knapsack type problems |
Scheithauer & Terno (1993SCHEITHAUER G & TERNO J. 1993. Modeling of packing problems. Optimization, 28(1): 63-84. Available at: https://doi.org/10.1080/02331939308843904. https://doi.org/10.1080/0233193930884390...
) |
mixed-integer linear optimization models |
quality zones or defects |
Chung et al. (1990CHUNG J, SCOTT III DR & HILLMAN DJ. 1990. Intelligent nesting system on 2-D highly irregular resources. In: TRIVEDI MM (Ed.), Applications of Artificial Intelligence VIII, vol. 1293. pp. 472-483. International Society for Optics and Photonics. Orlando, FL, United States: SPIE. Available at: https://doi.org/10.1117/12.21096. https://doi.org/10.1117/12.21096...
) |
hybrid heuristic |
Martins & Tsuzuki (2010MARTINS TC & TSUZUKI MSG. 2010. Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions. Expert Systems with Applications, 37: 1955-1972. Available at: https://doi.org/10.1016/j.eswa.2009.06.081. https://doi.org/10.1016/j.eswa.2009.06.0...
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simulated annealing |
Heistermann & Lengauer (1995HEISTERMANN J & LENGAUER T. 1995. The nesting problem in the leather manufacturing industry. Annals of Operations Research, 57: 147-173. Available at: https://doi.org/10.1007/BF02099695. https://doi.org/10.1007/BF02099695...
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constructive heuristic |
Valle et al. (2012VALLE AMD, QUEIROZ TA, MIYAZAWA FK & XAVIER EC. 2012. Heuristics for two-dimensional knapsack and cutting stock problems with items of irregular shape. Expert Systems with Applications , 39(16): 12589-12598. Available at: https://doi.org/10.1016/j.eswa.2012.05.025. https://doi.org/10.1016/j.eswa.2012.05.0...
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greedy randomized adaptive search procedure |
Han & Na (1994HAN GC & NA SJ. 1994. A New Multi-Stage Layout Approach for Optimal Nesting of 2-Dimensional Patterns with Boundary Constraints and Internal Defects. Transactions of the Korean Society of Mechanical Engineers, 18(12): 3236-3245. Available at: https://doi.org/10.22634/KSME.1994.18.12.3236. https://doi.org/10.22634/KSME.1994.18.12...
) |
two-stage heuristic |
Mundim & Queiroz (2012MUNDIM LR & QUEIROZ TA. 2012. A hybrid heuristic for the 0-1 knapsack problem with items of irregular shape. In: XXXVIII Conferência Latino-americana em Informática (CLEI). pp. 1-6. Medellín, Colombia. Available at: https://doi.org/10.1109/CLEI.2012.6427170. https://doi.org/10.1109/CLEI.2012.642717...
) |
greedy randomized adaptive search procedure with simulated annealing |
Tay & Lee (2002TAY FEH & LEE CFC. 2002. Pattern nesting on irregular-shaped stock using Genetic Algorithms. Engineering Applications of Artificial Intelligence, 15: 551-558. Available at: https://doi.org/10.1016/S0952-1976(03)00009-5. https://doi.org/10.1016/S0952-1976(03)00...
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genetic algorithm |
Dalalah et al. (2014DALALAH D, KHRAIS S & BATAINEH K. 2014. Waste minimization in irregular stock cutting. Journal of Manufacturing Systems, 33(1): 27-40. Available at: https://doi.org/10.1016/j.jmsy.2013.11.003. https://doi.org/10.1016/j.jmsy.2013.11.0...
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constructive heuristics |
Yuping et al. (2005YUPING Z, SHOUWEI J & CHUNLI Z. 2005. A very fast simulated re-annealing algorithm for the leather nesting problem. International Journal of Advanced Manufacturing Technology, 25(11): 1113-1118. Available at: https://doi.org/10.1007/s00170-003-1966-6. https://doi.org/10.1007/s00170-003-1966-...
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simulated annealing |
Baldacci et al. (2014BALDACCI R, BOSCHETTI MA, GANOVELLI M & MANIEZZO V. 2014. Algorithms for nesting with defects. Discrete Applied Mathematics, 163, Part 1: 17-33. Available at: https://doi.org/10.1016/j.dam.2012.03.026. https://doi.org/10.1016/j.dam.2012.03.02...
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mixed-integer linear optimization models |
Crispin et al. (2005CRISPIN A, CLAY P, TAYLOR G, BAYES T & REEDMAN D. 2005. Genetic algorithm coding methods for leather nesting. Applied Intelligence, 23: 9-20. Available at: https://doi.org/10.1007/s10489-005-2368-2. https://doi.org/10.1007/s10489-005-2368-...
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genetic algorithm |
Mundim et al. (2018MUNDIM LR, ANDRETTA M, CARRAVILLA MA & OLIVEIRA JF. 2018. A general heuristic for two-dimensional nesting problems with limited-size containers. International Journal of Production Research, 56(1-2): 709-732. Available at: https://doi.org/10.1080/00207543.2017.1394598. https://doi.org/10.1080/00207543.2017.13...
) |
general heuristic |
Lee et al. (2008LEE WC, MA H & CHENG BW. 2008. A heuristic for nesting problems of irregular shapes. Computer-Aided Design, 40(5): 625-633. Available at: https://doi.org/10.1016/j.cad.2008.02.008. https://doi.org/10.1016/j.cad.2008.02.00...
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constructive heuristic |
Souza Queiroz & Andretta (2020SOUZA QUEIROZ LR & ANDRETTA M. 2020. Two effective methods for the irregular knapsack problem. Applied Soft Computing, 95: 106485. Available at: https://doi.org/10.1016/j.asoc.2020.106485. https://doi.org/10.1016/j.asoc.2020.1064...
) |
biased random key genetic algorithm and variable neighborhood search |
Alves et al. (2012aALVES CMM, BRÁS PAF, CARVALHO JMV & PINTO TMP. 2012a. New constructive algorithms for leather nesting in the automotive industry. Computers & Operations Research, 39(7): 1487-1505. Available at: https://doi.org/10.1016/j.cor.2011.08.021. https://doi.org/10.1016/j.cor.2011.08.02...
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constructive heuristic |
Román (2020ROMÁN AE. 2020. An Evolutionary Algorithm for Solving the Two-Dimensional Irregular Shape Packing Problem Combined with the Knapsack Problem. Master in artificial intelligence. Polytechnic University of Catalonia. Barcelona, Spain.) |
evolutionary algorithm |
Alves et al. (2012bALVES CMM, BRÁS PAF, CARVALHO JMV & PINTO TMP. 2012b. A variable neighborhood search algorithm for the leather nesting problem. Mathematical Problems in Engineering, 183: 28. Available at: https://doi.org/10.1155/2012/254346. https://doi.org/10.1155/2012/254346...
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variable neighborhood search |
Mundim & Andretta (2014MUNDIM LR & ANDRETTA M. 2014. Problema de corte de itens irregulares na fabricação de luvas de couro. In: XLVI Simpósio Brasileiro de Pesquisa Operacional. pp. 1-12. Salvador-BA, Brasil.) |
hybrid heuristic |
uncertainties |
Mundim (2017MUNDIM LR, ANDRETTA M & QUEIROZ TA. 2017. A biased random key genetic algorithm for open dimension nesting problems using no-fit raster. Expert Systems with Applications , 81(15): 358-371. Available at: https://doi.org/10.1016/j.eswa.2017.03.059. https://doi.org/10.1016/j.eswa.2017.03.0...
) |
two-stage stochastic model |
Pinto et al. (2016PINTO TMP, ALVES CMM, CARVALHO JMV & BRÁS PAF. 2016. Heuristic methods for the leather nesting problem in the automotive industry. International Journal of Business Excellence, 9(3): 332-347. Available at: https://dx.doi.org/10.1504/IJBEX.2016.075594. https://dx.doi.org/10.1504/IJBEX.2016.07...
) |
constructive heuristic |
Souza Queiroz & Andretta (2022SOUZA QUEIROZ LR & ANDRETTA M. 2022. A branch-and-cut algorithm for the irregular strip packing problem with uncertain demands. International Transactions in Operational Research, 29(6): 3486-3513. Available at: https://doi.org/10.1111/itor.13122. https://doi.org/10.1111/itor.13122...
) |
two-stage stochastic model |
Reijntjes (2016REIJNTJES IE. 2016. Solving a nesting problem using the collision free region. Master in mathematics and computer science. Eindhoven University of Technology. Eindhoven, Netherlands.) |
branch-and-bound algorithm |
Chen et al. (2020CHEN K, ZHUANG J, ZHONG S & ZHENG S. 2020. Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate. Mathematics, 8(11). Available at: https://www.mdpi.com/2227-7390/8/11/1914. https://www.mdpi.com/2227-7390/8/11/1914...
) |
level based heuristic |