A Genetic Algorithm for the Nesting Problem With Continuous Rotations

The Nesting problem, or the irregular cutting and packing problem, aims to find the best position of irregular pieces within a board, minimizing the space used by them. The problem's relevance is that it is widely used in the furniture, textile, and footwear industries. We consider a two-dimensional scope with convex and non-convex parts, with continuous rotation. We implement a genetic algorithm that uses five positioning rules, five sorting rules, and two rotation rules to create individuals and populations. Two positioning rules outperformed the others, obtaining promising results compared with the literature.