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Title: Heuristic approaches for nesting irregular parts on fixed width infinite length rectangular sheets
Author: Vaid, S.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2000
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This thesis investigates solution approaches to the irregular nesting problem, in which a given set of pieces are to be placed without overlap onto a rectangular sheet of known width, in such a way as to minimise the length required. The objective is to develop and analyse fast solution procedures that may be applied to a variety of irregular shape data with consistent results. A survey of the literature identifies two basic approaches. In the first the pieces are nested into easier shapes, such as rectangles, prior to packing. In the second pieces are placed directly onto the stock sheet, incurring a computational overhead due to the added complexity of the necessary geometric calculations. The focus of this research is a comparison, in terms of solution time and quality, of these two approaches. It starts with an analysis of three families of rectangle packing heuristics. The possibility of improving solution quality, via compaction, when using these for irregular packing is investigated. Compaction routines based on linear programming and a more direct hole-filling approach are considered. Both rely on the geometric concept of the No-Fit Polygon (NFP) and modifications to an existing NFP algorithm are developed in order to deal with degenerate cases. A new direct placement heuristic, based on the NFP, is developed and used for comparative purposes. Finally, the possibility of using different orientations of the pieces is explored in two pilot studies. The first investigates two simple rules for orienting the pieces as they are placed, while the second investigates the more complex issue of clustering the pieces prior to placement. All developments are subjected to empirical analysis. This is based on a large and varied data set in the case of rectangular pieces, and on a set of representative problems from the literature in the case of irregular data.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available