This dissertation presents the applications of state-of-the-art computation techniques and data analysis algorithms in three physical and biological problems: assembling DNA pieces, optimizing self-assembly yield, and identifying correlations from large multivariate datasets. In the first topic, in-depth analysis of using Sequencing by Hybridization (SBH) to reconstruct target DNA sequences shows that a modified reconstruction algorithm can overcome the theoretical boundary without the need for different types of biochemical assays and is robust to error. In the second topic, consistent with theoretical predictions, simulations using Graphics Processing Unit (GPU) demonstrate how controlling the short-ranged interactions between particles and controlling the concentrations optimize the self-assembly yield of a desired structure, and nonequilibrium behavior when optimizing concentrations is also unveiled by leveraging the computation capacity of GPUs. In the last topic, a methodology to incorporate existing categorization information into the search process to efficiently reconstruct the optimal true correlation matrix for multivariate datasets is introduced. Simulations on both synthetic and real financial datasets show that the algorithm is able to detect signals below the Random Matrix Theory (RMT) threshold. These three problems are representatives of using massive computation techniques and data analysis algorithms to tackle optimization problems, and outperform theoretical boundary when incorporating prior information into the computation. / Engineering and Applied Sciences

[pt] O seqüenciamento por hibridação é uma alternativa interessante para a tarefa de seqüenciamento de DNA. Este método ainda está sendo aperfeiçoado e pode superar as técnicas utilizadas em termos de tempo e custo. Uma etapa crucial do método consiste em resolver um problema combinatório que pode ser formulado como um caso especial do problema do caixeiro viajante com coleta de prêmios. Neste trabalho, propõe-se uma nova heurística construtiva multi-partida para resolver este problema. Uma estratégia de aprendizado baseada em uma memória adaptativa e um procedimento de construção de vocabulário são utilizados para melhorar o desempenho da heurística multi-partida. A memória adaptativa é utilizada para intensificar as construções de novas soluções com os elementos que aparecem com uma freqüência maior nas melhores soluções encontradas anteriormente pela heurística multi-partida. O procedimento de construção de vocabulário consiste em construir novas soluções através da combinação de partes comuns a boas soluções. Testes computacionais mostraram que estas duas estratégias aumentam significativamente o desempenho da heurística multi-partida e são particularmente indicadas para problemas de escalonamento nos quais as melhores soluções são na maioria dos casos formadas por blocos de elementos que aparecem juntos com muita freqüência. A heurística proposta supera os resultados dos melhores algoritmos encontrados na literatura, tanto em termos da qualidade das soluções encontradas, como do tempo de computação. / [en] Sequencing by hybridization is an attractive alternative for DNA sequencing. This novel method can be less time and cost consuming than the techniques applied nowadays. A very important step of this method is to solve a combinatorial problem formulated as a special case of the prize-collecting traveling salesman problem. In this work, we propose a new multistart construtive heuristic to solve this problem. A learning strategy based on adaptive memory and a vocabulary building procedure are used to improve the performance of the multistart heuristic. The adaptive memory is used to intensify the construction of new solutions with the elements that appear frequently in the best solutions previously found by the multistart heuristic. The objective of the vocabulary building procedure is to construct new solutions combining parts of good solutions. Computational experiments have shown that these two methods significantly improves the performance of the multistart heuristic and are particularly suitable for scheduling problems whose best solutions are in most cases built by blocks of elements that appear together very often. The proposed heuristic obtains systematically better solutions and is less time consuming than the best algorithms found in the literature.