discrete but in any case ordinal.

On the other hand, we use the expression structural tuning for referring to the problem of defining which modules should be included and, in general, to the problem of tuning parameters that are either boolean or categorical. Finally, with tuning we refer to the composite structural and parametric tuning.

Tuning metaheuristics is a very sensitive issue both in practical applications and in academic studies. Nevertheless, a precise definition of the tuning problem is missing in the literature. In this thesis, we argue that the problem of tuning a metaheuristic can be profitably described and solved as a machine learning problem.

Indeed, looking at the problem of tuning metaheuristics from a machine learning perspective, we are in the position of giving a formal statement of the tuning problem and to propose an algorithm, called F-Race, for tackling the problem itself. Moreover, always from this standpoint, we are able to highlight and discuss some catches and faults in the current research methodology in the metaheuristics field, and to propose some guidelines.

The thesis contains experimental results on the use of F-Race and some examples of practical applications. Among others, we present a feasibility study carried out by the German-based software company SAP, that concerned the possible use of F-Race for tuning a commercial computer program for vehicle routing and scheduling problems. Moreover, we discuss the successful use of F-Race for tuning the best performing algorithm submitted to the International Timetabling Competition organized in 2003 by the Metaheuristics Network and sponsored by PATAT, the international series of conferences on the Practice and Theory of Automated Timetabling.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

Neste trabalho é apresentada uma nova abordagem de algoritmo evolutivo multiobjetivo, denominado MOEA/NSM (do inglês, Multiobjective Evolutionary Algorithm integrating NSGA-II, SPEA2 and MOEA/D features). O algoritmo preserva em geral, características de um algoritmo evolutivo, concentrando qualidades de outras abordagens de sucesso na literatura em uma única abordagem, para que elas trabalhem em conjunto, por meio de subpopulações. O objetivo do estudo foi combinar as principais características dos algoritmos NSGA-II, SPEA2 e MOEA/D, e incluir ainda uma técnica de busca local para melhorar a busca no espaço de objetivos. O algoritmo MOEA/NSM foi comparado às demais abordagens clássicas utilizando 9 datasets para o problema do caixeiro viajante biobjetivo. Além disso, foram realizados experimentos aplicando também a busca local nas abordagens clássicas, resultando em considerável melhora nos resultados para esses algoritmos. A partir das fronteiras de Pareto resultantes dos experimentos, foram aplicadas as métricas de avaliação por Hipervolume, Epsilon (ε), R2, EAF, além do teste de hipótese estatístico Shapiro-Wilk. Os resultados apontaram um melhor desempenho do MOEA/NSM em relação aos demais, mesmo aplicando a busca local nas outras abordagens. Nesse sentido, o MOEA/NSM pode ser considerado um algoritmo que consegue encontrar soluções não denominadas de qualidade, tanto quanto os algoritmos clássicos da literatura.
This work presents a new approach to the multiobjective evolutionary algorithm, called MOEA/NSM (Multiobjective Evolutionary Algorithm integrating NSGA-II, SPEA2 and MOEA/D features). The algorithm preserves, in general, the characteristics of an evolutionary algorithm, concentrating qualities of other approaches of success in the literature in a single approach, so that they work together, through subpopulations. The objective of the study was to combine the main characteristics of the NSGA-II, SPEA2 and MOEA/D algorithms, and also to include a local search technique to improve the objective space search. The MOEA/NSM algorithm was compared to the other classical approaches using 9 datasets for the biobjective traveling salesman problem. In addition, experiments were carried out also applying the local search in the classical approaches, resulting in a considerable improvement in the results for these algorithms. From the Pareto frontiers resulting from experiments, we applied the evaluation metrics by Hypervolume, Epsilon (ε), R2, EAF, in addition to the Shapiro-Wilk statistical hypothesis test. The results showed a better performance of the MOEA/NSM in relation to the others, even applying the local search in the others approaches. In this sense, the MOEA/NSM can be considered an algorithm that is able to find solutions not dominated of quality, as much as the classic algorithms of the literature.

CAPES
Este trabalho propõe uma modificação da meta-heurística Busca Harmônica (HS) a partir de uma nova abordagem baseada em população, empregando, também, algumas estratégias inspiradas em outras meta-heurísticas. Este novo modelo foi implementado utilizando a arquitetura de programação paralela CUDA em uma GPU. O uso de placas de processamento gráficas (GPU) para processamento de propósito geral está crescendo, e estas têm sido utilizadas por muitos pesquisadores para processamento científico. Seu uso se mostra interessante para meta-heurísticas populacionais, podendo realizar muitas operações simultaneamente. A HS é uma meta-heurística inspirada no objetivo de um músico em buscar uma harmonia perfeita. modelo proposto incluiu-se uma população de harmonias temporárias que são geradas a cada nova iteração, permitindo a realização simultânea de diversas avaliações de função. Assim aumenta-se o grau de paralelismo da HS, possibilitando maiores ganhos de velocidade com o uso de arquiteturas paralelas. O novo modelo proposto executado em GPU foi denominado Mega Harmony Search (MHS). Na implementação em GPU cada passo do algoritmo é tratado individualmente em forma de kernels com configurações particulares para cada um. Para demonstrar a eficácia do modelo proposto foram selecionados alguns problemas de benchmark, como a otimização de estruturas de proteínas, a otimização de treliças e problemas matemáticos. Através de experimentos fatoriais foi identificado um conjunto de parâmetros padrão, o qual foi utilizado nos outros experimentos. As análises realizadas sobre resultados experimentais mostram que o MHS apresentou solução de qualidade equivalente à HS e ganhos de velocidade, com a sua execução em GPU, superiores a 60x quando comparado a implementação em CPU. Em trabalhos futuros poderão ser estudadas novas modificações ao algoritmo, como a implementação de nichos e estudos de estratégias de interação entre eles.
This work propose a new approach for the metaheuristic Harmonic Search (HS), by using a population of solutiona and other strategies inspired in another metaheuristics. This new model was implemented using a parallel architecture of a graphical processing unity (GPU). The use of GPU for general-purpose processing is growing, specially for scientific processing. Its use is particularly interesting for populational metaheuristics, where multiple operations are executed simultaneously. The HS is a metaheuristic inspired by the way jazz musicians search for a perfect harmony. In the proposed model a population of temporary harmonies was included. Such population was generated at each iteration, enabling simultaneous evaluation of the objective function being optimized, and thus, increasing the level of parallelism of HS. The new approach implemented in GPU was named Mega Harmony Search (MHS), and each step of the algorithm is handled in the form of kernels with particular configurations for each one. To show the efficiency of MHS some benchmark problems were selected for testing, including mathematical optimization problems, protein structure prediction, and truss structure optimization. Factorial experiments were done so as to find the best set of parameters for the MHS. The analyzes carried out on the experimental results show that the solutions provided by MHS have comparable quality to those of the simple Harmony Search. However, by using GPU, MHS achieved a speedup of 60x, compared with the implementation in regular CPU. Future work will focus other improvements in the algorithm, such as the use of niches and species, as well a study of the interactions between them.

CNPq
A Transgenética Computacional é uma metáfora para o desenvolvimento de algoritmos evolucionários com base na teoria de evolução endossimbiótica e em outras interações do fluxo intracelular. Diversos algoritmos foram desenvolvidos com base nesta metáfora para problemas de Otimização Combinatória, em sua maioria com um único objetivo, obtendo bons resultados. Uma vez que a consideração de mais de um objetivo leva, em geral, a representações mais realistas de problemas práticos complexos, neste trabalho investiga-se o desenvolvimento de Algoritmos Transgenéticos para problemas multiobjetivo. Tais algoritmos são examinados em versões que utilizam elementos de outros algoritmos evolucionários multiobjetivo sendo eles o NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) e o MOEA/D (Multi-objective Evolutionary Algorithm based on Decomposition). Diante disso, este trabalho propõe duas novas metodologias utilizando a Transgenética Computacional acoplada ao NSGA-II e ao MOEA/D, denominadas NSTA (Non-Dominated Sorting Transgenetic Algorithm) e MOTA/D (Multi-objective Transgenetic Algorithm based on Decomposition), respectivamente. Para avaliar o desempenho das técnicas propostas, os algoritmos desenvolvidos foram aplicados a dois problemas de Otimização Combinatória, NP-difíceis,em versões com mais de um objetivo. O primeiro problema é o Caixeiro Comprador Biobjetivo e o segundo o Quadrático de Alocação multiobjetivo. Foram realizados experimentos com casos de teste disponíveis em bancos utilizados comumente por outros trabalhos da literatura. Os resultados dos algoritmos propostos foram comparados com os resultados obtidos com os algoritmos evolucionários multiobjetivo que os inspiraram. A análise dos dados obtidos com os experimentos computacionais mostram que a versão MOTA/D é a mais eficiente dentre os algoritmos do experimento com relação a qualidade da aproximação da fronteira de Pareto.
The Computational Transgenetic is a metaphor for the development of evolutionary algorithms based on the theory of evolution endosymbiotic and other intracellular interactions flow. Several algorithms have been developed based on this metaphor for combinatorial optimization problems, mostly with a single objective, obtaining good results. Once the account of more than one objective provides, in general, more realistic representations of complex practical problems, this work investigates the development of Transgenetic Algorithms for multiobjective problems. Such algorithms are examined in versions that use elements of other multiobjective evolutionary algorithms such as the NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) and the MOEA/D (Multi-objective Evolutionary Algorithm based on Decomposition). Therefore, this work proposes two new methods using Computational Transgenetic attached to NSGA-II and MOEA/D, named NSTA (Non-Dominated Sorting Transgenetic Algorithm) and MOTA/D (Multi-objective Transgenetic Algorithm based on Decomposition), respectively. To evaluate the proposed techniques performance, the experiments consider two NP-hard combinatorial optimization problems, in versions with more than one objective. The first problem is the Traveling Purchaser Problem and the second the Quadratic Assignment Problem. Experiments were performed with test cases available in benchmarks commonly used by other studies in the literature. The proposed algorithms' results were compared with those obtained by the multiobjetive evolutionary algorithms that inspired them. The analysis of data obtained by the computational experiment shows that the version MOTA/D is among the most efficient algorithms of the experiment with respect to the quality of the Pareto front approximation.

A Inteligência de Enxame (Swarm Intelligence) é uma área de estudos que busca soluções para problemas de otimização utilizando-se de técnicas computacionais inspiradas no comportamento social emergente encontrado na biologia. A metaheurística Particle Swarm Optimization (PSO) é relativamente nova e foi inspirada no comportamento social de bandos de pássaros. PSO tem apresentado bons resultados em alguns trabalhos recentes de otimização discreta, apesar de ter sido concebido originalmente para a otimização de problemas contínuos. Este trabalho trata o Problema de Atribuição de Tarefas - Task Assignment Problem (TAP), e apresenta uma aplicação: o problema de alocação de táxis e clientes, cujo objetivo da otimização está em minimizar a distância percorrida pela frota. Primeiramente, o problema é resolvido em um cenário estático, com duas versões do PSO discreto: a primeira abordagem é baseada em codificação binária e a segunda utiliza permutações para codificar as soluções. Os resultados obtidos mostram que a segunda abordagem é superior à primeira em termos de qualidade das soluções e tempo computacional, e é capaz de encontrar as soluções ótimas para o problema nas instâncias para as quais os valores ótimos são conhecidos. A partir disto, o algoritmo é adaptado para a otimização do problema em um ambiente dinâmico, com a aplicação de diferentes estratégias de resposta às mudanças. Os novos resultados mostram que a combinação de algumas abordagens habilita o algoritmo PSO a obter boas soluções ao longo da ocorrência de mudanças nas variáveis de decisão problema, em todas as instâncias testadas, com diferentes tamanhos e escalas de mudança.
Swarm Intelligence searches for solutions to optimization problems using computational techniques inspired in the emerging social behavior found in biology. The metaheuristic Particle Swarm Optimization (PSO) is relatively new and can be considered a metaphor of bird flocks. PSO has shown good results in some recent works of discrete optimization, despite it has been originally designed for continuous optimization problems. This paper deals with the Task Assignment Problem (TAP), and presents an application: the optimization problem of allocation of taxis and customers, whose goal is to minimize the distance traveled by the fleet. The problem is solved in a static scenario with two versions of the discrete PSO: the first approach that is based on a binary codification and the second one which uses permutations to encode the solution. The obtained results show that the second approach is superior than the first one in terms of quality of the solutions and computational time, and it is capable of achieving the known optimal values in the tested instances of the problem. From this, the algorithm is adapted for the optimization of the problem in a dynamic environment, with the application of different strategies to respond to changes. The new results show that some combination of approaches enables the PSO algorithm to achieve good solutions along the occurrence of changes in decision variables problem, in all instances tested, with different sizes and scales of change.

In ant societies, and, more in general, in insect societies, the activities of the individuals, as well as of the society as a whole, are not regulated by any explicit form of centralized control. On the other hand, adaptive and robust behaviors transcending the behavioral repertoire of the single individual can be easily observed at society level. These complex global behaviors are the result of self-organizing dynamics driven by local interactions and communications among a number of relatively simple individuals.

The simultaneous presence of these and other fascinating and unique characteristics have made ant societies an attractive and inspiring model for building new algorithms and new multi-agent systems. In the last decade, ant societies have been taken as a reference for an ever growing body of scientific work, mostly in the fields of robotics, operations research, and telecommunications.

Among the different works inspired by ant colonies, the Ant Colony Optimization metaheuristic (ACO) is probably the most successful and popular one. The ACO metaheuristic is a multi-agent framework for combinatorial optimization whose main components are: a set of ant-like agents, the use of memory and of stochastic decisions, and strategies of collective and distributed learning.

It finds its roots in the experimental observation of a specific foraging behavior of some ant colonies that, under appropriate conditions, are able to select the shortest path among few possible paths connecting their nest to a food site. The pheromone, a volatile chemical substance laid on the ground by the ants while walking and affecting in turn their moving decisions according to its local intensity, is the mediator of this behavior.

All the elements playing an essential role in the ant colony foraging behavior were understood, thoroughly reverse-engineered and put to work to solve problems of combinatorial optimization by Marco Dorigo and his co-workers at the beginning of the 1990's.

From that moment on it has been a flourishing of new combinatorial optimization algorithms designed after the first algorithms of Dorigo's et al. and of related scientific events.

In 1999 the ACO metaheuristic was defined by Dorigo, Di Caro and Gambardella with the purpose of providing a common framework for describing and analyzing all these algorithms inspired by the same ant colony behavior and by the same common process of reverse-engineering of this behavior. Therefore, the ACO metaheuristic was defined a posteriori, as the result of a synthesis effort effectuated on the study of the characteristics of all these ant-inspired algorithms and on the abstraction of their common traits.

The ACO's synthesis was also motivated by the usually good performance shown by the algorithms (e.g. for several important combinatorial problems like the quadratic assignment, vehicle routing and job shop scheduling, ACO implementations have outperformed state-of-the-art algorithms).

The definition and study of the ACO metaheuristic is one of the two fundamental goals of the thesis. The other one, strictly related to this former one, consists in the design, implementation, and testing of ACO instances for problems of adaptive routing in telecommunication networks.

This thesis is an in-depth journey through the ACO metaheuristic, during which we have (re)defined ACO and tried to get a clear understanding of its potentialities, limits, and relationships with other frameworks and with its biological background. The thesis takes into account all the developments that have followed the original 1999's definition, and provides a formal and comprehensive systematization of the subject, as well as an up-to-date and quite comprehensive review of current applications. We have also identified in dynamic problems in telecommunication networks the most appropriate domain of application for the ACO ideas. According to this understanding, in the most applicative part of the thesis we have focused on problems of adaptive routing in networks and we have developed and tested four new algorithms.

Adopting an original point of view with respect to the way ACO was firstly defined (but maintaining full conceptual and terminological consistency), ACO is here defined and mainly discussed in the terms of sequential decision processes and Monte Carlo sampling and learning.

More precisely, ACO is characterized as a policy search strategy aimed at learning the distributed parameters (called pheromone variables in accordance with the biological metaphor) of the stochastic decision policy which is used by so-called ant agents to generate solutions. Each ant represents in practice an independent sequential decision process aimed at constructing a possibly feasible solution for the optimization problem at hand by using only information local to the decision step.

Ants are repeatedly and concurrently generated in order to sample the solution set according to the current policy. The outcomes of the generated solutions are used to partially evaluate the current policy, spot the most promising search areas, and update the policy parameters in order to possibly focus the search in those promising areas while keeping a satisfactory level of overall exploration.

This way of looking at ACO has facilitated to disclose the strict relationships between ACO and other well-known frameworks, like dynamic programming, Markov and non-Markov decision processes, and reinforcement learning. In turn, this has favored reasoning on the general properties of ACO in terms of amount of complete state information which is used by the ACO's ants to take optimized decisions and to encode in pheromone variables memory of both the decisions that belonged to the sampled solutions and their quality.

The ACO's biological context of inspiration is fully acknowledged in the thesis. We report with extensive discussions on the shortest path behaviors of ant colonies and on the identification and analysis of the few nonlinear dynamics that are at the very core of self-organized behaviors in both the ants and other societal organizations. We discuss these dynamics in the general framework of stigmergic modeling, based on asynchronous environment-mediated communication protocols, and (pheromone) variables priming coordinated responses of a number of ``cheap' and concurrent agents.

The second half of the thesis is devoted to the study of the application of ACO to problems of online routing in telecommunication networks. This class of problems has been identified in the thesis as the most appropriate for the application of the multi-agent, distributed, and adaptive nature of the ACO architecture.

Four novel ACO algorithms for problems of adaptive routing in telecommunication networks are throughly described. The four algorithms cover a wide spectrum of possible types of network: two of them deliver best-effort traffic in wired IP networks, one is intended for quality-of-service (QoS) traffic in ATM networks, and the fourth is for best-effort traffic in mobile ad hoc networks.

The two algorithms for wired IP networks have been extensively tested by simulation studies and compared to state-of-the-art algorithms for a wide set of reference scenarios. The algorithm for mobile ad hoc networks is still under development, but quite extensive results and comparisons with a popular state-of-the-art algorithm are reported. No results are reported for the algorithm for QoS, which has not been fully tested. The observed experimental performance is excellent, especially for the case of wired IP networks: our algorithms always perform comparably or much better than the state-of-the-art competitors.

In the thesis we try to understand the rationale behind the brilliant performance obtained and the good level of popularity reached by our algorithms. More in general, we discuss the reasons of the general efficacy of the ACO approach for network routing problems compared to the characteristics of more classical approaches. Moving further, we also informally define Ant Colony Routing (ACR), a multi-agent framework explicitly integrating learning components into the ACO's design in order to define a general and in a sense futuristic architecture for autonomic network control.

Most of the material of the thesis comes from a re-elaboration of material co-authored and published in a number of books, journal papers, conference proceedings, and technical reports. The detailed list of references is provided in the Introduction.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

Orientador: Arnaldo Vieira Moura
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
Made available in DSpace on 2018-08-09T20:48:39Z (GMT). No. of bitstreams: 1 Ferber_DanielFelix_M.pdf: 2571168 bytes, checksum: 373e2b3bb3f1ca3735beb4c4303dc5d9 (MD5) Previous issue date: 2007
Resumo: O principal objetivo deste trabalho é a elaboração de heurísticas para auxiliar no projeto de cabeamento de redes telefônicas. O cabeamento será tratado desde os armários de distribuição até as caixas terminais. O auxílio de uma ferramenta computacional especializada no projeto de novas redes telefônicas abre caminhos para a minimização de custos e também reduz sensivelmente o tempo de planejamento. Inicialmente, estuda-se o problema para se obter uma especificação minuciosa, acompanhada de um modelo matemático. Com estas informações, desenvolve-se diferentes estratégias para algoritmos baseados na heurística GRASP, e compara-se os resultados experimentais obtidos
Abstract: The main goal of these studies is the design of heuristics to support the planning of wire cabling on a phone network. The cabling will be handled from the central distribution point to terminal boxes. The assistance of a computational tool specialized in the design of phone networks raises new opportunities for cost reduction and decreases considerably the time spent designing the network. The problem is first studied in order to achieve a detailed specification with a mathematical model. Based on this information, several different strategies are laid out based on a heuristic called GRASP and the experimental results are compared.
Mestrado
Otimização Combinatoria
Mestre em Computação

L’optimització combinatòria és un tipus específic d’optimització matemàtica on el domini de les variables és discret. Aquest tipus de problemes d’optimització tenen una gran aplicabilitat degut a la seva capacitat d’optimització sobre objectes unitaris i no divisibles. Més enllà dels algoritmes genèrics, la comunitat investigadora és molt activa proposant algorismes capaços d’abordar problemes d’optimització combinatòria per a problemes específics. L’objectiu d’aquesta tesi és investigar com ampliar l’aplicabilitat d’algorismes d’optimització combinatoria que exploten l’estructura dels problemes a resoldre. Ho fem des de la perspectiva del maquinari d’una computadora, perseguint l’explotació total dels recursos computacionals que ofereix el maquinari actual. Per assolir generalitat treballem amb tres problemes diferents. Primer abordem el problema de generació d’estructures de la coalició (CSGP). Trobem que l’algorisme d’última generació és IDP. Proposem un algoritme optimitzat i paral·lel capaç de resoldre el CSGP. Aconseguim això definint un nou mètode per dur a terme l’operació més crítica -Splitting-, així com definint un nou mètode per dividir l’operació de l’algoritme en els diferent subprocessos. A continuació, estudiem el problema de determinació del guanyador (WDP) per a les subhastes combinades (CA). Trobem que l’escalabilitat dels solucionadors d’avantguarda és limitada. Més concretament, mostrem com millorar la resolució de resultats de relaxació LP per al WDP en subhastes combinables de gran escala mitjançant l’aplicació de l’algoritme AD³. A continuació, contribuïm amb una versió optimitzada d’AD³ que també es pot executar en un escenari paral·lel de memòria compartida. Finalment, estudiem l’aplicació de AD³ per resoldre les relaxacions LP d’un problema més exigent de la computacionalment: El problema de la predició de cadenes laterals (SCP). Presentem una manera optimitzada de resoldre l’operació més crítica, la resol·lució d’un problema quadràtic per a un factor arbitrari. En tots els casos proposem algoritmes optimitzats que es poden escalar de forma paral·lela i que milloren notablement l’estat de la tècnica. Tres ordres de magnitud a IDP, i un ordre de magnitud a AD³. L’objectiu final d’aquest treball és demostrar com un disseny algorisme conscient de maquinari pot conduir a millores de rendiment significatives. Mostrem estratègies exportables a algorismes d’optimització combinatòria similars. Aquestes estratègies ajudaran al dissenyador d’algorismes a assolir més eficiència en les CPU modernes.
La optimización combinatoria es un tipo específico de optimización donde el dominio de las variables es discreto. Este tipo de problemas de optimización tienen una gran aplicabilidad debido a su capacidad de optimización sobre objetos unitarios y no divisibles. Más allá de los algoritmos genéricos, la comunidad investigadora es muy activa proponiendo algoritmos capaces de abordar problemas de optimización combinatoria para problemas específicos. El objetivo de esta tesis es investigar cómo ampliar la aplicabilidad de algoritmos de optimización combinatoria que explotan la estructura de los problemas a resolver. Lo hacemos desde la perspectiva del hardware de una computadora, persiguiendo la explotación total de los recursos computacionales que ofrece el hardware actual. Para alcanzar generalidad trabajamos con tres problemas diferentes. Primero abordamos el problema de generación de estructuras de la coalición (CSGP). Encontramos que el algoritmo de última generación es IDP. Proponemos un algoritmo optimizado y paralelo capaz de resolver el CSGP. Conseguimos esto deniendo un nuevo metodo para llevar a cabo la operacion mas crtica -Splitting-, así como deniendo un nuevo método para dividir la operación del algoritmo en los diferente subprocesos. A continuación, estudiamos el problema de determinación del ganador (WDP) para las subastas combinatorias (CA). Encontramos que la escalabilidad de los solucionadores de vanguardia es limitada. Más concretamente, mostramos cómo mejorar la resolución de resultados de relajación LP para el WDP en subastas combinatorias de gran escala mediante la aplicación del algoritmo AD³. A continuación, contribuimos con una versión optimizada de AD³ que también se puede ejecutar en un escenario paralelo de memoria compartida. Finalmente, estudiamos la aplicación de AD³ para resolver las relajaciones LP de un problema más exigente de la computacionalmente: El problema de la predición de cadenas laterales (SCP). Presentamos una manera optimizada de resolver la operación más crítica, la resolución de un problema cuadrático para un factor arbitrario. En todos los casos proponemos algoritmos optimizados que se pueden escalar de forma paralela y que mejoran notablemente el estado de la técnica. Tres órdenes de magnitud en IDP, y un orden de magnitud en AD³. El objetivo nal de este trabajo es demostrar como un diseño algoritmo consciente de hardware puede conducir a mejoras de rendimiento signicativas. Mostramos estrategias exportables a algoritmos de optimización combinatoria similares. Estas estrategias ayudarán al diseñador de algoritmos lograr más eficiencia en las CPU modernas.
Combinatorial Optimization is a specific type of mathematical optimization where variables' domain is discrete. This kind of optimization problems have an enormous applicability due to its ability to optimize over unitary and non-divisible objects. Beyond generic algorithms, the research community is very active proposing algorithms able to tackle specific combinatorial optimization problems. The goal of this thesis is to investigate how to widen the applicability of Combinatorial Optimization algorithms that exploit the structure of the problems to solve. We do so from a computer's hardware perspective, pursuing the full exploitation of computational resources offered by today's hardware. For the sake of generality we work on three different problems. First we tackle the Coalition Structure Generation Problem (CSGP). We find that the state-of-the-art algorithm is IDP. We propose an optimized and parallel algorithm able to solve the CSGP. We reach this by defining a novel method to perform the most critical operation --Splitting-- as well as by defining a novel method to divide the the algorithm's operation in threads. Then, we study the Winner Determination Problem (WDP) for Combinatorial Auctions (CA), which is very related to the CSGP. We find that state-of-the-art solvers' scalability is limited. More specifically we show how to improve results solving LP relaxations for the WDP in Large Scale Combinatorial Auctions by applying the AD³ algorithm. Then we contribute with an optimized version of AD³ which is also able to run in a shared-memory parallel scenario. Finally we study the application of AD³ to solve the LP relaxations of a more CPU demanding problem: The Side-Chain Prediction (SCP). We present an optimized way to solve the most critical operation which is solving a Quadratic Problem for an Arbitrary Factor. In all the cases we propose optimized algorithms that are scalable in parallel and that improve significantly the state-of-the-art. Three orders of magnitude speedup on IDP, one order of magnitude speedup in AD³. The ultimate purpose of this work is to demonstrate how a hardware-aware algorithmic design can lead to significant speedups. We show strategies that are exportable to similar Combinatorial Optimization algorithms. Such strategies will help the algorithm designer to achieve more efficiency in modern CPUs.

Combinatorial Optimization is becoming ever more crucial, in these days. From natural sciences to economics, passing through urban centers administration and personnel management, methodologies and algorithms with a strong theoretical background and a consolidated real-word effectiveness is more and more requested, in order to find, quickly, good solutions to complex strategical problems. Resource optimization is, nowadays, a fundamental ground for building the basements of successful projects. From the theoretical point of view, Combinatorial Optimization rests on stable and strong foundations, that allow researchers to face ever more challenging problems. However, from the application point of view, it seems that the rate of theoretical developments cannot cope with that enjoyed by modern hardware technologies, especially with reference to the one of processors industry. In this work we propose new parallel algorithms, designed for exploiting the new parallel architectures available on the market. We found that, exposing the inherent parallelism of some resolution techniques (like Dynamic Programming), the computational benefits are remarkable, lowering the execution times by more than an order of magnitude, and allowing to address instances with dimensions not possible before. We approached four Combinatorial Optimization’s notable problems: Packing Problem, Vehicle Routing Problem, Single Source Shortest Path Problem and a Network Design problem. For each of these problems we propose a collection of effective parallel solution algorithms, either for solving the full problem (Guillotine Cuts and SSSPP) or for enhancing a fundamental part of the solution method (VRP and ND). We endorse our claim by presenting computational results for all problems, either on standard benchmarks from the literature or, when possible, on data from real-world applications, where speed-ups of one order of magnitude are usually attained, not uncommonly scaling up to 40 X factors.

Cette thèse s'inscrit dans le domaine de l'optimisation combinatoire. Elle utilise l'approche polyèdrale pour résoudre des problèmes combinatoires qui se posent dans le contexte des réseaux de télécommunications. Nous introduisons et étudions le problème de synthèse de réseaux à composantes connexes unicycliques. Après avoir rappelé que le problème est facile à résoudre en absence d'autres contraintes, nous étudions de nouvelles variantes en intégrant de nouvelles contraintes techniques. Nous commençons par une contrainte portant sur la taille des cycles. Nous souhaitons interdire tous les cycles contenant au plus p sommets. Le problème est alors NP-Difficile. Des inégalités valides sont alors proposées pour ce problème. On montre sous des conditions bien précises que ces inégalités peuvent être des facettes. Plusieurs algorithmes polynomiaux ont été proposés pour la séparation des inégalités valides. Ces algorithme sont mis en oeuvre et des résultats numériques sont donnés. Nous nous focalisons par la suite sur un nouveau problème dit de Steiner consistant à partitionner un réseau en composantes unicycliques tout en imposant que certains sommets soient sur les cycles. On montre alors que ce problème est facile au sens de la complexité algorithmique en proposant un algorithme polynomial et une formulation étendue du problème. On présente également une description partielle de l'enveloppe convexe des vecteurs d'incidence de ces réseaux. La séparation des inégalités est également étudiée. Nous proposons notamment une généralisation de l'algorithme de Padberg-Rao pour séparer les inégalités Blossom. D'autres contraintes techniques sont prises en compte : contraintes de degrés, contrainte sur le nombre de composantes connexes, appartenance de certains sommets à une même composante connexe et enfin la séparation de certains sommets qui doivent être sur des composantes différentes. Enfin, nous faisons une étude spectrale de deux classes spécifiques de graphes unicycliques. Mots clés : Optimisation Combinatoire, Polyèdres, Algorithme à Plans Coupants, Graphes

Due to the complexity of multi-objective combinatorial optimization problems (MOCO), metaheuristics like multi-objective evolutionary algorithms (MOEA) are gaining importance to obtain a well-converged and well-dispersed Pareto-optimal frontier approximation. In this study, of the well-known MOCO problems, single-dimensional multi-objective knapsack problem and multi-objective assignment problem are taken into consideration. We develop a steady-state and elitist MOEA in order to approximate the Pareto-optimal frontiers. We utilize a territory concept in order to provide diversity over the Pareto-optimal frontiers of various problem instances. The motivation behind the territory definition is to attach the algorithm the advantage of fast execution by eliminating the need for an explicit diversity preserving operator. We also develop an interactive preference incorporation mechanism to converge to the regions that are of special interest for the decision maker by interacting with him/her during the optimization process.

Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Computer Science. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 443-458).
In this thesis, we revisit three algorithmic techniques: sparsification, cutting and collapsing. We use them to obtain the following results on convex and combinatorial optimization: --Linear Programming: We obtain the first improvement to the running time for linear programming in 25 years. The convergence rate of this randomized algorithm nearly matches the universal barrier for interior point methods. As a corollary, we obtain the first ... time randomized algorithm for solving the maximum flow problem on directed graphs with m edges and n vertices. This improves upon the previous fastest running time of achieved over 15 years ago by Goldberg and Rao. --Maximum Flow Problem: We obtain one of the first almost-linear time randomized algorithms for approximating the maximum flow in undirected graphs. As a corollary, we improve the running time of a wide range of algorithms that use the computation of maximum flows as a subroutine. --Non-Smooth Convex Optimization: We obtain the first nearly-cubic time randomized algorithm for convex problems under the black box model. As a corollary, this implies a polynomially faster algorithm for three fundamental problems in computer science: submodular function minimization, matroid intersection, and semidefinite programming. --Graph Sparsification: We obtain the first almost-linear time randomized algorithm for spectrally approximating any graph by one with just a linear number of edges. This sparse graph approximately preserves all cut values of the original graph and is useful for solving a wide range of combinatorial problems. This algorithm improves all previous linear-sized constructions, which required at least quadratic time. --Numerical Linear Algebra: Multigrid is an efficient method for solving large-scale linear systems which arise from graphs in low dimensions. It has been used extensively for 30 years in scientific computing. Unlike the previous approaches that make assumptions on the graphs, we give the first generalization of the multigrid that provably solves Laplacian systems of any graphs in nearly-linear expected time.
by Yin Tat Lee.
Ph. D.

In this thesis we present some combinatorial optimization problems, suggest models and algorithms for their effective solution. For each problem,we give its description, followed by a short literature review, provide methods to solve it and, finally, present computational results and comparisons with previous works to show the effectiveness of the proposed approaches. The considered problems are: the Generalized Traveling Salesman Problem (GTSP), the Bin Packing Problem with Conflicts(BPPC) and the Fair Layout Problem (FLOP).

De nos jours, il est peu de processus ou de tâches qui ne requièrent pas l'optimisation d'une quantité :diminuer le temps de livraison, diminuer l'espace utilisé, réduire les efforts de développement, C'est donc sans surprise que la recherche en optimisation soit l'un des domaines les plus actifs des sciences des technologies de l'information. En optimisation combinatoire, les métaheuristiques sont à compter parmi le fleuron des techniques algorithmiques. Mais ce succès est encore au prix d'une quantité significative de temps de conception et développement. Ne serait-il pas possible d'aller encore plus loin ?D'automatiser la préparation des métaheuristiques ?En particulier dans des conditions telles le manque de temps, l'ignorance de techniques spécialisées ou encore la mauvaise compréhension du problème traité ?C'est ce à quoi nous répondons dans la présente thèse au moyen d'une approche de méta-modélisation de la recherche :l'heuristique de la Gestalt.

Considérant la représentation du problème comme un levier que l'on peut activer sous le processus de recherche mené par une métaheuristique, la thèse suggère la construction d'une abstraction de cette représentation capable d'assister la métaheuristique à trouver de bonnes solutions en contraignant sa recherche. Cette approche, inspirée de la psychologie de la Gestalt, nous l'appelons l'heuristique de la Gestalt. Son fonctionnement repose principalement sur l'agrégation des variables de la représentation. Cette agrégation donne lieu à une abstraction structurelle, mais également fonctionnelle en ce sens que les opérateurs de la métaheuristique doivent désormais respecter l'intégrité des agrégats définis.

Après avoir établi le contexte de la dissertation, nous discutons de la transposition de la psychologie de la Gestalt dans le cadre de l'optimisation combinatoire et des métaheuristiques. S'ensuit la formalisation de l'heuristique de la Gestalt et la description de sa réalisation. Finalement, une série d'études expérimentales sont menées pour éprouver le concept avancé et valider l'implémentation basée sur les algorithmes évolutionnistes que nous proposons. En conclusion, nous affirmons que l'implémentation de l'heuristique de la Gestalt basée, entre autres, sur un algorithme génétique de groupement est capable d'assister positivement des algorithmes génétiques lorsque les instances de problèmes traitées possèdent une structure riche et complexe, que leur taille est importante, que l'on est tôt dans le processus d'optimisation et que l'algorithme génétique n'est pas paramétré spécifiquement.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

This thesis is about the computational complexity of several classes of combinatorial optimization problems, all related to the constraint satisfaction problems. A constraint language consists of a domain and a set of relations on the domain. For each such language there is a constraint satisfaction problem (CSP). In this problem we are given a set of variables and a collection of constraints, each of which is constraining some variables with a relation in the language. The goal is to determine if domain values can be assigned to the variables in a way that satisfies all constraints. An important question is for which constraint languages the corresponding CSP can be solved in polynomial time. We study this kind of question for optimization problems related to the CSPs. The main focus is on extended minimum cost homomorphism problems. These are optimization versions of CSPs where instances come with an objective function given by a weighted sum of unary cost functions, and where the goal is not only to determine if a solution exists, but to find one of minimum cost. We prove a complete classification of the complexity for these problems on three-element domains. We also obtain a classification for the so-called conservative case. Another class of combinatorial optimization problems are the surjective maximum CSPs. These problems are variants of CSPs where a non-negative weight is attached to each constraint, and the objective is to find a surjective mapping of the variables to values that maximizes the weighted sum of satisfied constraints. The surjectivity requirement causes these problems to behave quite different from for example the minimum cost homomorphism problems, and many powerful techniques are not applicable. We prove a dichotomy for the complexity of the problems in this class on two-element domains. An essential ingredient in the proof is an algorithm that solves a generalized version of the minimum cut problem. This algorithm might be of independent interest. In a final part we study properties of NP-hard optimization problems. This is done with the aid of restricted forms of polynomial-time reductions that for example preserves solvability in sub-exponential time. Two classes of optimization problems similar to those discussed above are considered, and for both we obtain what may be called an easiest NP-hard problem. We also establish some connections to the exponential time hypothesis.

本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである
Kyoto University (京都大学)
0048
新制・論文博士
博士(工学)
乙第10101号
論工博第3416号
新制||工||1146(附属図書館)
UT51-99-G578
(主査)教授 茨木 俊秀, 教授 岩間 一雄, 教授 加藤 直樹
学位規則第4条第2項該当