This thesis deals with the Nesting Problem, following an optimization approach. The Cutting and Packing problems in general, and their solution approaches, are presented, together with an exhaustive survey of the specific literature about nesting problems. The geometric side of the problem is also addressed and an algorithm to determine the relative position of two polygons is proposed. It is also presented an algorithm for the computation of the no-fit-polygon, that deals with the case in which the polygons have multiple points. A new polygon operator is introduced: the "merge" operator. The topological definition, together with the respective computational algorithm, are presented. Using this geometric manipulation capability of irregular pieces, nesting algorithms, based in the simulated annealing and tabu search metaheuristics, have been developed. these search techniques have been implemented under two different strategies. The first one is based on the minimization of the overlap between pieces. In a second one the pieces are sequentially placed, without overlap, by a new heuristic algorithm, the order by which the pieces are placed being controlled by the above mentioned search techniques. With these algorithms it has been possible to solve nesting problems in which the irregular pieces are to be laid in a rectangular plate, in an open-end rectangular plate and in an irregular shaped plate with defects. New constructive nesting algorithms have also been developed. These algorithms use the concepts of no-fit-polygon and polygon "merge" to lay the irregular pieces in an open-end rectangular plate. The sequential placement approach used implies the resolution of two sub-problems: choosing the next piece to place and finding the best position of that piece relatively to the already placed pieces. The first problem has been tackled with local search techniques and heuristic algorithms, while the second one was solved by optimization algorithms. These algorithms find the piece position that minimizes the area of the rectangular enclosure, minimizes the length of the rectangular enclosure, or maximizes the overlap of the pieces rectangular bounding box..Available from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga
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