Abstract

VELAZQUEZ-VILLEGAS, Fernando  and  SANTILLAN-GUTIERREZ, Saúl Daniel. Efficient Clustering for Irregular Geometries Based on Identification of Concavities. Ing. invest. y tecnol. [online]. 2014, vol.15, n.2, pp.233-240. ISSN 2594-0732.

Two dimensional clustering problem has much relevance in applications related to the efficient use of raw material, such as cutting stock, packing, etc. This is a very complex problem in which multiple bodies are accommodated efficiently in a way that they occupy as little space as possible. The complexity of the problem increases with the complexity of the bodies. Clearly the number of possible arrangements between bodies is huge. No Fit Polygon (NFP) allows to determine the entire relative positions between two patterns (regular or irregular) in contact, non-overlapping, therefore the best position can be selected. However, NFP generation requires a lot of calculations; besides, selecting the best cluster isn't a simple task because, between two irregular patterns in contact, hollows (unusable areas) and external concavities (usable areas) can be produced. This work presents a quick and simple method to reduce calculations associated with NFP generation and to minimize unusable areas in a cluster. This method consists of generating partial NFP, just on concave regions of the patterns, and selecting the best cluster using a total weighted efficiency, i.e. a weighted value of enclosure efficiency (ratio of occupied area on convex hull area) and hollow efficiency (ratio of occupied area on cluster area). The proposed method produces similar results as those obtained by other methods; however the shape of the clusters obtained allows to accommodate more parts in similar spaces, which is a desirable result when it comes to optimizing the use of material. We present two examples to show the performance of the proposal.

Keywords : optimal clustering; nesting; cutting stock problem; no fit polygon.

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