A Genetic Algorithm to Solve a Real 2-D Cutting Stock Problem with Setup Cost in the Paper Industry

This paper deals with the Two-Dimensional Cutting Stock Problem with Setup Cost (2CSP-S). This problem is composed of three optimization sub-problems: a 2-D Bin Packing (2BP) problem (to place images on patterns), a Linear Programming (LP) problem (to find for each pattern the number of stock sheets to be printed) and a combinatorial problem (to find the number of each image on each pattern). In this article, we solve the 2CSP-S focusing on this third sub-problem. A genetic algorithm was developed to automatically find the proper number of each image on patterns. It is important to notice that our approach is not a new packing technique. This work was conducted for a paper industry company and experiments were realized on real and artificial datasets.