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.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-20T11:31:40Z No. of bitstreams: 2 Dissertação - Danilo Alves Martins de Faria - 2013.pdf: 1188393 bytes, checksum: c56b169690f22bbbeaa2ee6fa46ade1c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-20T14:17:45Z (GMT) No. of bitstreams: 2 Dissertação - Danilo Alves Martins de Faria - 2013.pdf: 1188393 bytes, checksum: c56b169690f22bbbeaa2ee6fa46ade1c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-11-20T14:17:45Z (GMT). No. of bitstreams: 2 Dissertação - Danilo Alves Martins de Faria - 2013.pdf: 1188393 bytes, checksum: c56b169690f22bbbeaa2ee6fa46ade1c (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-10-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Network Design Problems (NDPs) are present in many areas, such as electric power distribution, communication networks, vehicle routing, phylogenetic trees among others. Many NDPs are classified as NP-Hard problems. Among the techniques used to solve them, we highlight the Evolutionary Algorithms (EA). These algorithms simulate the natural evolution of the species. However, in its standard form EAs have limitations to solve large scale NDPs, or with very specific characteristics. To solve these problems, many researchers have studied specific forms of representation of NDPs. Among these stands we show Node-Depth-Degre Encoding (NDDE). This representation produces only feasible solutions, regardless of the network characteristics. NDDE has two mutation operators Preserve Ancestor Operator (PAO) and Ancestor Change Operator (CAO) and the recombination operator EHR (Evolutionary History Recombination Operator) that uses historical applications of mutation, and was applied to NDPs more than one tree and had good results. Thus, this work proposes adapt EHR for NDPs classics represented by a single tree. In addition, two evolutionary algorithms are developed: the AE-RNPG, which uses only NDDE, with mutation operators. And the AE-EHR, which makes use of mutation operators and recombination operator EHR to the One Max Tree Problem. The results showed that the AE-EHR obtained better solutions than the EA-RNPG for most instances analyzed. / Problemas de Projeto de Redes (PPRs) estão presentes em diversas áreas, tais como reconfiguração de sistemas de distribuição de energia elétrica, projetos de redes de comunicação, roteamento de veículos, reconstrução de árvores filogenéticas entre outros. Vários PPRs pertencem à classe de problemas NP-Difíceis. Dentre as técnicas utilizadas para resolvê-los, destacam-se os Algoritmos Evolutivos (AE), cujo processo de resolução de um problema simula a evolução natural das espécies. Entretanto, os AEs em sua forma padrão também possuem limitações quanto a PPRs de larga escala, ou com características muito específicas. Para solucionar esses problemas, diversas pesquisas têm estudado formas específicas de estruturas de dados dos PPRs. Dentre essas destaca-se a representação Nó-Profundidade-Grau (RNPG). Essa representação produz apenas soluções factíveis, independente da característica da rede. A RNPG possui dois operadores de mutação Preserve Ancestor Operator (PAO) e Change Ancestor Operator (CAO) e o operador de recombinação EHR (Evolutionary History Recombination Operator), que utiliza o histórico de aplicações dos operadores de mutação, o qual tem sido aplicado a PPRs com mais de uma árvore com bons resultados. Este trabalho propõem a adequação do EHR para PPRs clássicos de uma única árvore. Além disso, são desenvolvidos dois algoritmos evolutivos: o AE-RNPG, que utiliza a RNPG somente com os operadores de mutação; e o AE-EHR, que faz uso tanto dos operadores de mutação quanto do operador de recombinação EHR para o problema da Árvore máxima. Os resultados obtidos mostram que o AE-EHR obtém melhores soluções do que o AE-RNPG para a maioria das instâncias analisadas.