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Journal articles on the topic 'Strip Packing problem'

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Published: 6 September 2023

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1

Chekanin, Vladislav A., and Alexander V. Chekanin. "Development of the Multimethod Genetic Algorithm for the Strip Packing Problem." Applied Mechanics and Materials 598 (July 2014): 377–81. http://dx.doi.org/10.4028/www.scientific.net/amm.598.377.

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The actual in industry strip packing problem which is NP-hard in strong sense is considered in paper. To the strip packing problem comes down solution of a large number of different practical problems, including problems in logistics, scheduling and planning. The new heuristics intended to pack a given set of rectangular two-dimensional objects in order to minimize of the total length of the filled part of container with an infinity length and fixed width are offered. The proposed multimethod genetic algorithm is investigated on well-known standard benchmarks of two-dimensional strip packing problems.

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2

Alvarez-Valdes, R., F. Parreño, and J. M. Tamarit. "Reactive GRASP for the strip-packing problem." Computers & Operations Research 35, no. 4 (April 2008): 1065–83. http://dx.doi.org/10.1016/j.cor.2006.07.004.

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3

Zhao, Xusheng, Yunqing Rao, and Jie Fang. "A reinforcement learning algorithm for the 2D-rectangular strip packing problem." Journal of Physics: Conference Series 2181, no. 1 (January 1, 2022): 012002. http://dx.doi.org/10.1088/1742-6596/2181/1/012002.

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Abstract The 2D packing problem is categorized as one branch of the cutting and packing problems, which is widely spread in the manufacturing industries. Over the years many metaheuristics have been proposed and applied on the packing problem. Recently, the approach combined with machine learning serves as a novel paradigm for solving the combinatorial optimization problem. However, the machine learning approaches have very limited literature reports on the appliance of the packing problem. We propose a reinforcement learning method for the 2D-rectangular strip packing problem. The solution is represented by the sequence of the items and the layout is constructed piece by piece. We use the lowest centroid placement rule for the piece placement, then a Q-learning based sequence optimization is applied. Three groups of conditions are set for the testing, the computational results show the Q-learning approach has good effect on the compaction of the layout.

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4

BOUGERET, MARIN, PIERRE-FRANCOIS DUTOT, KLAUS JANSEN, CHRISTINA ROBENEK, and DENIS TRYSTRAM. "APPROXIMATION ALGORITHMS FOR MULTIPLE STRIP PACKING AND SCHEDULING PARALLEL JOBS IN PLATFORMS." Discrete Mathematics, Algorithms and Applications 03, no. 04 (December 2011): 553–86. http://dx.doi.org/10.1142/s1793830911001413.

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We consider two strongly related problems, multiple strip packing and scheduling parallel jobs in platforms. In the first one we are given a list of n rectangles with heights and widths bounded by one and N strips of unit width and infinite height. The objective is to find a nonoverlapping orthogonal packing without rotations of all rectangles into the strips minimizing the maximum height used. In the scheduling problem we consider jobs instead of rectangles, i.e., we are allowed to cut the rectangles vertically and we may have target areas of different size, called platforms. A platform Pℓ is a collection of mℓ processors running at speed sℓ and the objective is to minimize the makespan, i.e., the latest finishing time of a job.

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5

Côté, Jean-François, Mauro Dell'Amico, and Manuel Iori. "Combinatorial Benders' Cuts for the Strip Packing Problem." Operations Research 62, no. 3 (June 2014): 643–61. http://dx.doi.org/10.1287/opre.2013.1248.

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6

Martello, Silvano, Michele Monaci, and Daniele Vigo. "An Exact Approach to the Strip-Packing Problem." INFORMS Journal on Computing 15, no. 3 (August 2003): 310–19. http://dx.doi.org/10.1287/ijoc.15.3.310.16082.

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7

Chen, Jianli, Wenxing Zhu, and Zheng Peng. "A heuristic algorithm for the strip packing problem." Journal of Heuristics 18, no. 4 (May 30, 2012): 677–97. http://dx.doi.org/10.1007/s10732-012-9203-9.

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8

Fang, Jie, Yunqing Rao, and Mingliang Shi. "A deep reinforcement learning algorithm for the rectangular strip packing problem." PLOS ONE 18, no. 3 (March 16, 2023): e0282598. http://dx.doi.org/10.1371/journal.pone.0282598.

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As a branch of the two-dimensional (2D) optimal blanking problem, rectangular strip packing is a typical non-deterministic polynomial (NP-hard) problem. The classical packing solution method relies on heuristic and metaheuristic algorithms. Usually, it needs to be designed with manual decisions to guide the solution, resulting in a small solution scale, weak generalization, and low solution efficiency. Inspired by deep learning and reinforcement learning, combined with the characteristics of rectangular piece packing, a novel algorithm based on deep reinforcement learning is proposed in this work to solve the rectangular strip packing problem. The pointer network with an encoder and decoder structure is taken as the basic network for the deep reinforcement learning algorithm. A model-free reinforcement learning algorithm is designed to train network parameters to optimize the packing sequence. This design can not only avoid designing heuristic rules separately for different problems but also use the deep networks with self-learning characteristics to solve different instances more widely. At the same time, a piece positioning algorithm based on the maximum rectangles bottom-left (Maxrects-BL) is designed to determine the placement position of pieces on the plate and calculate model rewards and packing parameters. Finally, instances are used to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can produce three better and five comparable results compared with some classical heuristic algorithms. In addition, the calculation time of the proposed algorithm is less than 1 second in all test instances, which shows a good generalization, solution efficiency, and practical application potential.

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9

Horn, Matthias, Emir Demirović, and Neil Yorke-Smith. "Parallel Batch Processing for the Coating Problem." Proceedings of the International Conference on Automated Planning and Scheduling 33, no. 1 (July 1, 2023): 171–79. http://dx.doi.org/10.1609/icaps.v33i1.27192.

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We solve a challenging scheduling problem with parallel batch processing and two-dimensional shelf strip packing constraints that arises in the tool coating field. Tools are assembled on so-called planetaries (batches) before they are loaded into coating machines to get coated. The assembling is not trivial and must fulfil specific constraints, which we refer to as shelf strip packing constraints. Further, each tool is associated with a starting time window s.t. tools can only be put on the same planetary if their time window overlap. The objective is to minimise the makespan and the number of required planetaries. Since the problem naturally decomposes into scheduling and packing parts, we tackle the problem with a two-phase logic-based Benders decomposition approach. The master problem assigns items to batches. The first phase solves as subproblem the packing problem by checking if the assignment is feasible, whereas the second phase solves the scheduling subproblem. The approach is compared with a monolithic mixed integer linear programming approach as well as a monolithic constraint programming approach. Experimental evaluation shows that our proposed approach outperforms the state-of-the-art benchmarks by solving more instances to optimality in a shorter time.

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10

Domović, Daniel, Tomislav Rolich, and Marin Golub. "Evolutionary hyper-heuristic for solving the strip-packing problem." Journal of The Textile Institute 110, no. 8 (January 4, 2019): 1141–51. http://dx.doi.org/10.1080/00405000.2018.1550136.

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11

LEE, HEUNGSOON FELIX, and E. C. SEWELL. "The strip-packing problem for a boat manufacturing firm." IIE Transactions 31, no. 7 (July 1999): 639–51. http://dx.doi.org/10.1080/07408179908969865.

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12

Bansal, Nikhil, Xin Han, Kazuo Iwama, Maxim Sviridenko, and Guochuan Zhang. "A Harmonic Algorithm for the 3D Strip Packing Problem." SIAM Journal on Computing 42, no. 2 (January 2013): 579–92. http://dx.doi.org/10.1137/070691607.

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13

Rakotonirainy, Rosephine G., and Jan H. van Vuuren. "Improved metaheuristics for the two-dimensional strip packing problem." Applied Soft Computing 92 (July 2020): 106268. http://dx.doi.org/10.1016/j.asoc.2020.106268.

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14

Bortfeldt, Andreas, and Daniel Mack. "A heuristic for the three-dimensional strip packing problem." European Journal of Operational Research 183, no. 3 (December 2007): 1267–79. http://dx.doi.org/10.1016/j.ejor.2005.07.031.

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15

Hifi, Mhand. "Exact algorithms for the guillotine strip cutting/packing problem." Computers & Operations Research 25, no. 11 (November 1998): 925–40. http://dx.doi.org/10.1016/s0305-0548(98)00008-2.

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16

Kozin, I. V., and S. E. Batovskyi. "Fragmentary Structures in a Two-Dimensional Strip Packing Problem." Cybernetics and Systems Analysis 55, no. 6 (November 2019): 943–48. http://dx.doi.org/10.1007/s10559-019-00204-w.

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17

de Queiroz, Thiago Alves, and Flávio Keidi Miyazawa. "Order and static stability into the strip packing problem." Annals of Operations Research 223, no. 1 (May 25, 2014): 137–54. http://dx.doi.org/10.1007/s10479-014-1634-2.

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18

da Silveira, Jefferson L. M., Flávio K. Miyazawa, and Eduardo C. Xavier. "Heuristics for the strip packing problem with unloading constraints." Computers & Operations Research 40, no. 4 (April 2013): 991–1003. http://dx.doi.org/10.1016/j.cor.2012.11.003.

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19

Bekrar, Abdelghani, and Imed Kacem. "An Exact Method for the 2D Guillotine Strip Packing Problem." Advances in Operations Research 2009 (2009): 1–20. http://dx.doi.org/10.1155/2009/732010.

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We consider the two-dimensional strip packing problem with guillotine cuts. The problem consists in packing a set of rectangular items on one strip of widthWand infinite height. The items packed without overlapping must be extracted by a series of cuts that go from one edge to the opposite edge (guillotine constraint). To solve this problem, we use a dichotomic algorithm that uses a lower bound, an upper bound, and a feasibility test algorithm. The lower bound is based on solving a linear program by introducing new valid inequalities. A new heuristic is used to compute the upper bound. Computational results show that the dichotomic algorithm, using the new bounds, gives good results compared to existing methods.

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20

KUBACH, TIMO, ANDREAS BORTFELDT, THOMAS TILLI, and HERMANN GEHRING. "GREEDY ALGORITHMS FOR PACKING UNEQUAL SPHERES INTO A CUBOIDAL STRIP OR A CUBOID." Asia-Pacific Journal of Operational Research 28, no. 06 (December 2011): 739–53. http://dx.doi.org/10.1142/s0217595911003326.

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Given a finite set of spheres of different sizes, we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given cuboid so that the wasted space is minimized. To solve these problems two greedy algorithms were developed which adapt the algorithms proposed by Huang et al. (2005) to the 3D case with some important enhancements. The resulting methods were tested using the instances provided by Stoyan et al. (2003). Additionally, two series of 12 instances each for the 3D-SPP and for the 3D-KP are introduced and results for these new instances are also reported.

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21

Huang, Huijun, and Yuzhong Li. "Optimization of a Rural Portfolio Credit Granting System Using Improved Two-Dimensional Strip Packing Grouping Delay Problem." Systems 10, no. 5 (October 21, 2022): 193. http://dx.doi.org/10.3390/systems10050193.

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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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22

Glybovets, M. M., N. M. Gulayeva, and I. O. Morozov. "Analysis of Genetic Algorithms for solving the 2D Orthogonal Strip Packing Problem." PROBLEMS IN PROGRAMMING, no. 4 (December 2016): 104–16. http://dx.doi.org/10.15407/pp2016.04.104.

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A class of genetic algorithms for solving the 2D Strip Packing Problem is investigated. The theoretical analysis of the complexity of implementing decoders MERA and BLF is done. Original implementations of these MERA and BLF decoders enhanced with a number of heuristic optimizations are proposed. Genetic algorithm for solving the 2D Strip Packing Problem for special cases (allowed/forbidden objects rotation by 90°) with the use of MERA/BLF decoders is proposed. Extensive computational experiments with well-known instances are performed to analyze different configurations of basic parameters of proposed genetic algorithm. The comparison of the obtained algorithm with other known algorithms is given.

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23

Júnior, Bonfim Amaro, Plácido Rogério Pinheiro, Rommel Dias Saraiva, and Pedro Gabriel Calíope Dantas Pinheiro. "Dealing with Nonregular Shapes Packing." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/548957.

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This paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-left). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no-fit polygon based heuristic that shifts polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach.

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24

Gómez-Villouta, Giglia, Jean-Philippe Hamiez, and Jin-Kao Hao. "A Reinforced Tabu Search Approach for 2D Strip Packing." International Journal of Applied Metaheuristic Computing 1, no. 3 (July 2010): 20–36. http://dx.doi.org/10.4018/jamc.2010070102.

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This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

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25

Cid-Garcia, Nestor M., and Yasmin A. Rios-Solis. "Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology." PLOS ONE 16, no. 1 (January 14, 2021): e0245267. http://dx.doi.org/10.1371/journal.pone.0245267.

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We use the Positions and Covering methodology to obtain exact solutions for the two-dimensional, non-guillotine restricted, strip packing problem. In this classical NP-hard problem, a given set of rectangular items has to be packed into a strip of fixed weight and infinite height. The objective consists in determining the minimum height of the strip. The Positions and Covering methodology is based on a two-stage procedure. First, it is generated, in a pseudo-polynomial way, a set of valid positions in which an item can be packed into the strip. Then, by using a set-covering formulation, the best configuration of items into the strip is selected. Based on the literature benchmark, experimental results validate the quality of the solutions and method’s effectiveness for small and medium-size instances. To the best of our knowledge, this is the first approach that generates optimal solutions for some literature instances for which the optimal solution was unknown before this study.

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26

Horn, Matthias, Emir Demirović, and Neil Yorke-Smith. "Solving the Multi-Choice Two Dimensional Shelf Strip Packing Problem with Time Windows." Proceedings of the International Conference on Automated Planning and Scheduling 33, no. 1 (July 1, 2023): 491–99. http://dx.doi.org/10.1609/icaps.v33i1.27229.

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In the tool coating field, scheduling of production lines requires solving an optimisation problem which we call the multi-choice two-dimensional shelf strip packing problem with time windows. A set of rectangular items needs to be packed in two stages: items are placed on shelves, which in turn are placed on one of several available strips. Crucially, the item's width depends on the chosen strip and each item is associated with a time window such that items can only be placed on the same shelf if their time windows overlap. In collaboration with an industrial partner, this real-world optimisation problem is tackled in this paper by both exact and heuristic methods. The exact method is an arc-flow-based integer linear programming formulation, solved with the commercial solver CPLEX. Experimental evaluation shows that this approach can solve instances to proven optimality with up to 20 different item sizes. Larger, more realistic instances are solved heuristically by an adaptive large neighbourhood search, using first fit and best fit decreasing approaches as repair heuristics. In this way, we obtain high-quality solutions with a remaining optimality gap below 3.3% for instances with up to 2000 different item sizes. The work reported is due to be incorporated into an end-to-end decision support system with the industrial partner.

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27

Junior, Bonfim A., Plácido R. Pinheiro, and Rommel D. Saraiva. "A Hybrid Methodology for Tackling the Irregular Strip Packing Problem*." IFAC Proceedings Volumes 46, no. 7 (May 2013): 396–401. http://dx.doi.org/10.3182/20130522-3-br-4036.00041.

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28

PENG, Bi-Tao, and Yong-Wu ZHOU. "Recursive Heuristic Algorithm for the 2D Rectangular Strip Packing Problem." Journal of Software 23, no. 10 (November 13, 2012): 2600–2611. http://dx.doi.org/10.3724/sp.j.1001.2012.04187.

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29

Cherri, Luiz Henrique, Maria Antónia Carravilla, and Franklina Maria Bragion Toledo. "A MODEL-BASED HEURISTIC FOR THE IRREGULAR STRIP PACKING PROBLEM." Pesquisa Operacional 36, no. 3 (December 2016): 447–68. http://dx.doi.org/10.1590/0101-7438.2016.036.03.0447.

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30

Trushnikov, M. A. "On one problem of Koffman-Shor connected with strip packing." Proceedings of the Institute for System Programming of RAS 22 (2012): 435–55. http://dx.doi.org/10.15514/ispras-2012-22-24.

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31

Chen, Huan, Furong Ye, and Yain-Whar Si. "A Hybrid Algorithm for Strip Packing Problem with Rotation Constraint." MATEC Web of Conferences 68 (2016): 06001. http://dx.doi.org/10.1051/matecconf/20166806001.

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32

Boschetti, Marco Antonio, and Lorenza Montaletti. "An Exact Algorithm for the Two-Dimensional Strip-Packing Problem." Operations Research 58, no. 6 (December 2010): 1774–91. http://dx.doi.org/10.1287/opre.1100.0833.

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33

Cui, Y., T. Gu, and Y. Zhong. "A recursive algorithm for the rectangular guillotine strip packing problem." Engineering Optimization 40, no. 4 (April 2008): 347–60. http://dx.doi.org/10.1080/03052150701753356.

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34

Buchwald, Torsten, and Guntram Scheithauer. "Upper bounds for heuristic approaches to the strip packing problem." International Transactions in Operational Research 23, no. 1-2 (May 30, 2014): 93–119. http://dx.doi.org/10.1111/itor.12100.

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35

Babaoğlu, İsmail. "Solving 2D strip packing problem using fruit fly optimization algorithm." Procedia Computer Science 111 (2017): 52–57. http://dx.doi.org/10.1016/j.procs.2017.06.009.

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36

Alvarez-Valdes, R., F. Parreño, and J. M. Tamarit. "A branch and bound algorithm for the strip packing problem." OR Spectrum 31, no. 2 (March 7, 2008): 431–59. http://dx.doi.org/10.1007/s00291-008-0128-5.

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37

Wei, Lijun, Wee-Chong Oon, Wenbin Zhu, and Andrew Lim. "A reference length approach for the 3D strip packing problem." European Journal of Operational Research 220, no. 1 (July 2012): 37–47. http://dx.doi.org/10.1016/j.ejor.2012.01.039.

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38

He, Kun, Yan Jin, and Wenqi Huang. "Heuristics for two-dimensional strip packing problem with 90° rotations." Expert Systems with Applications 40, no. 14 (October 2013): 5542–50. http://dx.doi.org/10.1016/j.eswa.2013.04.005.

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39

Sugi, Masao, Yusuke Shiomi, Tsuyoshi Okubo, Hidetoshi Nagai, Kazuyoshi Inoue, and Jun Ota. "Solution of the Rectangular Strip Packing Problem Considering a 3-Stage Guillotine Cutting Constraint with Finite Slitter Blades." International Journal of Automation Technology 14, no. 3 (May 5, 2020): 447–58. http://dx.doi.org/10.20965/ijat.2020.p0447.

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In this study, we propose a new algorithm to solve the rectangular strip packing problem (RSPP), a variant of the cutting stock problem in which the mother materials have a common fixed width and infinite length. Based on the column-generation technique with three improvements, the proposed algorithm can solve large-scale problems involving tens of thousands of materials within a reasonable time, considering practical cutting constraints, i.e., the three-stage guillotine cutting constraint and the limitations of slitter blades. The proposed algorithm is evaluated in terms of its packing efficiency and calculation time.

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40

Leao, Aline A. S., Franklina M. B. Toledo, José Fernando Oliveira, and Maria Antónia Carravilla. "A semi-continuous MIP model for the irregular strip packing problem." International Journal of Production Research 54, no. 3 (May 13, 2015): 712–21. http://dx.doi.org/10.1080/00207543.2015.1041571.

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41

Verstichel, Jannes, Patrick De Causmaecker, and Greet Vanden Berghe. "An improved best-fit heuristic for the orthogonal strip packing problem." International Transactions in Operational Research 20, no. 5 (June 27, 2013): 711–30. http://dx.doi.org/10.1111/itor.12030.

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42

Allen, S. D., E. K. Burke, and G. Kendall. "A hybrid placement strategy for the three-dimensional strip packing problem." European Journal of Operational Research 209, no. 3 (March 2011): 219–27. http://dx.doi.org/10.1016/j.ejor.2010.09.023.

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43

Zhang, Defu, Yan Kang, and Ansheng Deng. "A new heuristic recursive algorithm for the strip rectangular packing problem." Computers & Operations Research 33, no. 8 (August 2006): 2209–17. http://dx.doi.org/10.1016/j.cor.2005.01.009.

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44

Cui, Yaodong, Liu Yang, and Qiulian Chen. "Heuristic for the rectangular strip packing problem with rotation of items." Computers & Operations Research 40, no. 4 (April 2013): 1094–99. http://dx.doi.org/10.1016/j.cor.2012.11.020.

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45

Rodrigues, Marcos Okamura, and Franklina M. B. Toledo. "A clique covering MIP model for the irregular strip packing problem." Computers & Operations Research 87 (November 2017): 221–34. http://dx.doi.org/10.1016/j.cor.2016.11.006.

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46

MRAD, Mehdi, Tamer G. ALı, Ali BALMA, Anis GHARBı, Ali SAMHAN, and M. A. LOULY. "The Two-Dimensional Strip Cutting Problem: Improved Results on Real-World Instances." Eurasia Proceedings of Educational and Social Sciences 22 (December 31, 2021): 1–10. http://dx.doi.org/10.55549/epess.1040517.

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Cutting and packing problems arise in various industrial settings such as production of metal, glass sheets, papers, etc. The demand of items should be met while minimizing loss of waste material. One of the most known as a contemporary problem in field of operations research is the two-dimensional strip cutting problem. A set of m rectangular items is to be cut from a two-dimensional strip of width W and infinite height. Each item i (i=1,2,…,m) has a width wi, a height hi, and a demand di. The objective is to determine how to cut the demanded items using the minimum height of strip and meet all the demands, while respecting the two stages of guillotine cuts. We address the arc-flow formulation for this NP-hard problem. A graph compression method is proposed and it is shown that substantially better results are achieved in obtaining optimal or near-optimal solutions of real-world instances.

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47

Chen, Bili, Yong Wang, and Shuangyuan Yang. "A Hybrid Demon Algorithm for the Two-Dimensional Orthogonal Strip Packing Problem." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/541931.

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This paper develops a hybrid demon algorithm for a two-dimensional orthogonal strip packing problem. This algorithm combines a placement procedure based on an improved heuristic, local search, and demon algorithm involved in setting one parameter. The hybrid algorithm is tested on a wide set of benchmark instances taken from the literature and compared with other well-known algorithms. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm.

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48

Soh, Takehide, Katsumi Inoue, Naoyuki Tamura, Mutsunori Banbara, and Hidetomo Nabeshima. "A SAT-based Method for Solving the Two-dimensional Strip Packing Problem." Fundamenta Informaticae 102, no. 3-4 (2010): 467–87. http://dx.doi.org/10.3233/fi-2010-314.

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Oliveira, José Fernando, Alvaro Neuenfeldt Júnior, Elsa Silva, and Maria Antónia Carravilla. "A SURVEY ON HEURISTICS FOR THE TWO-DIMENSIONAL RECTANGULAR STRIP PACKING PROBLEM." Pesquisa Operacional 36, no. 2 (August 2016): 197–226. http://dx.doi.org/10.1590/0101-7438.2016.036.02.0197.

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Rodrigues, Marcos Okamura, Luiz Henrique Cherri, and Leandro Resende Mundim. "MIP models for the irregular strip packing problem: new symmetry breaking constraints." ITM Web of Conferences 14 (2017): 00005. http://dx.doi.org/10.1051/itmconf/20171400005.

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