Abstract
Unequal area facility layout problems deal with the placement of departments in a particular area. In these problems, unsettled rectangular-shaped blocks with an aspect ratio limitation are arranged in a given space. This has been widely studied for facility planning design and operating efficiency. Therefore, many metaheuristic approaches have been suggested to determine optimal solutions. In this study, monarch butterfly optimization, a recently developed algorithm, is presented to solve an unequal area facility layout problem. A slicing tree representation is used to form a layout structure as well as greedy acceptance, which accelerates the monarch butterfly optimization’s search performance. A set of well-known instances from existing studies is tested to evaluate the algorithm’s effectiveness. Meaningful results are obtained from various categories. The proposed algorithm generates solutions that match the best results from previous research, and it provides such solutions within a comparable amount of time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data sharing is not applicable to this article as no new data were created. Datasets are referred in this article.
Availability of data and material
Not applicable (datasets are referred).
References
Abedinia O, Zareinejad M, Doranehgard MH, Fathi G, Ghadimi N (2019) Optimal offering and bidding strategies of renewable energy based large consumer using a novel hybrid robust-stochastic approach. J Clean Prod 215:878–889. https://doi.org/10.1016/j.jclepro.2019.01.085
Armour GC, Buffa ES (1963) A Heuristic algorithm and simulation approach to relative location of facilities. Manag Sci 9(2):294–309. https://doi.org/10.1287/mnsc.9.2.294
Arora S, Singh S (2017) Node localization in wireless sensor networks using butterfly optimization algorithm. Arab J Sci Eng 42:3325–3335. https://doi.org/10.1007/s13369-017-2471-9
Azadivar F, Wang J (2000) Facility layout optimization using simulation and genetic algorithms. Int J Prod Res 38(17):4369–4383. https://doi.org/10.1080/00207540050205154
Bacanin N, Bezdan T, Tuba E, Srumberger I, Tuba M (2020) Monarch butterfly optimization based convolutional neural network design. Mathematics 8(6):936. https://doi.org/10.3390/math8060936
Bazaraa MS (1975) Computerized layout design: A branch and bound approach. AIIE Trans 7(4):432–438. https://doi.org/10.1080/05695557508975028
Bozer YA, Meller RD (1997) A reexamination of the distance-based facility layout problem. IIE Trans 29(7):549–560. https://doi.org/10.1080/07408179708966365
Bozer YA, Wang CT (2012) A graph-pair representation and MIP-model-based heuristic for the unequal-area facility layout problem. Eur J Oper Res 218(2):382–391. https://doi.org/10.1016/j.ejor.2011.10.052
Bukchin Y, Tzur M (2014) A new MILP approach for the facility process-layout design problem with rectangular and L/T shape departments. Int J Prod Res 52(24):7339–7359. https://doi.org/10.1080/00207543.2014.930534
Castillo I, Westerlund J, Emet S, Westerlund T (2005) Optimization of block layout design problems with unequal areas: a comparison of MILP and MINLP optimization methods. Comput Chem Eng 30(1):54–69. https://doi.org/10.1016/j.compchemeng.2005.07.012
Castillo I, Westerlund T (2005) An ε-accurate model for optimal unequal-area block layout design. Comput Oper Res 32(3):429–447. https://doi.org/10.1016/S0305-0548(03)00246-6
Chae J, Regan AC (2016) Layout design problems with heterogeneous area constraints. Comput Ind Eng 102:198–207. https://doi.org/10.1016/j.cie.2016.10.016
Chang M, Lin H (2012) A flexible bay structure representation and ant colony system for unequal area facility layout problems. In: World congress on engineering and computer science, vol III, pp 2–7
Chen S, Chen R, Gao J (2017) A monarch butterfly optimization for the dynamic vehicle routing problem. Algorithms 10(3):107. https://doi.org/10.3390/a10030107
Chittratanawat S, Noble JS (1999) An integrated approach for facility layout, P/D location and material handling system design. Int J Prod Res 37(3):683–706. https://doi.org/10.1080/002075499191733
Co H, Wu A, Reisman A (1989) A throughput-maximizing factory planning and layout model. Int J Prod Res 27(1):1–12
Deechongkit S, Srinon R (2014) New mixed integer programming for facility layout design without loss of department area. Ind Eng Lett 4(8):21–28
Dorigo M, Di-Caro G (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol 2. IEEE, pp 1470–1477
Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: a survey. Annu Rev Control 31(2):255–267. https://doi.org/10.1016/j.arcontrol.2007.04.001
Dunker T, Radons G, Westkämper E (2003) A coevolutionary algorithm for a facility layout problem. Int J Prod Res 41(15):3479–3500. https://doi.org/10.1080/0020754031000118125
Friedrich C, Klausnitzer A, Lasch R (2018) Integrated slicing tree approach for solving the facility layout problem with input and output locations based on contour distance. Eur J Oper Res 270(3):837–851. https://doi.org/10.1016/j.ejor.2018.01.001
Garcia-Hernandez L, Salas-Morera L, Garcia-Hernandez JA, Salcedo-Sanz S, Valente de Oliveira J (2019) Applying the coral reefs optimization algorithm for solving unequal area facility layout problems. Expert Syst Appl 138:112819. https://doi.org/10.1016/j.eswa.2019.07.036
Ghanem WAHM, Jantan A (2018) Hybridizing artificial bee colony with monarch butterfly optimization for numerical optimization problems. Neural Comput Appl 30:163–181. https://doi.org/10.1007/s00521-016-2665-1
Ghetas M, Yong CH, Sumari P (2016) Harmony-based monarch butterfly optimization algorithm. In: Proceedings—5th ieee international conference on control system, computing and engineering, ICCSCE 2015, pp 156–161. https://doi.org/10.1109/ICCSCE.2015.7482176
Glover F (1989) Tabu search—part 1. ORSA J Comput 1(3):190–206. https://doi.org/10.1287/ijoc.1.3.190
Gonçalves JF, Resende MGC (2015) A biased random-key genetic algorithm for the unequal area facility layout problem. Eur J Oper Res 246(1):86–107. https://doi.org/10.1016/j.ejor.2015.04.029
Hasda RK, Bhattacharjya RK, Bennis F (2017) Modified genetic algorithms for solving facility layout problems. Int J Interact Des Manuf (IJIDeM) 11(3):713–725. https://doi.org/10.1007/s12008-016-0362-z
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: Algorithm and applications. Futur Gener Comput Syst 97:849–872
Hernández Gress ES, Mora-Vargas J, Herrera Del Canto LE, Díaz-Santillán E (2011) A genetic algorithm for optimal unequal-area block layout design. Int J Prod Res 49(8):2183–2195. https://doi.org/10.1080/00207540903130868
Hosseini-Nasab H, Fereidouni S, Fatemi Ghomi SMT, Fakhrzad MB (2017) Classification of facility layout problems: a review study. Int J Adv Manuf Technol 94:957–977. https://doi.org/10.1007/s00170-017-0895-8
Ingole S, Singh D (2017) Unequal-area, fixed-shape facility layout problems using the firefly algorithm. Eng Optim 49(7):1097–1115. https://doi.org/10.1080/0305215X.2016.1235327
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95—international conference on neural networks, vol 4, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Kang S, Chae J (2017) Harmony search for the layout design of an unequal area facility. Expert Syst Appl 79:269–281. https://doi.org/10.1016/j.eswa.2017.02.047
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471. https://doi.org/10.1007/s10898-007-9149-x
Kaufman L, Broeckx F (1978) An algorithm for the quadratic assignment problem using Bender’s decomposition. Eur J Oper Res. https://doi.org/10.1016/0377-2217(78)90095-4
Khodaei H, Hajiali M, Darvishan A, Sepehr M, Ghadimi N (2018) Fuzzy-based heat and power hub models for cost-emission operation of an industrial consumer using compromise programming. Appl Therm Eng 137:395–405. https://doi.org/10.1016/j.applthermaleng.2018.04.008
Kim M, Chae J (2019) Monarch butterfly optimization for facility layout design based on a single loop material handling path. Mathematics 7(2):154. https://doi.org/10.3390/math7020154
Kim JG, Kim YD (1998) A space partitioning method for facility layout problems with shape constraints. IIE Trans 30(10):947–957. https://doi.org/10.1080/07408179808966548
Kochhar JS, Foster BT, Heragu SS (1998) HOPE: a genetic algorithm for the unequal area facility layout problem. Comput Oper Res 25(7–8):583–594. https://doi.org/10.1016/S0305-0548(97)00100-7
Komarudin, Wong KY (2010) Applying ant system for solving unequal area facility layout problems. Eur J Oper Res 202(3):730–746. https://doi.org/10.1016/j.ejor.2009.06.016
Konak A, Kulturel-Konak S, Norman BA, Smith AE (2006) A new mixed integer programming formulation for facility layout design using flexible bays. Oper Res Lett 34(6):660–672. https://doi.org/10.1016/j.orl.2005.09.009
Kulturel-Konak S (2012) A linear programming embedded probabilistic tabu search for the unequal-area facility layout problem with flexible bays. Eur J Oper Res 223(3):614–625. https://doi.org/10.1016/j.ejor.2012.07.019
Kulturel-Konak S, Konak A (2011a) A new relaxed flexible bay structure representation and particle swarm optimization for the unequal area facility layout problem. Eng Optim 43(12):1263–1287. https://doi.org/10.1080/0305215X.2010.548864
Kulturel-Konak S, Konak A (2011b) Unequal area flexible bay facility layout using ant colony optimisation. Int J Prod Res 49(7):1877–1902. https://doi.org/10.1080/00207541003614371
Kulturel-Konak S, Konak A (2013) Linear programming based genetic algorithm for the unequal area facility layout problem. Int J Prod Res 51(14):4302–4324. https://doi.org/10.1080/00207543.2013.774481
Lee YH, Lee MH (2002) A shape-based block layout approach to facility layout problems using hybrid genetic algorithm. Comput Ind Eng 42(2–4):237–248. https://doi.org/10.1016/S0360-8352(02)00018-9
Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst 111:300–323
Liu Q, Meller RD (2007) A sequence-pair representation and MIP-model-based heuristic for the facility layout problem with rectangular departments. IIE Trans 39(4):377–394. https://doi.org/10.1080/07408170600844108
McKendall AR, Hakobyan A (2010) Heuristics for the dynamic facility layout problem with unequal-area departments. Eur J Oper Res 201(1):171–182. https://doi.org/10.1016/j.ejor.2009.02.028
Meller RD, Gau K-Y (1996) The facility layout problem: recent and emerging trends and perspectives. J Manuf Syst 15(5):351–366. https://doi.org/10.1016/0278-6125(96)84198-7
Meller RD, Narayanan V, Vance PH (1998) Optimal facility layout design. Oper Res Lett 23(3–5):117–127. https://doi.org/10.1016/S0167-6377(98)00024-8
Mirjalili S (2015) Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249
Molina D, Poyatos J, Del Ser J, García S, Hussain A, Herrera F (2020) Comprehensive taxonomies of nature-and bio-inspired optimization:inspiration versus algorithmic behavior, critical analysis recommendations. Cogn Comput 12(5):897–939. https://doi.org/10.1007/s12559-020-09730-8
Montreuil B (1991) A modelling framework for integrating layout design and flow network design. Prog Mater Handl Logist 2:95–115. https://doi.org/10.1007/978-3-642-84356-3_8
Nugent CE, Vollmann TE, Ruml J (1968) An experimental comparison of techniques for the assignment of facilities to locations. Oper Res 16(1):150–173. https://doi.org/10.1287/opre.16.1.150
Paes FG, Pessoa AA, Vidal T (2017) A hybrid genetic algorithm with decomposition phases for the unequal area facility layout problem. Eur J Oper Res 256(3):742–756. https://doi.org/10.1016/j.ejor.2016.07.022
Palomo-Romero JM, Salas-Morera L, García-Hernández L (2017) An island model genetic algorithm for unequal area facility layout problems. Expert Syst Appl 68:151–162. https://doi.org/10.1016/j.eswa.2016.10.004
Peters BA, Yang T (1997) Integrated facility layout and material handling system design in semiconductor fabrication facilities. IEEE Trans Semicond Manuf 10(3):360–369. https://doi.org/10.1109/66.618209
Ripon KSN, Glette K, Khan KN, Hovin M, Torresen J (2013) Adaptive variable neighborhood search for solving multi-objective facility layout problems with unequal area facilities. Swarm Evol Comput 8:1–12. https://doi.org/10.1016/j.swevo.2012.07.003
Saeedi M, Moradi M, Hosseini M et al (2019) Robust optimization based optimal chiller loading under cooling demand uncertainty. Appl Therm Eng 148:1081–1091. https://doi.org/10.1016/j.applthermaleng.2018.11.122
Scholz D, Jaehn F, Junker A (2010) Extensions to STaTS for practical applications of the facility layout problem. Eur J Oper Res 204(3):463–472. https://doi.org/10.1016/j.ejor.2009.11.012
Scholz D, Petrick A, Domschke W (2009) STaTS: a slicing tree and Tabu search based heuristic for the unequal area facility layout problem. Eur J Oper Res 197(1):166–178. https://doi.org/10.1016/j.ejor.2008.06.028
Sherali HD, Fraticelli BMP, Meller RD (2003) Enhanced model formulations for optimal facility layout. Oper Res 51(4):629–644. https://doi.org/10.1287/opre.51.4.629.16096
Sikaroudi AME, Shahanaghi K (2016) Facility layout by collision detection and force exertion heuristics. J Manuf Syst 41:21–30. https://doi.org/10.1016/j.jmsy.2016.07.001
Singh SP, Sharma RRK (2006) A review of different approaches to the facility layout problems. Int J Adv Manuf Technol 30:425–433. https://doi.org/10.1007/s00170-005-0087-9
Strumberger I, Šarac M, Marković D, Bacanin N (2018) Hybridized monarch butterfly algorithm for global optimization problems. Int J Comput 3:63–68
Strumberger I, Tuba E, Bacanin N, Beko N, Tuba M (2020) Modified and hybridized monarch butterfly algorithms for multi-objective optimization. In: Hybrid intelligent systems. Springer, Berlin, pp 449–458
Tam KY (1992a) A simulated annealing algorithm for allocating space to manufacturing cells. Int J Prod Res 30(1):63–87. https://doi.org/10.1080/00207549208942878
Tam KY (1992b) Genetic algorithms, function optimization, and facility layout design. Eur J Oper Res 63(2):322–346. https://doi.org/10.1016/0377-2217(92)90034-7
Tate DM, Smith AE (1995) Unequal-area facility layout by genetic search. IIE Trans 27(4):465–472. https://doi.org/10.1080/07408179508936763
Ulutas B (2012) A modified flexible bay and slicing structure for unequal area facilities. In: IFAC proceedings volumes (IFAC-PapersOnline), vol 14. IFAC. https://doi.org/10.3182/20120523-3-RO-2023.00362
Ulutas BH, Kulturel-Konak S (2012) An artificial immune system based algorithm to solve unequal area facility layout problem. Expert Syst Appl 39(5):5384–5395. https://doi.org/10.1016/j.eswa.2011.11.046
Ulutas BH, Kulturel-Konak S (2013) Assessing hypermutation operators of a clonal selection algorithm for the unequal area facility layout problem. Eng Optim 45(3):375–395. https://doi.org/10.1080/0305215X.2012.678492
van Camp DJ, Carter MW, Vannelli A (1992) A nonlinear optimization approach for solving facility layout problems. Eur J Oper Res 57(2):174–189. https://doi.org/10.1016/0377-2217(92)90041-7
Wang GG (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Comput 10:151–164. https://doi.org/10.1007/s12293-016-0212-3
Wang GG, Deb S, Zhao X, Cui Z (2018a) A new monarch butterfly optimization with an improved crossover operator. Oper Res Int J 18:731–755. https://doi.org/10.1007/s12351-016-0251-z
Wang GG, Deb S, Coelho LDS (2018b) Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. Int J Bio-Inspired Comput 12(1):1–22
Wang GG, Deb S, Coelho LdS (2015) Elephant herding optimization. In: 2015 3rd international symposium on computational and business intelligence (ISCBI), pp 1–5. https://doi.org/10.1109/ISCBI.2015.8.
Wang GG, Hao GS, Cheng S, Qin Q (2016) A discrete monarch butterfly optimization for Chinese TSP problem. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), LNCS, vol 9712, pp 165–173. https://doi.org/10.1007/978-3-319-41000-5_16
Wang MJ, Hu MH, Ku MY (2005) A solution to the unequal area facilities layout problem by genetic algorithm. Comput Ind 56(2):207–220. https://doi.org/10.1016/j.compind.2004.06.003
Wong KY, Komarudin (2010) Solving facility layout problems using flexible bay structure representation and ant system algorithm. Expert Syst Appl 37(7):5523–5527. https://doi.org/10.1016/j.eswa.2009.12.080
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
M. Kim and J. Chae were involved in conception and design of study; M. Kim and J. Chae were involved in resources and acquisition of data; M. Kim was involved in methodology and software; M. Kim and J. Chae were involved in analysis and interpretation of data; M. Kim was involved in writing original draft presentation; J. Chae was involved in revising the manuscript critically for important intellectual content; M. Kim was involved in visualization; J. Chae was involved in supervision and project administration.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
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
Kim, M., Chae, J. A monarch butterfly optimization for an unequal area facility layout problem. Soft Comput 25, 14933–14953 (2021). https://doi.org/10.1007/s00500-021-06076-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-021-06076-7