Graph neural network comparison for 2D nesting efficiency estimation

Minimizing the level of material consumption in textile production is a major concern. The cornerstone of this optimization task is the nesting problem, whose goal is to lay a set of irregular 2D parts out onto a rectangular surface, called the nesting zone, while respecting a set of constraints. Knowing the efficiency—ratio of usable to used up material enables the optimization of several textile production problems. Unfortunately, knowing the efficiency requires the nesting problem to be solved, which is computationally intensive and has been proven to be NP-hard. This paper introduces a regression approach to estimate efficiency without solving the nesting problem. Our approach models the 2D nesting problem as a graph where the nodes are images derived from parts and the edges hold the constraints. The method then consists of combining convolutional neural networks for addressing the image-based aspects and graph neural networks (GNNs) for the constraint aspects. We evaluate several neural message passing approaches on our dataset and obtain results that are sufficiently accurate for enabling several business use cases, where our model best solves this task with a mean absolute error of 1.65. We provide open access to our dataset, whose properties differ from those of other graph datasets found in the literature. This dataset is constructed on 100,000 real customers’ nesting data. Along the way, we compare the performance and generalization capabilities of four GNN architectures obtained from the literature on this dataset.