Heuristic for constrained two-dimensional three-staged patterns

Cui, Yi-Ping; Cui, Yaodong; Tang, Tianbing; Hu, Wei

doi:10.1057/jors.2014.33

Cited by 7 publications

(9 citation statements)

References 21 publications

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“…The averaged calculation time for each instance of algorithm is 0.20 seconds in [16], 0.014 seconds in [21], 35.22 seconds in [22], 0.18 seconds in [23], 701.83 seconds in [10] and 0.56 seconds in this paper. It should be noted that the algorithm in [10] is exact algorithm and the maximum solution time was set to 900 seconds.…”

Section: B Benchmark Instances Of Large Sizementioning

confidence: 78%

“…Table 3 shows the statistical results of the pattern value in this paper and five other published papers. The pattern value of different algorithm is derived from table 1 in [16], table 4 in [21], section 3 in [22], table 2 in [23], and table 3 in [10].…”

Section: B Benchmark Instances Of Large Sizementioning

confidence: 99%

“…For the homogenous strip corner-occupying cutting pattern, Cui and Chen proposed a recursion approach to consider a set of cutting patterns with specified geometric features, and used a bound technique to discard unpromising branches [22]. For the three-staged cutting pattern, Cui et al proposed a heuristic algorithm with one exact procedure and two heuristic procedures [23]. Some of the above algorithms have shorter computation time but lower solution quality, while others have better solution quality but longer computation time.…”

Section: Introductionmentioning

confidence: 99%

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A Block Corner-Occupying Heuristic Algorithm for Constrained Two-Dimensional Guillotine Cutting Problem of Rectangular Items

Pan

2019

IEEE Access

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Aiming at the constrained two-dimensional guillotine cutting problem of rectangular items, a heuristic algorithm with block corner-occupying pattern is presented in this paper. It can maximize the pattern value for the totally included items, but the occurring frequency of each item type doesn't exceed its upper bound. Several rows and columns of identical items are packed at the left-bottom corner of the sheet, and the remaining part is divided into two sub-sheets. The sub-sheets are then packed and divided in the same way till no items can be packed. This upper bound and normal size methods applied in the algorithm will avoid the unnecessary calculation. The algorithm is compared with 9 literature algorithms with benchmark instances and random instances. Computational results show that, compared with the 8 heuristic algorithms, the pattern value of this algorithm is increased by 0.787% to 6.119% and the calculation time is reasonable. Compared with the exact algorithm, for large size instances the pattern value of this algorithm is 0.090% lower than it, but the calculation time is only 0.079% of it.INDEX TERMS Corner-occupying pattern, constrained two-dimensional guillotine cutting problem, heuristic algorithm.

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Section: B Benchmark Instances Of Large Sizementioning

confidence: 78%

Section: B Benchmark Instances Of Large Sizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Block Corner-Occupying Heuristic Algorithm for Constrained Two-Dimensional Guillotine Cutting Problem of Rectangular Items

Pan

2019

IEEE Access

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“…Heuristic solutions can be obtained by approaches focusing on the two-staged case, either free (Lodi and Monaci, 2003;Hifi an M'Hallah, 2005;Macedo et al, 2010;Mrad et al, 2012) or pgroup (Yanasse and Katsurayama, 2005;Yanasse and Morabito, 2006;, and on the three-staged case (Puchinger and Raidl, 2007;Silva et al, 2010;Cui et al, 2015b). Besides these papers, other simplifications have been proposed with the aim of reducing the solution space through the elimination of intricate cutting schemes.…”

Section: Heuristic and Metaheuristic Approachesmentioning

confidence: 99%

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

Russo¹,

Boccia

Sforza³

et al. 2019

Int Trans Operational Res

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In the two‐dimensional (2D) cutting (2DC) problem, a large rectangular sheet has to be dissected into smaller rectangular pieces with the aim of maximizing the total profit associated with the extracted pieces. When the number of copies of each piece to be extracted is bounded, it is referred to as constrained 2DC (C2DC) problem. The C2DC has been widely studied by the operations research community for its applications and theoretical issues. In this work, we recall the best exact and heuristic solving approaches for the C2DC and we provide a review and a categorization of the available upper bounds. We also discuss improvements and combinations of these upper bounds and give directions for their effective exploitation. Finally, we demonstrate the loss of accuracy of several exact methods present in literature because of the effect of the used antiredundancy strategies on the implemented bounding criteria. This work, based on more than 90 contributions, has a twofold target. For researchers working in C2DC, it provides a useful insight on the topic. For expert practitioners, it represents a systematic collection of the main findings and achievements, posing also the basis for future research.

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“…Cutting and packing problems have attracted much research interest (Beeker and Appa, 2015;Cui et al, 2015;Moreira de Carvalho et al, 2015). One such problem is the one-dimensional cutting stock problem (1DCSP).…”

Section: Introductionmentioning

confidence: 99%

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

Cui

Song

Chen

et al. 2017

Journal of the Operational Research Society

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In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.

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Heuristic for constrained two-dimensional three-staged patterns

Cited by 7 publications

References 21 publications

A Block Corner-Occupying Heuristic Algorithm for Constrained Two-Dimensional Guillotine Cutting Problem of Rectangular Items

A Block Corner-Occupying Heuristic Algorithm for Constrained Two-Dimensional Guillotine Cutting Problem of Rectangular Items

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

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