An introduction to the two‐dimensional rectangular cutting and packing problem

Oliveira, Óscar; Gamboa, Dorabela; Silva, Elsa

doi:10.1111/itor.13236

Cited by 5 publications

(7 citation statements)

References 138 publications

(237 reference statements)

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“…How do you find the optimal cutting path? Packing the parts in the plate remainders is a classical two-dimensional layout optimization problem that has been researched for many years, with detailed studies available in [4][5][6]. Since we assumed that the parts to be cut have already been packed in plate remainders, the first sub-problem is not discussed in this study.…”

Section: Introductionmentioning

confidence: 99%

An Optimization Method for CNC Laser Combination Cutting of Irregular Plate Remainders

Zhang

et al. 2023

Coatings

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The key research question in this study is how to cut pieces in irregular plate remainders, because there are many irregular plate leftovers created during the CNC (Computer Numerical Control) process. This will increase material utilization and allow plate leftovers to be reused. One of the issues being researched is how to arrange plate remainders on the surface of the CNC machine; this issue is known as combination layout optimization. The other issue being researched is combination cutting-path optimization of plate remainders, which aims to determine the cutting path of parts of plate remainders. A genetic algorithm based on the gravity-center NFP (No-Fit Polygon) method was applied to optimize the layout pattern, and then the geometric coordinates of a part included in one plate remainder after packing were obtained by geometric transformation with the help of a three-layer graphic data correlation model, which quickly identified the inside and outside contours of parts. A colony algorithm based on the mathematical model of cutting-path optimization was used to optimize the cutting path of the parts in the plate remainders. Finally, some simulation tests were performed to illustrate the feasibility and effectiveness of the proposed method. The results of the algorithm for packing irregular shapes for some instances show that our algorithm outperforms the other algorithms. On most instances, the average plate utilization ratio using our algorithm, after running 20 times, is improved by 1% to 9% in comparison to the best plate utilization ratio using the tree search algorithm. The best idle travel of an example achieved by the algorithm in this paper is 7632 mm after running the cutting-path optimization algorithm 20 times, while that of the traditional equivalent TSP (Traveling Salesman Problem) algorithm is 11,625 mm, which significantly demonstrates the efficiency of the algorithm.

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Section: Introductionmentioning

confidence: 99%

An Optimization Method for CNC Laser Combination Cutting of Irregular Plate Remainders

Zhang

et al. 2023

Coatings

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“…Knapsack problems (KP) can be encountered in plenty of real‐world applications: cutting and packing (Hifi, 2004; Oliveira et al., 2023; de Souza Queiroz and Andretta, 2022), multimedia (Akbar et al., 2006), cryptography (Merkle and Hellman, 1978), logistics (Perboli et al., 2014), telecommunications, and resource allocation (Plata‐Gonzalez et al., 2019). This type of problem can play a central role in modeling various complex combinatorial optimization problems, where the considered models can be used as a driving strategy for the design of powerful exact and approximate algorithms.…”

Section: Introductionmentioning

confidence: 99%

Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

Boukhari

Hifi

2023

Int Trans Operational Res

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In this paper, the multiple‐choice knapsack problem with setups is tackled with an iterative method, where both local branching and descent method cooperate. First, an iterative procedure is designed for solving a series of mixed integer programming problems combined with a special reduced subproblem; that is, a combined model built by injecting some valid cardinality constraints. Second, the local branching‐based learning strategy is embedded into an iterative search to mimic the variable neighborhood descent method, such that the local branching strategy drives the search process for enhancing the quality of the solutions. Third, the proposed method is experimentally analyzed on benchmark instances extracted from the literature, where its provided (lower) bounds are compared to those reached by methods published in the literature and the Cplex solver. Finally, its performance is evaluated by providing a statistical analysis.

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“…Rodrigues et al (2023) also present a flexible formulation (supporting limited and unlimited stages, exact and non-exact patterns), and their focus is a restricted heuristic version of their model. Besides these new formulations, at least two new surveys worth mentioning were published by Oliveira et al (2023) (reviewing the whole area of two-dimensional rectangular cutting and packing) and Iori et al (2021) (focusing on exact methods for two-dimensional cutting and packing) and also an instance library (2DPacklib) presented in Iori et al (2022).…”

Section: Introductionmentioning

confidence: 99%

“…Besides these new formulations, at least two new surveys worth mentioning were published by Oliveira et al. (2023) (reviewing the whole area of two‐dimensional rectangular cutting and packing) and Iori et al. (2021) (focusing on exact methods for two‐dimensional cutting and packing) and also an instance library ( 2DPacklib ) presented in Iori et al.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of mathematical formulations for the two‐dimensional guillotine cutting problem

Becker

Martin

Araújo

et al. 2023

Int Trans Operational Res

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About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo‐polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch‐and‐bound time thanks to the symmetries broken by the hybridisation.

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An introduction to the two‐dimensional rectangular cutting and packing problem

Cited by 5 publications

References 138 publications

An Optimization Method for CNC Laser Combination Cutting of Irregular Plate Remainders

An Optimization Method for CNC Laser Combination Cutting of Irregular Plate Remainders

Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

Comparative analysis of mathematical formulations for the two‐dimensional guillotine cutting problem

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