Abstract
ABSTRACT Solving nesting problems or irregular strip packing problems is to position polygons on a fixed width and unlimited length strip, obeying polygon integrity containment constraints and nonoverlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we use separation lines, i.e., straight lines that separate polygons. We present a nonlinear programming model that considers free rotations of the polygons and of the separation lines. This model uses a considerable smaller number of variables than the few other approaches proposed in the literature. We use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotations.
Highlights
Irregular strip packing problems have a great relevance in production processes, such as garment, manufacturing and furniture making
We present a nonlinear programming model that considers free rotations of the polygons and of the separation lines
When we deal with nonconvex polygons, we make sure that the translations and rotations are the same for all polygons belonging to the partition of the nonconvex polygon
Summary
Irregular strip packing problems have a great relevance in production processes, such as garment, manufacturing and furniture making. In the literature, we find a visual system for packing problem of irregular pieces with free rotation into a rectangular board that aims to minimize the waste [16] This algorithm is based on Physics, the rubber band physics movement. Nonlinear programming models have been proposed for representing the irregular packing problem, such as [8, 14, 15, 23, 29] In all these models free rotation of the pieces is allowed. In [8] a model for a strip packing problem was presented In this model phi-functions are used to ensure non-overlapping of the pieces. In this paper we propose a nonlinear mathematical model for an irregular strip packing problem which deals only with polygons which may be convex or nonconvex, and that can rotate freely. A model of an irregular strip packing problem that considers free rotations is presented.
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