# Nesting Process Automation in the Footwear Industry: A Hybrid Approach to Minimize Material Waste
## 2 State of the Art
The focus is defined as a specific edge location for positioning the next piece, with two modes: fixed focus, where parts are consistently positioned on the same side, and variable focus, where parts are placed in different areas of the master surface. The algorithm iteratively places parts in the best provisional position from all tests, followed by a compaction algorithm to optimize positioning. * [PERSON] et al. [34] make significant contributions to genetic algorithms by presenting coding methodologies that, beyond standard parameters, incorporate both leather quality and specific quality requirements for the parts. Their approach also considers directionality, addressing stretching requirements for both the parts and the leather. * [PERSON] et al. [35] uses raster representation due to its lower computational cost, as polygonal solutions with free rotations hinder the use of NFPs, which expedite calculations in polygon-based heuristics (rotating a part invalidates the precomputed NFP). This study proposes generating global solutions through different constructive placement procedures, which are then employed in an iterative algorithm based on a Lagrangian relaxation approximation -a technique with proven effectiveness in heuristic frameworks [36] and widely applied in minimizing the traveling salesman problem. * [PERSON] et al. [37] conducted one of the most recent studies, with an in-depth exploration detailed in [PERSON]'s doctoral thesis [8; 38]. This work presents a genetic algorithm to solve the nesting problem with the objective of waste minimization, and previous studies by the author also introduce a fitness function for this genetic algorithm [8; 39]. The solutions presented in these studies, however, are not directly applicable to the cases examined in this article. As noted in much of the literature, part typology--particularly part size--is a critical consideration in nesting. The nesting algorithms studied so far are designed for a varied set of input pieces in different sizes, especially medium and small. In these cases, the space between two neighboring pieces can be filled by a third, smaller one, thus improving the use of material and reducing its waste. In the case studies of this article, the number of pieces found in non-conventional footwear types, such as moccasins and Strobel, is small and of large size. For these cases, the algorithms studied are not optimized, generating nestings with a higher wastage than those obtained with manual positioning. Moreover, these methods lack the possibility of limiting the range of solutions. This is especially important in the problem of nesting in footwear, since leather is a natural element, it is not homogeneous and does not have the same consistency over its entire surface. Experts know these characteristics and place the parts of the shoe that will suffer most from wear (e.g., the toe cap) in the strongest areas of the leather. With this algorithm, parts can be placed in a certain area; within this area, the algorithm will seek to place them in such a way as to produce the best nesting, although it will not allow them to move outside this area. This is not possible with the algorithms analyzed. The use of a hybrid method allows the advantages of each of the algorithms to be combined, minimizing the calculation time and equaling the results of manual positioning in terms of wastage. Because current automatic algorithms do not obtain good nesting results for these types of pieces, the positioning must be conducted manually, or by using dies for manual cutting. This has a negative economic impact, as the time taken to cut these types of construction is longer, and usually involves a higher consumption of material, as it generates more waste.