Genetic Modelling Approach for the Two-Dimensional Variable-Sized Cutting Stock Problem

P. Terán Viadero, M. A. Carravilla, J. F. Oliveira, F. J. Martín Campo, A. Alonso Ayuso

This work addresses the Two-Dimensional Variable-Sized Cutting Stock Problem (2DVSCSP), motivated by a real industrial application in honeycomb cardboard production. In this setting, stock dimensions are not predefined and must be determined jointly with cutting patterns to minimise material usage under exact two-stage guillotine constraints. This introduces strong interdependencies between decisions, increasing problem complexity.

We propose a genetic modelling framework solved using a Biased Random Key Genetic Algorithm. Solutions are represented through a problem-specific chromosome encoding and a decoder that simultaneously defines stock sizes and cutting patterns, ensuring feasibility by construction. Computational results show that the approach provides high-quality solutions and adapts well to different settings.

Keywords: Cutting Stock Problem Variable-Sized Stock Biased Random Key Genetic Algorithm

F. Huguet, L. M. Plà-Aragonés, V. Albornoz, M. Pohl

I. Méndez Fernández, A. García Hernández-Díaz, R. Gordaliza Ruiz, S. Pérez Peló, J. Sánchez-Oro Calvo

L. Canonne