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

Abstract

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.

Comparison of two metaheuristics to solve a 2-D cutting stock problem with set-up cost in the paper industry

“…In Bonnevay, Aubertin and Lazert (2015) and Bonnevay, Aubertin and Gavin (2015), a well-known algorithm (see Section 3.1) and a classical linear programming solver were used to solve the sub-problems (i) and (ii). And to solve the sub-problem (iii), paper by Bonnevay, Aubertin and Lazert (2015) proposes a simulated annealing algorithm (SA-2CSP-S) and paper by Bonnevay, Aubertin and Gavin (2015) proposes a genetic algorithm (GA-2CSP-S).…”

“…And to solve the sub-problem (iii), paper by Bonnevay, Aubertin and Lazert (2015) proposes a simulated annealing algorithm (SA-2CSP-S) and paper by Bonnevay, Aubertin and Gavin (2015) proposes a genetic algorithm (GA-2CSP-S). The following subsections detail the common algorithmic elementary components of these two algorithms.…”

“…To create some random initial solutions, to build the neighbourhood of the simulated annealing algorithm of Bonnevay, Aubertin and Lazert (2015), to build the mutation operator in Bonnevay, Aubertin and Gavin (2015) or to improve a solution with an hillclimbing process, we define a neighbourhood of any solution s by modifying the m-tuple (p 1 , . .…”

“…To create the initial solution of the simulated annealing algorithm in Bonnevay, Aubertin and Lazert (2015) or the initial population of the genetic algorithm in Bonnevay, Aubertin and Gavin (2015), a feasible solution should be generated. The first step of our process is inspired by Imahori et al (2003).…”

“…As SA-2CSP-S, the genetic algorithm of Bonnevay, Aubertin and Gavin (2015), GA-2CSP-S (see Algorithm 4), uses the previous methods and the operators Crossover and Mutation (see Sections 4.2.1 and 4.2.2). There are NbGen generations (loop line 9).…”