Darbo tikslas yra išanalizuoti keliaujančio pirklio algoritmo realizacijos galimybes egzistuojančiose navigacinėse sistemose, bei išanalizavus pasirinktus algoritmus keliaujančio pirklio problemai spręsti, parinkti tinkamiausią algoritmą pagal turimus atminties ir skaičiavimo resursus bei problemos sudėtingumą. Tyrimo rezultatai parodė, jog nėra tinkamiausio algoritmo visiems atvejams, nes skirtingose situacijose skirtingi algoritmai rodo geriausius rezultatus. / The investigation had a list of objectives: analyze the capabilities and resources of a range of chosen GPS navigation devices; analyze the needs and requirements of traveling salesman related GPS navigator functions for regular users; analyze what types of TSP algorithms are used in existing navigation software products; analyze the capabilities of various TSP algorithms with regard to used resources and speed of calculations; determine which algorithms are optimal for a range of specific situations. Research of different algorithms led to a conclusion that there is no single algorithm that is always better than the rest. Under different circumstances, different algorithms showed different results. Some were clearly optimal in some situations, while others competed with each other in other situations. The key element to success of an algorithm was how much time it got to do it's calculations. The amount of the input data changed the duration of the calculations but the algorithm function declination rate remained mostly the same with different sets of input data.

The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NP-complete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. In addition to vehicle routing, many other applications, e.g., computer wiring, cutting wallpaper, job sequencing or several data visualization techniques, require the solution of a TSP. In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

In this thesis we focus on two NP-hard and intensively studied problems: The travelling salesman problem (TSP), which aims to find a minimum cost tour that visits every node exactly once in a complete weighted graph, and the 2-edge-connected spanning subgraph problem (2ECSS), which aims to find a minimum size 2-edge-connected spanning subgraph in a given graph. TSP and 2ECSS have many real world applications. However, both problems are NP-hard which means it is unlikely that polynomial time algorithms exist to solve them, so methods that return close to optimal solutions are sought. In this thesis we mainly focus on k-approximation algorithms for the two problems, which efficiently return a solution within k times of the optimal solution. For a special case of TSP called graph TSP, using ideas from Momke and Svensson, we present a 25/18-approximation algorithm for a special class of graphs using circulations and T-joins, which improves the previous known best bound of 7/5 for such graphs. Moreover, if the graph does not contain special nodes, our algorithm ensures the ratio of 4/3. For 2ECSS, given any k-edge-connected graph G=(V,E), |V|=n, |E|=m, we present an approximation algorithm that gives a 2-edge-connected spanning subgraph with the number of edges at most n+(m-n)/(k-1)-(k-2)/(k-1) with a novel use of circulations, which improves both the approximation ratio and the simplicity of the proof compared to a result by Huh in 2004.

Constructing the genomic median of several given genomes is crucial in developing evolutionary trees, since the genomic median provides an estimate for the ordering of the genes in a common ancestor of the given genomes. This is due to the fact that the content of DNA molecules is often similar, but the difference is mainly in the order in which the genes appear in various genomes. The mutations that affect this ordering are called genome rearrangements, and many structural differences between genomes can be studied using genome rearrangements. In this thesis our main focus is on applying combinatorial optimization techniques to genomic median problems, with particular emphasis on the breakpoint distance as a measure of the difference between two genomes. We will study different variations of the breakpoint median problem from signed to unsigned, unichromosomal to multichromosomal, and linear to circular to mixed. We show how these median problems can be formulated in terms of problems in combinatorial optimization, and take advantage of well-known combinatorial optimization techniques and apply these powerful methods to study various median problems. Some of these median problems are polynomial and many are NP-hard. We find efficient algorithms and approximation methods for median problems based on well-known combinatorial optimization structures. The focus is on algorithmic and combinatorial aspects of genomic medians, and how they can be utilized to obtain optimal median solutions.

Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Thomas, Robin; Committee Co-Chair: Cook, William J.; Committee Member: Dvorak, Zdenek; Committee Member: Parker, Robert G.; Committee Member: Yu, Xingxing.

Thesis (M.S.)--Texas State University--San Marcos, 2008. / Vita. Includes bibliographical references (leaves 50-51). Also available on microfilm.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-07-01Bitstream added on 2014-06-13T18:30:54Z : No. of bitstreams: 1 carretero_mm_me_sjrp.pdf: 795127 bytes, checksum: 64b07e80db6689945e91fc1c317deb3c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / 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. / 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.

Orientador: Luziane Ferreira de Mendonça / Dissertação ( mestrado profissional) - Universidade Estadual de Campionas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T15:32:08Z (GMT). No. of bitstreams: 1 Tavora_RogerioCarvalhoMendes_M.pdf: 4616708 bytes, checksum: 3a393a830c9e1127f5694b0a56d9fcd9 (MD5) Previous issue date: 2011 / Resumo: Comemorando os 200 anos de Academia Militar no Brasil a partir de março de 2011, estão previstas várias implementações e melhorias na estrutura de visitação da AMAN que, consequentemente, vão gerar um aumento substancial no número de grupos visitantes no ano de seu bicentenário. Diante dos fatos percebe-se a necessidade de um modelo matemático eficiente cuja finalidade seja permitir aos grupos visitantes percorrerem trajetos otimizados, ou seja, que passem pelos pontos principais de visitação no menor tempo e distância possíveis. O modelo matemático a ser adotado neste trabalho é o Problema do Caixeiro Viajante (Traveling Salesman Problem - TSP), um clássico da Otimização Combinatória pertencente 'a classe de problemas NP - difícil, que já possui eficientes algoritmos desenvolvidos. Serão utilizadas heurísticas próprias para a resolução do TSP com o intuito de se obter numericamente itinerários ótimos de visitação, considerando os diferentes grupos visitantes e suas dificuldades de acesso, dentre outras particularidades. / Abstract: Celebrating 200 years of the Military Academy in Brazil from March 2011, provides a lot of implementations and improvements in the structure of visitation of AMAN, consequently, will generate substantial growth in the number of visiting groups in the year of its bicentennial. Given the facts we see the need for an efficient mathematical model whose purpose is to allow visitors to wander paths optimized groups, ie passing through the main points of visitation in the shortest possible time and distance. The mathematical model to be adopted in this work is TSP (Traveling Salesman Problem - TSP), a classic combinatorial optimization class of problems NP - hard, that have already efficient algorithms. We will use own heuristics for solving the TSP in order to obtain numerically optimal routes for visitors, considering the various visiting groups and their difficulties of access, among other features. / Mestrado / Mestre em Matemática

Orientadores: Fernando Jose Von Zuben, Leandro Nunes de Castro / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-15T01:42:44Z (GMT). No. of bitstreams: 1 Gomes_LalinkadeCamposTeixeira_D.pdf: 3303378 bytes, checksum: 65adc8d5ec20cd1f431eaca2fe3765cc (MD5) Previous issue date: 2006 / Resumo: Problemas de otimização combinatória apresentam grande relevância prática e surgem em uma ampla gama de aplicações. Em geral, a otimização combinatória está associada a uma explosão de candidatos à solução, inviabilizando a aplicação de métodos exatos. Frente à intratabilidade desta classe de problemas via métodos exatos, nos últimos anos tem havido um crescente interesse por métodos heurísticos capazes de encontrar soluções de alta qualidade, não necessariamente ótimas. Considerando o notório sucesso empírico de meta-heurísticas concebidas através da inspiração biológica e na natureza, essas abordagens vêm ganhando cada vez mais atenção por parte de pesquisadores. É fato conhecido que não existe uma única metodologia capaz de sempre produzir os melhores resultados para todas as classes de problemas, ou mesmo para todas as instâncias de uma mesma classe. Assim, a busca de solução para problemas de natureza combinatória constitui uma linha de pesquisa desafiadora. Nesta tese são considerados problemas de otimização combinatória multicritério e multimodal. Como principal contribuição, destaca-se a concepção de novas meta-heurísticas para a solução de problemas combinatórios de elevada complexidade, tendo sido propostas duas classes de ferramentas computacionais. A primeira envolve um método híbrido fundamentado em mapas auto-organizáveis de Kohonen e inferência nebulosa, em que um conjunto de regras guia o processo de treinamento do mapa de modo a permitir o tratamento de problemas com restrições e múltiplos objetivos. A segunda abordagem baseia-se em sistemas imunológicos artificiais. Em particular, a abordagem imunológica levou à proposição de meta-heurísticas capazes de encontrar e manter diversas soluções de alta qualidade, viabilizando o tratamento de problemas multimodais. Como casos de estudo, foram consideradas duas classes de problemas de otimização combinatória multimodal: o problema de roteamento de veículos capacitados e o problema do caixeiro viajante simétrico. As técnicas propostas foram também adaptadas para a solução de problemas de bioinformática, em particular ao problema de análise de dados de expressão gênica, produzindo resultados diferenciados e indicando um elevado potencial para aplicações práticas. / Abstract: Combinatorial optimization problems possess a high practical relevance and emerge on a wide range of applications. Usually, combinatorial optimization is associated with an explosion of candidates to the solution, making exact methods unfeasible. Before the unfeasibility of exact methods when dealing with this class of problems, lately there has been an increasing interest in heuristic methods capable of finding high-quality solutions, not necessarily the optimal one. Considering the widely known empirical success of metaheuristics conceived with inspiration on biological systems and on the nature itself, such approaches are receiving more and more attention from the scientific community. Evidently, there is no single methodology able to always produce the best results for all classes of problems, or even for all instances of one specific class. That is why the search for solutions to combinatorial problems remains a challenging task. This thesis considers multicriteria and multimodal combinatorial optimization problems. As the main contribution, one can emphasize the conception of new metaheuristics designed to the solution of high-complexity combinatorial optimization problems, and two classes of computational tools have been proposed. The first one involves hybrid method based on Kohonen self-organizing maps and fuzzy inference, in which a set of rules guides the training of the self-organizing maps in order to allow the handling of problems with constraints and multiple objectives. The second approach is based on artificial immune systems. Particularly, the immune-inspired approach leads to the proposal of metaheuristics capable of finding out and maintaining multiple high-quality solutions, making it possible to deal with multimodal problems. As case studies, the capacitated vehicle routing problem and the symmetric traveling salesman problem are considered, giving rise to combinatorial and multimodal problems. The proposed techniques were also adapted to the solution of problems in the field of bioinformatics, specifically the analysis of gene expression data, leading to distinguished results and indicating a high potential for practical applications. / Doutorado / Engenharia de Computação / Doutor em Engenharia Elétrica

Mixed-Integer Programming has been a vital tool for the chemical engineer in the recent decades and is employed extensively in process design and control. This dissertation presents some new Mixed-Integer Programming formulations developed for two well-studied problems, one with a central role in the area of Optimisation, the other of great interest to the chemical industry. These are the Travelling Salesman Problem and the problem of scheduling cleaning actions for heat exchanger networks subject to fouling. The Travelling Salesman Problem finds a plethora of applications in many scientific disciplines, Chemical Engineering included. None of the mathematical programming formulations proposed for solving the problem considers fewer than O(n^2) binary degrees of freedom. The first part of this dissertation introduces a novel mathematical description of the Travelling Salesman Problem that succeeds in reducing the binary degrees of freedom to O(nlog2(n)). Three Mixed-Integer Linear Programming formulations are developed and the computational performance of these is tested through computational studies. Sophisticated methods are now available for scheduling the cleaning actions for networks of heat exchangers subject to fouling. In the majority of these, only one form of cleaning is used, which restores the performance of the exchanger back to its clean level. A recent study revised the scheduling problem for the case where there are several cleaning methods available. The second part of this dissertation extends their approach, developed for individual units, to heat exchanger networks and explores the concept of selection of cleaning techniques further. Mixed-Integer Programming formulations are proposed for the scheduling task, for two fouling scenarios: (i) chemical reaction fouling and (ii) biological fouling. A series of results are presented for the implementation of the scheduling formulations to networks of different sizes.