Abstract
In this paper, the authors present a new algorithm efficient solution to the packing problem in two dimensions. The authors propose a new heuristic using the value of the electromagnetic field to determine the best position to place a circular object in a configuration of other circular objects previously packed. Also, this algorithm simulates two processes to compact objects already placed, inspired by gravitational forces, to minimize the empty space in the container and maximizing the number of objects in the container. To determine the efficacy of this algorithm, the authors carried out experiments with twenty-four instances. Parallel computing can contribute to making decision processes such as optimization and prediction more agile and faster. Real-time decision making involves the use of solution methodologies and algorithms. For this reason the present manuscript shows an alternative for the solution of a classic industry problem that must be solved quickly. Packaging optimization can help reduce waste of container material. The material used to transport the products can reduce its environmental impact due to an efficient packaging process. Light-weighting can also be accomplished by reducing the amount of packaging material used.
Similar content being viewed by others
References
Ababei C (2009) Parallel placement for fpgas revisited. In: Proceedings of the ACM/SIGDA international symposium on field programmable gate arrays. ACM, pp 280–280
Addis B, Locatelli M, Schoen F (2008) Disk packing in a square: a new global optimization approach. Informs J Comput 20(4):516–524
Al-Mudahka I, Hifi M, M’Hallah R (2011) Packing circles in the smallest circel: an adaptive hybrid algorithm. J Oper Res Soc 62:1917–1930
Alba E, Luque G, Nesmachnow S (2013) Parallel metaheuristics: recent advances and new trends. Int Trans Oper Res 20(1):1–48. https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1475-3995.2012.00862.x
Birgin EG, Gentil JM (2010) New and improved results for packing identical unitary radius circles within triangles, rectangles and strips. Comput Oper Res 37(7):1318–1327. https://doi.org/10.1016/j.cor.2009.09.017. http://www.sciencedirect.com/science/article/pii/S0305054809002354. Algorithmic and Computational Methods in Retrial Queues
Boll DW, Donovan J, Graham RL, Lubachevsky BD (2000) Improving dense packings of equal disks in a square. Electron J Comb 7(1):1–9
Brinker J, G‘̀und‘̀uz HI (2016) Optimization of demand-related packaging sizes using a p-median approach. Int J Adv Manuf Technol 87(5):2259–2268. https://doi.org/10.1007/s00170-016-8630-4
Casotto A, Romeo F, Sangiovanni-Vincentelli A (1987) A parallel simulated annealing algorithm for the placement of macro-cells. IEEE Trans Comput-Aided Des Integr Circ Syst 6 (5):838–847. https://doi.org/10.1109/TCAD.1987.1270327
Chrisochoides N (1996) Multithreaded model for the dynamic load-balancing of parallel adaptive pde computations. Appl Numer Math 20(4):349–365. https://doi.org/10.1016/0168-9274(95)00104-2. http://www.sciencedirect.com/science/article/pii/0168927495001042. Adaptive mesh refinement methods for CFD applications
Darema F, Kirkpatrick S, Norton VA (1987) Parallel algorithms for chip placement by simulated annealing. IBM J Res Dev 31(3):391–402. https://doi.org/10.1147/rd.313.0391
Dell’Amico M, Díza JCD, Lori M (2012) The bin packing problem with precedence constraints. Oper Res 60(6):1491–1504
Delévacq A, Delisle P, Gravel M, Krajecki M (2013) Parallel ant colony optimization on graphics processing units. J Parallel Distrib Comput 73(1):52–61. https://doi.org/10.1016/j.jpdc.2012.01.003. http://www.sciencedirect.com/science/article/pii/S0743731512000044. Metaheuristics on GPUs
Dunin-Borkowski RE (2014) Recent progress in electromagnetic field mapping at the nanoscale. Microscopy 63:i1–i1
Dyckhoff H (1990) A typology of cutting and packing problems. Eur J Oper Res 44(2):145–159. https://doi.org/10.1016/0377-2217(90)90350-K. http://www.sciencedirect.com/science/article/pii/037722179090350K. Cutting and Packing
Fasano G (2014) Solving Non-standard Packing Problems by Global Optimization and Heuristics. Springer Publishing Company, Incorporated
Felten EW, McNamee D (1992) Improving the performance of message-passing applications by multithreading. In: Proceedings scalable high performance computing conference SHPCC-92. https://doi.org/10.1109/SHPCC.1992.232684, pp 84–89
Fernández A, Gil C, Baños R, Montoya MG (2013) A parallel multi-objective algorithm for two-dimensional bin packing with rotations and load balancing. Expert Syst Appl 40(13):5169–5180. https://doi.org/10.1016/j.eswa.2013.03.015. http://www.sciencedirect.com/science/article/pii/S0957417413001656
Galiev SI, Lisafina MS (2013) Linear models for the approximate solution of the problem of packing equal circles into a given domain. Eur J Oper Res 230(3):505–514
G‘̀ulc‘̀u Ş, Kodaz H (2015) A novel parallel multi-swarm algorithm based on comprehensive learning particle swarm optimization. Eng Appl Artif Intel 45:33–45
Haus JW (2016) Introduction to nanophotonics. In: Haus JW (ed) Fundamentals and applications of nanophotonics. Woodhead Publishing, pp 1–11
Ivanov D, Dolgui A, Sokolov B, Werner F, Ivanova M (2016) A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0. Int J Prod Res 54(2):386–402. https://doi.org/10.1080/00207543.2014.999958
Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, New York. http://cdsweb.cern.ch/record/490457
Kalas I, Arjomandi E, Gao GR, O’Farrell B (1994) Ftl: a multithreaded environment for parallel computation. In: Proceedings of the 1994 conference of the centre for advanced studies on collaborative research, CASCON ’94. http://dl.acm.org/citation.cfm?id=782185.782218. IBM Press, pp 33–
Kravitz SA, Rutenbar RA (1987) Placement by simulated annealing on a multiprocessor. IEEE Trans Comput-Aided Des Integr Circ Syst 6(4):534–549. https://doi.org/10.1109/TCAD.1987.1270301
Kubica BJ, Wodniak A (2010) Optimization of the multi-threaded interval algorithm for the pareto-set computation. Journal of Telecommunications and Information Technology, 70–75
le Feber B (2015) Nanoscale electric and magnetic optical vector fields: mapping & injection. Ph.D. thesis, University of Twente
Lisafina MS, Galiev SI (2013) Numerical optimization methods for packing equal orthogonally oriented ellipses in a rectangular domain. Comput Math Math Phys 53(11):1748–1762
Litvinchev I, Infante L, Ozuna L (2015) Packing circular-like objects in a rectangular container. J Comput Syst Sci Int 54(2):259–267. https://doi.org/10.1134/S1064230715020070
Martinez-Rios F (2017) A new hybridized algorithm based on population-based simulated annealing with an experimental study of phase transition in 3-sat. Procedia Comput Sci 116:427–434. https://doi.org/10.1016/j.procs.2017.10.022. http://www.sciencedirect.com/science/article/pii/S1877050917320653. Discovery and innovation of computer science technology in artificial intelligence era: The 2nd International Conference on Computer Science and Computational Intelligence (ICCSCI 2017)
Martinez-Rios F (2017) A new hybridized algorithm based on population-based simulated annealing with an experimental study of phase transition in 3-sat. Procedia Comput Sci 116:427–434. Discovery and innovation of computer science technology in artificial intelligence era: The 2nd International Conference on Computer Science and Computational Intelligence (ICCSCI 2017)
Martinez-Rios F, Marmolejo-Saucedo JA (2019) Packing instances. www.packingproblem.com
Martinez-Rios F, Marmolejo-Saucedo JA, Murillo-Suarez A (2018) A new heuristic algorithm to solve circle packing problem inspired by nanoscale electromagnetic fields and gravitational effects. In: 2018 Nanotechnology for Instrumentation and Measurement (NANOfIM). https://doi.org/10.1109/NANOFIM.2018.8688621, pp 1–6
Martinez-Rios F, Murillo-Suarez A (2018) A new swarm algorithm for global optimization of multimodal functions over multi-threading architecture hybridized with simulating annealing. Procedia Comput Sci 135:449–456. https://doi.org/10.1016/j.procs.2018.08.196. http://www.sciencedirect.com/science/article/pii/S1877050918314868. The 3rd International Conference on Computer Science and Computational Intelligence (ICCSCI 2018) : Empowering Smart Technology in Digital Era for a Better Life
McKinnon AC (2005) The economic and environmental benefits of increasing maximum truck weight: the british experience. Transp Res Part D: Transp Environ 10(1):77–95. https://doi.org/10.1016/j.trd.2004.09.006. http://www.sciencedirect.com/science/article/pii/S1361920904000641
M‘̀uller JM, Voigt KI (2018) The impact of industry 4.0 on supply chains in engineer-to-order industries - an exploratory case study. IFAC-PapersOnLine 51(11):122–127. https://doi.org/10.1016/j.ifacol.2018.08.245. http://www.sciencedirect.com/science/article/pii/S2405896318313697. 16th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2018
Richie JE, Ababei C (2017) Optimization of patch antennas via multithreaded simulated annealing based design exploration. J Comput Des Eng 4(4):249–255. https://doi.org/10.1016/j.jcde.2017.06.004. http://www.sciencedirect.com/science/article/pii/S2288430017300702
Sarangan A (2016) Quantum mechanics and computation in nanophotonics. In: Haus JW (ed) Fundamentals and applications of nanophotonics. Woodhead Publishing, pp 45–87
Rubiano da Silva N, M‘̀oller M, Feist A, Ulrichs H, Ropers C, Sch‘̀afer S (2018) Nanoscale mapping of ultrafast magnetization dynamics with femtosecond lorentz microscopy. Phys Rev X 8:031052
Steuwe C, Erdelyi M, Szekeres G, Csete M, Baumberg JJ, Mahajan S, Kaminski CF (2015) Visualizing electromagnetic fields at the nanoscale by single molecule localization. Nano Lett 15(5):3217–3223
Szabó PG, Markót MC, Csendes T, Specht E, Casado LG, Garcãa I (2007) New approaches to circle packing in a square: with program codes (springer optimization and its applications). Springer, Berlin
Takeda J, Yoshioka K, Minami Y, Katayama I (2018) Nanoscale electron manipulation in metals with intense thz electric fields. J Phys D: Appl Phys 51(10):103001
Torres-Escobar R, Marmolejo-Saucedo JA, Litvinchev I (2018) Binary monkey algorithm for approximate packing non-congruent circles in a rectangular container. Wirel Netw, 1–10. https://doi.org/10.1007/s11276-018-1869-y
Torres-Escobar R, Marmolejo-Saucedo JA, Litvinchev I, Vasant P (2019) Monkey algorithm for packing circles with binary variables. In: Vasant P, Zelinka I, Weber GW (eds) Intelligent computing & optimization. Springer International Publishing, Cham, pp 547–559
W‘̀ascher G, Haußner H, Schumann H (2007) An improved typology of cutting and packing problems. Europ J Oper Res 183(3):1109–1130. https://doi.org/10.1016/j.ejor.2005.12.047. http://www.sciencedirect.com/science/article/pii/S037722170600292X
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Martinez-Rios, F., Marmolejo-Saucedo, J.A., García-Jacas, C.R. et al. μ𝜃-EGF: A New Multi-Thread and Nature-Inspired Algorithm for the Packing Problem. Mobile Netw Appl 25, 2105–2117 (2020). https://doi.org/10.1007/s11036-020-01558-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11036-020-01558-8