Adaptando Uma Solução GRASP ao Problema da Cobertura Mínima de Vértices

O Problema da Cobertura Mínima de Vértices (PCVM) é um problema NP-Difícil de grande interesse prático. Muitos problemas do mundo real podem ser relacionados ao PCVM, por exemplo, escalonamento de tarefas, desenho de circuitos VLSI, problemas de bioinformática, para citar apenas alguns. Este artigo reporta o uso da heurística GRASP associada ao uso de uma técnica de otimização local, denominada LOT. A heurística resultante foi denominada GRASPlot. O objetivo deste artigo é reportar uma série de experimentos computacionais utilizando o GRASPlot para instâncias de grafos encontradas na biblioteca BHOSLIB confrontando os resultados da heurística proposta com soluções ótimas disponibilizadas pela biblioteca

Enumeration and symmetry of edit metric spaces

This thesis addresses the problem of enumerating the size of the k-spheres of a fixed word for the edit metric as well as discussing the symmetry group of the edit graph in order to create an edit metric error correcting code. The application of such error correcting codes is to the correction of sequencing errors in DNA barcodes, short stretches of DNA incorporated into genomic libraries to identify source tissue or other information about the source of a given DNA sequence. As sequencing errors not only substitute characters but potentially insert and delete them, the traditional Hamming metric used in standard error correcting codes is not useful. The natural metric, the edit distance, is algebraically complex as compared to the Hamming metric. In this thesis the exact size of edit spheres of radius 1 and 2 are computed for any binary or q-ary string. The number of edit distance d neighbors of two special types of strings is also presented. Structural information about the edit metric space, in particular a representation as a pyramid of hypercubes and the symmetry group of the space, is given. This result begins the process of reconstructing the theory of error correcting codes for the edit metric and yields practical advice for the design of heuristic algorithms, e.g. evolutionary algorithms, used in practice to create error correcting DNA barcodes

Evolutionary Algorithms for Vertex Cover

This paper reports work investigating various evolutionary approaches to vertex cover (VC), a well-known NP-Hard optimization problem. Central to each of the algorithms is a novel encoding scheme for VC and related problems that treats each chromosome as a binary decision diagram. As a result, the encoding allows only a (guaranteed optimal) subset of feasible solutions. The encoding also incorporates features of a powerful traditional heuristic for VC that allow initial EA populations to be seeded in known promising regions of the search space. The resulting evolutionary algorithms have displayed exceptionally strong empirical performance on various vertex cover, independent set, and maximum clique problem classes