Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

Cid-García, Néstor M.; Ríos-Solís, Yasmín Á.

doi:10.1371/journal.pone.0245267

Cited by 5 publications

(6 citation statements)

References 63 publications

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“…A hybrid metaheuristic approach that relies on a local search algorithm to deliver satisfying rectangles placements on the horizontal axis and an exact procedure to find rectangles positions on the vertical axis is shown in [ 23 ] for the 2D-SPP, being competitive on moderate-sized instances when compared to the best-known approaches. Also, [ 24 ] used the positions and covering methodology to obtain exact solutions for the 2D-SPP, generating a set of valid positions in which a rectangle can be packed into the strip and, with a set-covering formulation, selecting the best configuration of rectangles. Also, the method was found to be useful for small and medium-size instances, as well as proving optimality for new literature instances.…”

Section: Research Frameworkmentioning

confidence: 99%

The machining torch movement for the rectangular plasma sheet metal cut

Neuenfeldt Júnior,

Francescatto,

Araújo

et al. 2023

PLoS ONE

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The sheet metals can be cut into rectangular or irregular pieces, where the main objective is to minimize the sheet metal’s physical waste. However, the operating time, the number of movements to cut all rectangles edges, and the cutting process quality, must be considered. The objective of this research was to compare the machining torch movement behavior using optimal and alternative solutions for rectangular plasma sheet metal cuts. A bottom-left-fill heuristic and a tabu search heuristic were used to find the alternative solution, while the optimal solution was obtained with a mixed-integer linear programming. The comparison was developed considering three parameters: the total processing time, the effective distance traveled by the machining torch to cut the metal, and the movement distance traveled by the machining torch without cutting the metal. The packing layout given by alternative solutions can reduce the operational cutting processing time and the distance covered by the machining torch movement. From an economic perspective, optimal solutions are recommended when compared to alternative solutions given the lower expenses with raw material waste.

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Section: Research Frameworkmentioning

confidence: 99%

The machining torch movement for the rectangular plasma sheet metal cut

Neuenfeldt Júnior,

Francescatto,

Araújo

et al. 2023

PLoS ONE

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“…Condition (6) states that all rectangles R ki (x ki ,y ki ) are placed in a horizontal strip box of height H and length L. According to Condition (5), the optimization goal is to minimize all delay lengths. Condition (8) ensures that the position relations between any two pairs of rectangles can only be one of the four directions, namely, the determinable variables u ri,sj , u sj, ri , v ri,sj , and v sj,ri , and only one of the four position relations can be equal to 1. Condition (7) indicates that all rectangles will not overlap horizontally or vertically; this model can also be taken as a Padberg-type model due to the use of binary variables.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Deterministic algorithms mainly use models to construct accurate solutions or improve the branch pricing method to improve the optimization ability and efficiency of the algorithm. Cid-Garcia et al [8] used the location and coverage method to obtain the two-dimensional, non-guillotine-constrained 2SP exact solution, generated a set of effective locations in the form of pseudo polynomials, and selected the best configuration of the strip box items by using the set coverage formula. Qi et al [9] studied the relationship between the lower left coordinates of the rectangles and strip boxes and established linear integer programming models of nonrotating and rotating two-dimensional rectangular strip boxes to ensure that the two rectangles would not be placed repeatedly.…”

Section: Introductionmentioning

confidence: 99%

Optimization of a Rural Portfolio Credit Granting System Using Improved Two-Dimensional Strip Packing Grouping Delay Problem

Huang

2022

Systems

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Rural preferential loans usually take the form of portfolio credits. From the perspective of public interest, the total delay time for obtaining loans is expected to be minimized. To use rural portfolio credits effectively, the two-dimensional strip packing grouping delay problem (2SPGDP) is improved to optimize the rural portfolio credit granting system. First, 2SPGDP is established by adding grouping constraints and the latest start time constraints to the two-dimensional strip packing problem, and the total delay is taken as the optimization objective. Second, based on the depth search reverse spanning tree (DSRST) and the insert spare space (ISS) method, the branch-and-bound reverse order insert algorithm (BB-RIA) is designed. Finally, the lag pruning operator (LPO) is designed to reduce lag. The improved model (2SPGDP) and BB-RIA-LPO algorithm are used to solve several classical two-dimensional strip packing problems and a specific rural portfolio credit case. Compared with the Bottom-Left and Branch and Bound Algorithm, our model and algorithm improve the success rate by 25% and reduce the total delay by 6%. The case of rural portfolio credit illustrates the operability and effectiveness of this method.

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“…Also, for the 2D-SPP, new exact methods and algorithms were proposed in recent years, without considering practical constraints. In [ 29 ], a methodology called Positions and Covering was developed, providing exact and previously unknown solutions for literature instances with validated results and effectiveness for small and medium-size instances. Additionally, [ 30 ] proposed a novel algorithm based on deep reinforcement learning, achieving superior optimization results, and demonstrating high solution efficiency, generalization, and potential for practical applications.…”

Section: Introductionmentioning

confidence: 99%

Impact of minimum distance constraints on sheet metal waste for plasma cutting

Francescatto,

Luiz Neuenfeldt Júnior,

Silva

et al. 2023

PLoS ONE

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We approached the two-dimensional rectangular strip packing problem (2D-SPP), where the main goal is to pack a given number of rectangles without any overlap to minimize the height of the strip. Real-life constraints must be considered when developing 2D-SPP algorithms to deliver solutions that will improve the cutting processes. In the 2D-SPP literature, a gap related to studies approaching constraints in real-life scenarios was identified. Therefore, the impact of real-life constraints found in the plasma cutting process in sheet metal waste was analyzed. A mathematical model from the literature was modified to obtain packing arrangements with plasma cutting constraints. The combination of size and number of rectangles, as well as strip width, was the main factor that affected the packing arrangement, limiting the allocation of rectangles and generating empty spaces. In summary, considering the sheet metal waste context, instances with smaller widths should be avoided in practical operations for high minimum distance constraint values, returning the worst packing arrangements. For low minimum distance constraint values, smaller width instances can be used in practical operations, as the packing arrangement is acceptable. Finally, this article can reduce material waste and enhance the cutting process in the sheet metal industry, by showing packing characteristics which lead to higher amounts of raw material waste.

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Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

Cited by 5 publications

References 63 publications

The machining torch movement for the rectangular plasma sheet metal cut

The machining torch movement for the rectangular plasma sheet metal cut

Optimization of a Rural Portfolio Credit Granting System Using Improved Two-Dimensional Strip Packing Grouping Delay Problem

Impact of minimum distance constraints on sheet metal waste for plasma cutting

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