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

Round 1

Reviewer 1 Report

In this paper the authors formulate the famous cutting stock problem in terms of the Ising model. They set up an appropriate Hamiltonian and then search for the ground state which presumably corresponds to the optimum. The problem can now be attacked with the tools typical of statistical physics but this probably did not make the problem easier. The translation to the new problem is succinctly presented and looks easy to follow for anyone who wants to try this out. The authors suggest a string of possible improvements to their model. They seem to test their model on standard benchmark problems but this reviewer is unfamiliar with these. It could be of interest if the authors could say more about the size of the original problem (no of variables and equations, time to solve on a standard computer) and its new size in terms of the Ising model (no of spins, time to compute ground state). This would perhaps help the reader decide if the translation is a viable approach. Other than that, I recommend this for publication in Algorithms.

Author Response

Thank you for your comment. I answered your comment and revised my manuscript.

We solved the more huge problem of our previous study at actual production data (material size is from 100 to 2000, and the number of items is over 800) using the heuristic method, and we wanted to try it in this study (ref. no.14). However, the quantum annealer has a limit of the number of spins. For example, D-Wave can use about 2000 spins, and Digital Annealer can use 8192. The optimizer can use more than a quantum annealer; it is not realistic to apply the actual production data. I added the number of spins, computer environment, and calculation time in this experiment.

Reviewer 2 Report

This manuscript looks good in that it proposes a creative algorithm to solve the cutting-stock problem. However, the followings should be performed to be published this time.

1. authors must add far more references relevant to cutting stock problem.
2. Cutting stock problem have been solved directly by available commercial solvers such as GAMS and LINGO even though the size of it is quite large. Authors need to justify why this algorithm is meaningful compared with direct optimization
3. The contents and result of experiment are needed to be explained more concretely.
4. Authors must connect the results with their conclusion in more detail.
5. I am not sure whether authors used professional English editing service or not. Otherwise, I recommend it.

Author Response

Thank you for your comment. I answered your comment and revised my manuscript.

 

1. I added 10 new references.
2. We solved some commercial solvers (CPLEX, Gurobi) in this problem. However, the objective is not solving this huge BPP problem but the formulation of the new BPP problem in the Ising model. Furthermore, the quantum annealer has a strict limitation on the number of spins. The Google OR tools was used in this study.
3. I added the explanation of the result that why acceptance rate is high.
4. I added the discussion of the conclusion
5. I have already used English editing service. I apologize for our English that it is hard to read.

Round 2

Reviewer 1 Report

The authors have improved the ms by adding more background information and have anwered my questions. I note however that some new minor language errors also crept in but these should be quick fixes.

210: "and a programing is used Python"; 268: "this is first trying", "273: "are depend", 275: "more flex"