Ising formulations for two-dimensional cutting stock problem with setup cost

TL;DR

This paper introduces an Ising model formulation for the two-dimensional cutting stock problem with setup costs, demonstrating its effectiveness through computational experiments and suggesting future improvements and quantum annealing applications.

Contribution

The paper presents a novel Ising model translation for the 2-D CSP with setup costs, enabling new computational approaches for this complex problem.

Findings

The Ising model accurately represents the 2-D CSP.

Acceptance rates in experiments ranged from 0.2% to 49.4%.

Error rates from optimal solutions ranged up to 25.9%.

Abstract

We proposed the method that translates the 2-D 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 low as 0.2% to 9.8% and from 21.8% to 49.4%. (3) Error rates from optimal solution were broad as 0% to 25.9%. As the future work, (1) Improve the Hamiltonian for Constraints. (2) Improve the proposed model to adjust more complex 2-D CSP and reduce the number of spins when it deals with large materials and components. (3) Conduct experiments using a quantum annealer.