A variable neighborhood search algorithm for the leather nesting problem

Abstract

The leather nesting problem is a cutting and packing optimization problem that consists in finding the best layout for a set of irregular pieces within a natural leather hide with an irregular surface and contour. In this paper, we address a real application of this problem related to the production of car seats in the automotive industry. The high quality requirements imposed on these products combined with the heterogeneity of the leather hides make the problem very complex to solve in practice. Very few results are reported in the literature for the leather nesting problem. Furthermore, the majority of the approaches impose some additional constraints to the layouts related to the particular application that is considered. In this paper, we propose a variable neighborhood search algorithm for the general leather nesting problem. We describe a fast constructive heuristic that generates a feasible layout guided by the information provided by inner-fit polygons, and we introduce new neighborhood structures based on the sequence by which the pieces are placed on the hide and on the quality of the fitness of the pieces in the current layout. To evaluate the performance of our approaches, we conducted an extensive set of computational experiments on real instances. The results of these experiments are reported at the end of the paper.