Cache replacement policies have applications that are nearly ubiquitous in technology. Among these is an interesting subset which occurs when referentially transparent functions are memoized, eg. in compilers, in dynamic programming, and other software caches. In many applications the least recently used (LRU) approach likely preserves items most needed by memoized function calls. However, despite its popularity LRU is expensive to implement, which has caused a spate of research initiatives aimed at approximating its cache miss performance in exchange for faster and more memory efficient implementations. We present a novel caching algorithm, Far From Recently Used (FFRU), which offers a simple, but highly configurable mechanism for providing lower bounds on the usage recency of items evicted from the cache. This algorithm preserves the constant time amortized cost of insertions and updates and minimizes the memory overhead needed to administer the eviction guarantees. We study the cache miss performance of several memoized optimization problems which vary in the number of subproblems generated and the access patterns exhibited by their recursive calls. We study their cache miss performance using LRU cache replacement, then show the performance of FFRU in these same problem scenarios. We show that for equivalent minimum eviction age guarantees, FFRU incurs fewer cache misses than LRU, and does so using less memory. We also present some variations of the algorithms studied (Fibonacci, KMP, LCS, and Euclidean TSP) which exploit the characteristics of the cache replacement algorithms being employed, further resulting in improved cache miss performance. We present a novel implementation of a well known approximation algorithm for the Euclidean Traveling Salesman Problem due to Sanjeev Arora. Our implementation of this algorithm outperforms the currently known implementations of the same. It has long remained an open question whether or not algorithms relying on geometric divisions of space can be implemented into practical tools, and our powerful implementation of Arora's algorithm establishes a new benchmark in that arena. / Computer and Information Science

Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist formany problems up to several ten thousand points. Themajor difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-artmethods when applied to TSP instances with non-uniformly distributed coordinates.

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The thesis deals with optimization problems which arise at distribution planning. These problems can often be easily formulated as integer programming problems, but rarely can be solved using mixed integer programming techniques. Therefore, it is necessary to study the efficiency of heuristic algorithms. The main focus of the thesis is on the vehicle routing problem with time windows. A tabu search algorithm for this problem was developed and implemented. It uses integer programming to solve the set partitioning problem in order to find optimal distribution of all customers into feasible routes found during the search. The results of the classical integer programming approach, basic insertion heuristic and presented tabu search algorithm are compared in a numerical study.

Este trabalho realiza uma análise dos modelos pertencentes à Computação Neural e à Computação Evolutiva visando identificar semelhanças entre as áreas e sustentar mapeamentos entre as semelhanças identificadas. Neste contexto, a identificação de similaridades visando à resolução de problemas de otimização combinatorial resulta em uma comparação entre a Máquina de Boltzmann e os Algoritmos Evolutivos binários com população composta por um único indivíduo pai e um único indivíduo descendente. Como forma de auxiliar nas análises, o trabalho utiliza o Problema do Caixeiro Viajante como plataforma de ensaios, propondo mapeamentos entre as equações da Máquina de Boltzmann e os operadores evolutivos da Estratégia Evolutiva (1+1)-ES. / An analysis between the Evolutionary Computation and the Neural Computation fields was presented in order to identify similarities and mappings between the theories. In the analysis, the identification of similarities between the models designed for combinatorial optimization problems results in a comparison between the Boltzmann Machine and the Two-Membered Evolutionary Algorithms. In order to analyze the class of combinatorial optimization problems, this work used the Traveling Salesman Problem as a study subject, where the Boltzmann Machine equations were used to implement the evolutionary operators of an Evolution Strategy (1+1)-ES.

Este trabalho realiza uma análise dos modelos pertencentes à Computação Neural e à Computação Evolutiva visando identificar semelhanças entre as áreas e sustentar mapeamentos entre as semelhanças identificadas. Neste contexto, a identificação de similaridades visando à resolução de problemas de otimização combinatorial resulta em uma comparação entre a Máquina de Boltzmann e os Algoritmos Evolutivos binários com população composta por um único indivíduo pai e um único indivíduo descendente. Como forma de auxiliar nas análises, o trabalho utiliza o Problema do Caixeiro Viajante como plataforma de ensaios, propondo mapeamentos entre as equações da Máquina de Boltzmann e os operadores evolutivos da Estratégia Evolutiva (1+1)-ES. / An analysis between the Evolutionary Computation and the Neural Computation fields was presented in order to identify similarities and mappings between the theories. In the analysis, the identification of similarities between the models designed for combinatorial optimization problems results in a comparison between the Boltzmann Machine and the Two-Membered Evolutionary Algorithms. In order to analyze the class of combinatorial optimization problems, this work used the Traveling Salesman Problem as a study subject, where the Boltzmann Machine equations were used to implement the evolutionary operators of an Evolution Strategy (1+1)-ES.

O problema do caixeiro viajante (PCV) é um problema clássico de otimização que possui diversas variações, aplicações e instâncias. Encontrar a solução ótima para muitas instâncias desse problema é geralmente muito difícil devido o alto custo computacional. Vários métodos de otimização, conhecidos como meta-heurísticas (MHs), são capazes de encontrar boas soluções para o PCV. Muitos algoritmos baseados em diversas MHs têm sido propostos e investigados para diferentes variações do PCV. Como não existe um algoritmo universal que encontre a melhor solução para todas as instâncias de um problema, diferentes MHs podem prover a melhor solução para diferentes instâncias do PCV. Desse modo, a seleção a priori da MH que produza a melhor solução para uma dada instância é uma tarefa difícil. A pesquisa desenvolvida nesta tese investiga o uso de abordagens de meta-aprendizado para selecionar as MHs mais promissoras para novas instâncias de PCV. Essas abordagens induzem meta-modelos preditivos a partir do treinamento das técnicas de aprendizado de máquina em um conjunto de meta-dados. Cada meta-exemplo, em nosso conjunto de meta-dados, representa uma instância de PCV descrita por características (meta-atributos) do PCV e pelo desempenho das MHs (meta-atributo alvo) para essa instância. Os meta-modelos induzidos são usados para indicar os valores do meta-atributo alvo para novas instâncias do PCV. Vários experimentos foram realizados durante a investigação desta pesquisa e resultados importantes foram obtidos / The traveling salesman problem (TSP) is a classical optimization problem that has several variations, applications and instances. To find the optimal solution for many instances of this problem is usually a very hard task due to high computational cost. Various optimization methods, known as metaheuristics (MHs), are capable to generate good solutions for the TSP. Many algorithms based on different MHs have been proposed and investigated for different variations of the TSP. Different MHs can provide the best optimization solution for different TSP instances, since there is no a universal algorithm able to find the best solution for all instances. Thus, a priori selection of the MH that produces the best solution for a given instance is a hard task. The research developed in this thesis investigates the use of meta-learning approaches to select the most promising MHs for new TSP instances. These approaches induce predictive meta-models from the training of machine learning techniques on a set of meta-data. In our meta-data, each meta-example is a TSP instance described by problem characteristics (meta-features) and performance of MHs (target meta-features) for this instance. The induced meta-models are used to indicate the values of the target meta-feature for new TSP instances. During the investigation of this research, several experiments were performed and important results were obtained

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

The work presented in this PhD studies and proposes cellular computation parallel models able to address different types of NP-hard optimization problems defined in the Euclidean space, and their implementation on the Graphics Processing Unit (GPU) platform. The goal is to allow both dealing with large size problems and provide substantial acceleration factors by massive parallelism. The field of applications concerns vehicle embedded systems for stereovision as well as transportation problems in the plane, as vehicle routing problems. The main characteristic of the cellular model is that it decomposes the plane into an appropriate number of cellular units, each responsible of a constant part of the input data, and such that each cell corresponds to a single processing unit. Hence, the number of processing units and required memory are with linear increasing relationship to the optimization problem size, which makes the model able to deal with very large size problems.The effectiveness of the proposed cellular models has been tested on the GPU parallel platform on four applications. The first application is a stereo-matching problem. It concerns color stereovision. The problem input is a stereo image pair, and the output a disparity map that represents depths in the 3D scene. The goal is to implement and compare GPU/CPU winner-takes-all local dense stereo-matching methods dealing with CFA (color filter array) image pairs. The second application focuses on the possible GPU improvements able to reach near real-time stereo-matching computation. The third and fourth applications deal with a cellular GPU implementation of the self-organizing map neural network in the plane. The third application concerns structured mesh generation according to the disparity map to allow 3D surface compressed representation. Then, the fourth application is to address large size Euclidean traveling salesman problems (TSP) with up to 33708 cities.In all applications, GPU implementations allow substantial acceleration factors over CPU versions, as the problem size increases and for similar or higher quality results. The GPU speedup factor over CPU was of 20 times faster for the CFA image pairs, but GPU computation time is about 0.2s for a small image pair from Middlebury database. The near real-time stereovision algorithm takes about 0.017s for a small image pair, which is one of the fastest records in the Middlebury benchmark with moderate quality. The structured mesh generation is evaluated on Middlebury data set to gauge the GPU acceleration factor and quality obtained. The acceleration factor for the GPU parallel self-organizing map over the CPU version, on the largest TSP problem with 33708 cities, is of 30 times faster.

The tree-width and branch-width of a graph are two well-studied examples of parameters that measure how well a given graph can be decomposed into a tree structure. In this thesis we give several results and applications concerning these concepts, in particular if the graph is embedded on a surface. In the first part of this thesis we develop a geometric description of tangles in graphs embedded on a fixed surface (tangles are the obstructions for low branch-width), generalizing a result of Robertson and Seymour. We use this result to establish a relationship between the branch-width of an embedded graph and the carving-width of an associated graph, generalizing a result for the plane of Seymour and Thomas. We also discuss how these results relate to the polynomial-time algorithm to determine the branch-width of planar graphs of Seymour and Thomas, and explain why their method does not generalize to surfaces other than the sphere. We also prove a result concerning the class C_2k of minor-minimal graphs of branch-width 2k in the plane, for an integer k at least 2. We show that applying a certain construction to a class of graphs in the projective plane yields a subclass of C_2k, but also show that not all members of C_2k arise in this way if k is at least 3. The last part of the thesis is concerned with applications of graphs of bounded tree-width to the Traveling Salesman Problem (TSP). We first show how one can solve the separation problem for comb inequalities (with an arbitrary number of teeth) in linear time if the tree-width is bounded. In the second part, we modify an algorithm of Letchford et al. using tree-decompositions to obtain a practical method for separating a different class of TSP inequalities, called simple DP constraints, and study their effectiveness for solving TSP instances.