A Study of Ising Formulations for Minimizing Setup Cost in the Two-Dimensional Cutting Stock Problem

Abstract

We proposed the method that translates the two-dimensional CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results are obtained. (1) The proposed Ising model adequately represents the target problem. (2) Acceptance rates were as low as 0.2% to 9.8% and from 21.8% to 49.4%. (3) Error rates from optimal solution were as broad as 0% to 25.9%. For future work, we propose the following changes: (1) Improve the Hamiltonian for constraints. (2) Improve the proposed model to adjust more complex two-dimensional CSP and reduce the number of spins when it deals with large materials and components. (3) Conduct experiments using a quantum annealer.