The work proposed in this dissertation is the field of combinatorial optimization, which aims to find a solution to these types of problems at a low computational time and effectively. The combinatorial optimization studies a set of discrete solutions, which have a finite number of elements, to find the best viable solution to the problems of this magnitude. One of the main approaches that area is the Traveling Salesman Problem (TSP), mainly due to the size of possible solutions to the problem, so that is intractable computation by exhaustive search methods. Given all these features, this work is to study and develop evolutionary strategies for the resolution of the Problem of Traveling Salesman with Heterogeneous Demands (TSPHD), a variation of the classic TSP. The evolutionary strategies belong to the class of evolutionary computation, and methods of search based on the theory of the evolution of species, where the best individuals compete for survival. The evolutionary strategies differ from other optimization techniques, as the search is conducted in a population of solutions, not a single point. To solve the problem are proposed four evolutionary algorithms, using heuristics techniques and metaheurísticas for its implementation. The results were obtained from tests using instances of low density (low connection), and compared with the exact solution (optimal solution) and other progressive methods in the literature. These results are evaluated on the basis of their quality and time for its implementation. / O trabalho proposto nessa dissertação pertence à área de otimização combinatória, a qual visa encontrar uma solução para esses tipos de problema em um tempo computacional baixo e de forma eficaz. A otimização combinatória estuda um conjunto discreto de soluções, os quais possuem um número finito de elementos, para se poder encontrar a melhor solução viável para os problemas dessa grandeza. Uma das principais abordagens dessa área é o Problema do Caixeiro Viajante (PCV), principalmente devido à dimensão de possíveis soluções para o problema, fazendo com que seja intratável computacionalmente por métodos de buscas exaustivas. Face a todas essas características, este trabalho tem por objetivo estudar e desenvolver estratégias evolutivas para a resolução do Problema do Caixeiro Viajante com Demandas Heterogêneas (PCVDH), uma variação do PCV clássico. As estratégias evolutivas pertencem à classe da computação evolutiva, sendo métodos de busca inspirados na teoria da evolução das espécies, onde os melhores indivíduos competem pela sobrevivência. As estratégias evolutivas diferem das demais técnicas de otimização, pois a busca é realizada em uma população de soluções, não em um único ponto. Para a resolução do problema são propostos quatro algoritmos evolutivos, utilizando técnicas heurísticas e metaheurísticas para sua aplicação. Os resultados foram obtidos com testes utilizando instâncias de baixa densidade (baixa conexão), e comparados com a sua solução exata (solução ótima) e com outros métodos evolutivos encontrados na literatura. Esses resultados são avaliados com base na sua qualidade e tempo decorrido para sua execução.

Orientador: Maria do Socorro Nogueira Rangel / Banca: Alistair Clark / Banca: Silvio Alexandre de Araujo / Resumo: Em alguns setores, o planejamento da produção envolve dois aspectos: o dimensionamento do tamanho dos lotes e a programação da produção (sequenciamento dos lotes). O primeiro problema consiste em determinar o tamanho dos lotes de produção de cada item a ser produzido em uma ou mais máquinas em cada período ao longo de um horizonte de planejamento finito. O segundo problema consiste em encontrar a ordem em que os lotes devem ser produzidos em um dado conjunto de máquinas. Estes dois aspectos do planejamento da produção podem ser tratados de forma independente: em um estágio é resolvido o problema de dimensionamento dos lotes e no outro, realizado antes ou depois, é resolvido o problema de seqüenciamento. No entanto, uma tendência recente na literatura são trabalhos que apresentam modelos matemáticos que capturam simultaneamente as relações entre os dois problemas. Na literatura pode-se encontrar modelos integrados que incluem restrições de eliminação de subrotas, propostas para o Problema do Caixeiro Viajante (PCV), para formular as restrições de sequenciamento. No entanto, alguns dos modelos propostos usam restrições de ordem polinomial que fornecem uma relaxação linear fraca. O objetivo desse trabalho é avaliar o uso de inequações válidas, propostas na literatura, para obtenção de formulações mais fortes para o problema integrado de dimensionamento e sequenciamento da produção. Resultados computacionais usando exemplares aleatórios e exemplares da literatura mostram que as reformulações propostas são eficientes para cenários em que o modelo original não é eficiente. / Abstract: Often, the production planning involves the lot sizing and scheduling of items. The first problem is to determine the lot size of each item to be produced in one or more machines in each period over a finite planning horizon. The second problem is to find the order in which the items will be produced. These two aspects of the production planning can be treated independently: in one stage the lot sizing problem is solved, and in the other, that can be executed before or after, the scheduling problem is solved. A recent trend in the literature is to propose mathematical models that capture the relationships between these two problems. In the literature one can find integrated models that include subtour elimination constraints, proposed for the Traveling Salesman Problem, to formulate the scheduling decisions. However, in some of these models, constraints of polynomial order, that provides a weak linear relaxation, are used.The purpose of this study is to evaluate the use of valid inequalities proposed in the literature to obtain stronger formulations to the lot and scheduling problem. Computational results using random instances and instances from the literature show that the proposed formulations have a better performance in scenarios where the original model is not efficient. / Mestre

Orientador: Maria do Socorro Nogueira Rangel / Banca: Deisemara Ferreira / Banca: Silvio Alexandre Araujo / Resumo: Neste trabalho, propomos um modelo integrado de dimensionamento de lotes e programação da produção para uma fábrica de refrigerantes de pequeno porte denominado P1S1MTS. Neste modelo, as decisões de dimensionamento foram baseadas no modelo P1S1M encontrado na literatura, formulado com base no modelo GLSP. As decisões de sequenciamento foram modeladas utilizando restrições do problema do caixeiro viajante assimétrico. Para validação do modelo proposto e comparação entre os modelos P1S1MTS e P1S1M foram feitos testes computacionais com exemplares ilustrativos. Foram realizados também testes com exemplares baseados em dados reais da fábrica de refrigerantes e exemplares gerados aleatoriamente. Os testes foram resolvidos pelo método Branch-and-Cut incluído no pacote computacional CPLEX 10.0. Notamos que com algumas modificações, é possível que ambos os modelos retratem a mesma situação. A partir destas modificações e com os resultados obtidos, concluímos que a resolução de exempalres do modelo P1S1MTS apresentou um tempo de execução computacioanl menor que a resolução de exemplares do modelo P1S1M gerados com os mesmos dados. / Abstract: In this work we propose a lot sizing and scheduling model, P1S1MTS, for a smallscale soft drink plant. In this model, the lot sising decisions were based on the P1s!m model found in the literaure. To model the scheduling decisions constraints of the asynmetric traveling salesman problem are used. For the validation of the proposed model and a comparison between the P1S1MTS and the P1S1M models computational tests were executed with illustratuve examples. Tests were also executed with examples based on real data and randomly generated instances. Tests were also executed with examples based on real data and randomly in the software CPLEX 10.0. The results showed taht, with some minor modifications, it is possible that both models depict same situation. From the results obtained we concluded that the P1s!MTS model presented a computational time performance better than the P1S1M model. / Mestre

Made available in DSpace on 2014-12-17T14:52:47Z (GMT). No. of bitstreams: 1 ThalesLS.pdf: 825402 bytes, checksum: 8e0d2b64fc7287a7921fa605343a8bb6 (MD5) Previous issue date: 2008-12-23 / Particle Swarm Optimization is a metaheuristic that arose in order to simulate the behavior of a number of birds in flight, with its random movement locally, but globally determined. This technique has been widely used to address non-liner continuous problems and yet little explored in discrete problems. This paper presents the operation of this metaheuristic, and propose strategies for implementation of optimization discret problems as form of execution parallel as sequential. The computational experiments were performed to instances of the TSP, selected in the library TSPLIB contenct to 3038 nodes, showing the improvement of performance of parallel methods for their sequential versions, in executation time and results / Otimiza??o por Enxame de Part?culas ou Particle Swarm Optimization (PSO) ? uma metaheur?stica que surgiu na inten??o de simular o comportamento de um conjunto de p?ssaros em v?o, com seu movimento localmente aleat?rio, mas globalmente determinado. Esta t?cnica tem sido muito utilizada na resolu??o de problemas cont?nuos n?o-lineares e ainda pouco explorada em problemas discretos. Este trabalho apresenta o funcionamento desta metaheur?stica, al?m de propor estrat?gias para sua aplica??o em problemas de otimiza??o discreta tanto na sua forma de execu??o seq?encial quanto paralela. Os experimentos computacionais foram realizados para inst?ncias do problema do caixeiro viajante, selecionados na biblioteca TSPLIB contendo at? 1002 n?s, mostrando a melhoria de desempenho dos m?todos paralelos em rela??o as suas vers?es seq?enciais, em tempo de execu??o e resultados

Orientador: Akebo Yamakami / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-08T23:52:00Z (GMT). No. of bitstreams: 1 Carvalho_MarciaBragade_M.pdf: 2154346 bytes, checksum: caafd847980349294a73d2ad38d6414c (MD5) Previous issue date: 2007 / Resumo: Dentre as várias técnicas heurísticas e exatas existentes para a resolução de problemas combinatórios, os algoritmos populacionais de otimização por colônia de formigas e genéticos têm se destacado devido à sua boa performance. Em especial os algoritmos de colônia de formigas são considerados atualmente como uma das técnicas mais bem sucedidas para a resolução de vários problemas combinatórios, dentre eles o problema do caixeiro viajante. Neste trabalho é apresentado um algoritmo híbrido que trabalha com as meta-heurísticas de sistema de colônia de formigas e genético conjuntamente aplicados no problema do caixeiro viajante simétrico. Além disso, apresentamos uma proposta para o algoritmo de formigas quando temos incertezas associadas aos parâmetros do problema. Os resultados obtidos com as metodologias propostas apresentam resultados satisfatórios para todas as instâncias utilizadas / Abstract: Amongst the several existing heuristical and accurate techniques for the resolution of combinatorial problems, the population algorithms ant colony optimization and genetic have been detached due to their good performance. In special the ant colony algorithms are considered currently as one of the techniques most succeeded for the resolution of some combinatorial problems, amongst them the travelling salesman problem. In this work is presented a hybrid algorithm which works with the ant colony system and genetic metaheuristics jointly applied in the symmetric travelling salesman problem. Moreover, we presented a proposal for the ant algorithm when we have uncertainties associated to problem parameters. The results gotten with the methodology proposals present resulted satisfactory for all the used instances / Mestrado / Automação / Mestre em Engenharia Elétrica

This report covers an investigation of the methods and algorithms required to plan and perform semi-autonomous photo missions on Apple iPad devices using data exported from Google Earth. Flight time was to be minimized, taking wind velocity and aircraft performance into account. Google Earth was used both to define what photos to take, and to define the allowable mission area for the aircraft. A benchmark mission was created containing 30 photo operations in a 250 by 500 m area containing several no-fly-areas. The report demonstrates that photos taken in Google Earth can be reproduced in reality with good visual resemblance. High quality paths between all possible photo operation pairs in the benchmark mission could be found in seconds using the Theta* algorithm in a 3D grid representation with six-edge connectivity (Up, Down, North, South, East, West). Smoothing the path in a post-processing step was shown to further increase the quality of the path at a very low computational cost. An optimal route between the operations in the benchmark mission, using the paths found by Theta*, could be found in less than half a minute using a Branch-and-Bound algorithm. It was however also found that prematurely terminating the algorithm after five seconds yielded a route that was close enough to optimal not to warrant running the algorithm to completion.

This thesis consists of two parts: text and programming part. It is divided into seven chapters. Its main goal is to compare heuristics for dynamic traveling salesman problem in a few perspectives. The text part of this thesis theoretically describes heuristic methods and in the programming part are wake up to life via VBA in MS Excel. The results of computational experiments on these heuristic methods are presented in the last chapter. In the first part, the traveling salesman problem and its solution are being described. Characteristic of the modification in a form of dynamic traveling salesman problem follow. Next chapter presents the programming solution chosen heuristics. The final chapter presents experimental results obtain with programmed heuristics.

Routing problems are ones of the most famous members of the group of the classical optimalization combinatorial problems. Travelling salesman problem and problems derived from it have been attracting mathematics and analysts, since they were firstly formulated, and accelerating a development of new methods and approaches that can be used for a wide range of another real-life problems. This thesis aims to demonstrate an usefulness and a flexibility of shown metaheristic methods. Results are compared with outputs of alternative algorithms or known optimal solutions where it is possible. To fulfill this goal the VBA application has been developed. The results of experiments are presented and the application is decribed in a second part of this thesis. A reader should be sufficiently instructed which way he could choose to solve similar types of problems

The main goal of this work is to implement a system, which will be able to optimize routes between warehouses and selected customers and visualize them using maps by the Google Inc. This problem is being analyzed not only on the theoretical, but also, and mainly, on the practical aspects and tries to find a gap in the market with similar applications.

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