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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Robustness and Preferences in Combinatorial Optimization

Hites, Romina 15 December 2005 (has links)
In this thesis, we study robust combinatorial problems with interval data. We introduce several new measures of robustness in response to the drawbacks of existing measures of robustness. The idea of these new measures is to ensure that the solutions are satisfactory for the decision maker in all scenarios, including the worst case scenario. Therefore, we have introduced a threshold over the worst case costs, in which above this threshold, solutions are no longer satisfactory for the decision maker. It is, however, important to consider other criteria than just the worst case. Therefore, in each of these new measures, a second criteria is used to evaluate the performance of the solution in other scenarios such as the best case one. We also study the robust deviation p-elements problem. In fact, we study when this solution is equal to the optimal solution in the scenario where the cost of each element is the midpoint of its corresponding interval. Then, we finally formulate the robust combinatorial problem with interval data as a bicriteria problem. We also integrate the decision maker's preferences over certain types of solutions into the model. We propose a method that uses these preferences to find the set of solutions that are never preferred by any other solution. We call this set the final set. We study the properties of the final sets from a coherence point of view and from a robust point of view. From a coherence point of view, we study necessary and sufficient conditions for the final set to be monotonic, for the corresponding preferences to be without cycles, and for the set to be stable. Those that do not satisfy these properties are eliminated since we believe these properties to be essential. We also study other properties such as the transitivity of the preference and indifference relations and more. We note that many of our final sets are included in one another and some are even intersections of other final sets. From a robust point of view, we compare our final sets with different measures of robustness and with the first- and second-degree stochastic dominance. We show which sets contain all of these solutions and which only contain these types of solutions. Therefore, when the decision maker chooses his preferences to find the final set, he knows what types of solutions may or may not be in the set. Lastly, we implement this method and apply it to the Robust Shortest Path Problem. We look at how this method performs using different types of randomly generated instances.
2

A Comparative Study Of Tree Encodings For Evolutionary Computing

Saka, Esin 01 July 2005 (has links) (PDF)
One of the most important factors on the success of evolutionary algorithms (EAs) about trees is the representation of them. The representation should exhibit efficiency, locality and heritability to enable effective evolutionary computing. Neville proposed three different methods for encoding labeled trees. The first one is similar with Pr&uuml / fer&#039 / s encoding. In 2001, it is reported that, the use of Pr&uuml / fer numbers is a poor representation of spanning trees for evolutionary search, since it has low locality for random trees. In the thesis Neville&#039 / s other two encodings, namely Neville branch numbers and Neville leaf numbers, are studied. For their performance in EA their properties and algorithms for encoding and decoding them are also examined. Optimal algorithms with time and space complexities of O(n) , where n is the number of nodes, for encoding and decoding Neville branch numbers are given. The localities of Neville&#039 / s encodings are investigated. It is shown that, although the localities of Neville branch and leaf numbers are perfect for star type trees, they are low for random trees. Neville branch and Neville leaf numbers are compared with other codings in EAs and SA for four problems: &#039 / onemax tree problem&#039 / , &#039 / degree-constrained minimum spanning tree problem&#039 / , &#039 / all spanning trees problem&#039 / and &#039 / all degree constrained spanning trees problem&#039 / . It is shown that, neither Neville nor Pr&uuml / fer encodings are suitable for EAs. These encodings are suitable for only tree enumeration and degree computation. Algorithms which are timewise and spacewise optimal for &#039 / all spanning trees problem&#039 / (ASTP) for complete graphs, are given by using Neville branch encoding. Computed time and space complexities for solving ASTP of complete graphs are O(nn-2) and O(n) if trees are only enumerated and O(nn-1) and O(n) if all spanning trees are printed , respectively, where n is the number of nodes. Similarly, &#039 / all degree constrained spanning trees problem&#039 / of a complete graph is solvable in O(nn-1) time and O(n) space.
3

DESENVOLVIMENTO DE METAHEURÍSTICAS PARA O PROBLEMA DA ÁRVORE GERADORA MÍNIMA GENERALIZADO

Cristo, Fernando de 20 March 2008 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The generalized minimum spanning tree problem is present in several situations of the real world, such as in the context of the telecommunications, transports and grouping of data, where a net of necessary clusters to be connected using a node of each cluster. In that work it is presented the project and the implementation of an algorithm of tabu search with path relinking and iterated local search for the generalized minimum spanning tree problem and your variant with at least one vertex by group. In the computational tests 271 instances of TSPLIB were used generated through the grouping methods Center Clustering and Grid Clustering, and more 20 instances for the extension of the problem with at least one vertex by group. The results demonstrate the efficiency of the algorithm proposed in the obtaining of satisfactory solutions for the two problems. / O problema da árvore geradora mínima generalizado está presente em várias situações do mundo real, tais como no contexto das telecomunicações, transportes e agrupamento de dados, nas quais uma rede de grupos precisa ser conectada utilizando um nodo de cada grupo. Nesse trabalho é apresentado o projeto e a implementação de um algoritmo de busca tabu com reconexão de caminhos e busca local iterativa para o problema da árvore geradora mínima generalizado e sua variante com pelo menos um vértice por grupo. Nos testes computacionais foram utilizadas 271 instâncias da TSPLIB geradas através dos métodos de agrupamento Center Clustering e Grid Clustering, e mais 20 instâncias para a extensão do problema com pelo menos um vértice por grupo. Os resultados demonstram a eficiência do algoritmo proposto na obtenção de soluções satisfatórias para os dois problemas.
4

Approches de résolution exacte et approchée en optimisation combinatoire multi-objectif, application au problème de l'arbre couvrant de poids minimal / Exact and approximate solving approaches in multi-objective combinatorial optimization, application to the minimum weight spanning tree problem

Lacour, Renaud 02 July 2014 (has links)
On s'attache dans cette thèse à plusieurs aspects liés à la résolution de problèmes multi-objectifs, sans se limiter au cas biobjectif. Nous considérons la résolution exacte, dans le sens de la détermination de l'ensemble des points non dominés, ainsi que la résolution approchée dans laquelle on cherche une approximation de cet ensemble dont la qualité est garantie a priori.Nous nous intéressons d'abord au problème de la détermination d'une représentation explicite de la région de recherche. La région de recherche, étant donné un ensemble de points réalisables connus, exclut la partie de l'espace des objectifs que dominent ces points et constitue donc la partie de l'espace des objectifs où les efforts futurs doivent être concentrés dans la perspective de déterminer tous les points non dominés.Puis nous considérons le recours aux algorithmes de séparation et évaluation ainsi qu'aux algorithmes de ranking afin de proposer une nouvelle méthode hybride de détermination de l'ensemble des points non dominés. Nous montrons que celle-ci peut également servir à obtenir une approximation de l'ensemble des points non dominés. Cette méthode est implantée pour le problème de l'arbre couvrant de poids minimal. Les quelques propriétés de ce problème que nous passons en revue nous permettent de spécialiser certaines procédures et d'intégrer des prétraitements spécifiques. L'intérêt de cette approche est alors soutenu à l'aide de résultats expérimentaux. / This thesis deals with several aspects related to solving multi-objective problems, without restriction to the bi-objective case. We consider exact solving, which generates the nondominated set, and approximate solving, which computes an approximation of the nondominated set with a priori guarantee on the quality.We first consider the determination of an explicit representation of the search region. The search region, defined with respect to a set of known feasible points, excludes from the objective space the part which is dominated by these points. Future efforts to find all nondominated points should therefore be concentrated on the search region.Then we review branch and bound and ranking algorithms and we propose a new hybrid approach for the determination of the nondominated set. We show how the proposed method can be adapted to generate an approximation of the nondominated set. This approach is instantiated on the minimum spanning tree problem. We review several properties of this problem which enable us to specialize some procedures of the proposed approach and integrate specific preprocessing rules. This approach is finally supported through experimental results.
5

Robustness and preferences in combinatorial optimization

Hites, Romina 15 December 2005 (has links)
In this thesis, we study robust combinatorial problems with interval data. We introduce several new measures of robustness in response to the drawbacks of existing measures of robustness. The idea of these new measures is to ensure that the solutions are satisfactory for the decision maker in all scenarios, including the worst case scenario. Therefore, we have introduced a threshold over the worst case costs, in which above this threshold, solutions are no longer satisfactory for the decision maker. It is, however, important to consider other criteria than just the worst case.<p>Therefore, in each of these new measures, a second criteria is used to evaluate the performance of the solution in other scenarios such as the best case one. <p><p>We also study the robust deviation p-elements problem. In fact, we study when this solution is equal to the optimal solution in the scenario where the cost of each element is the midpoint of its corresponding interval. <p><p>Then, we finally formulate the robust combinatorial problem with interval data as a bicriteria problem. We also integrate the decision maker's preferences over certain types of solutions into the model. We propose a method that uses these preferences to find the set of solutions that are never preferred by any other solution. We call this set the final set. <p><p>We study the properties of the final sets from a coherence point of view and from a robust point of view. From a coherence point of view, we study necessary and sufficient conditions for the final set to be monotonic, for the corresponding preferences to be without cycles, and for the set to be stable.<p>Those that do not satisfy these properties are eliminated since we believe these properties to be essential. We also study other properties such as the transitivity of the preference and indifference relations and more. We note that many of our final sets are included in one another and some are even intersections of other final sets. From a robust point of view, we compare our final sets with different measures of robustness and with the first- and second-degree stochastic dominance. We show which sets contain all of these solutions and which only contain these types of solutions. Therefore, when the decision maker chooses his preferences to find the final set, he knows what types of solutions may or may not be in the set.<p><p>Lastly, we implement this method and apply it to the Robust Shortest Path Problem. We look at how this method performs using different types of randomly generated instances. <p> / Doctorat en sciences, Orientation recherche opérationnelle / info:eu-repo/semantics/nonPublished

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