Multiresolution based overlap minimization algorithm for irregular packing problems

Irregular nesting is a subgroup of cutting and packing problems in which a set of irregular items must be inserted in a rectangular container with a variable width. It is often found in industries such as textile, wood and shipbuilding and an efficient solution usually renders an economical and environmental positive impact. Due to the complex geometry of items, the no overlapping rule is hard to guarantee and, therefore, geometric tools are usually employed. In this work, a raster method is proposed to solve the overlap minimization problem, which can be adapted to solve the irregular nesting problem. A map of overlap values is created and is employed to find the minimum overlap placement for each item. A multiresolution approach is used to reduce the size of the map and, consequently, accelerate the search process. The results from tests performed using 4 benchmark tests indicates that more compact layouts can be obtained using multiple resolutions. Moreover, the results are competitive when compared to other solutions in the literature. Copyright c ©2015 IFAC.