Abstract
This paper proposes a learning-based simulated annealing (LSA) algorithm to tackle the NP-hard unequal area facility layout problem (UA-FLP). The goal of UA-FLP is to optimize the material flow between facilities of different sizes to enhance manufacturing efficiency. The LSA algorithm incorporates a novel solution representation, an improved penalty function and a diverse set of neighborhood operators to refine the search space. By utilizing a reinforcement learning-based controller, LSA enables a flexible and efficient exploration through state detection and fast feedback. A two-stage greedy local search is employed to further exploit the search space and enhance solution quality. Additional features include temperature sampling generation to minimize parameter settings, a greedy initial solution production to relax infeasible restrictions. Experimental results on 16 well-known instances validate LSA’s high proficiency compared to several state-of-the-art algorithms, and it exceeds 7 best-known solutions within a comparable time, particularly its excellent performance in large instances within a short execution time.
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The data and materials used or analyzed during the current study are available from the first author on reasonable request.
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References
Ahmadi A, Pishvaee MS, Jokar MRA (2017) A survey on multi-floor facility layout problems. Comput Ind Eng 107:158–170. https://doi.org/10.1016/j.cie.2017.03.015
Ahmadi-Javid A, Ardestani-Jaafari A (2021) The unequal area facility layout problem with shortest single-loop AGV path: how material handling method matters. Int J Prod Res 59:2352–2374. https://doi.org/10.1080/00207543.2020.1733124
Anand S, Saravanasankar S, Subbaraj P (2012) Customized simulated annealing based decision algorithms for combinatorial optimization in VLSI floorplanning problem. Comput Optim Appl 52:667–689. https://doi.org/10.1007/s10589-011-9442-y
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
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
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
García-Hernández L, Salas-Morera L, Garcia-Hernandez JA, Salcedo-Sanz S, de Oliveira JV (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
García-Hernández L, Garcia-Hernandez JA, Salas-Morera L, Carmona-Muñoz C, Alghamdi NS, de Oliveira JV, Salcedo-Sanz S (2020a) Addressing unequal area facility layout problems with the coral reef optimization algorithm with substrate layers. Eng Appl Artif Intell 93:103697. https://doi.org/10.1016/j.engappai.2020.103697
García-Hernández L, Salas-Morera L, Carmona-Muñoz C, Abraham A (2020b) A novel multi-objective interactive coral reefs optimization algorithm for the unequal area facility layout problem. Swarm Evol Comput 55:100688. https://doi.org/10.1016/j.swevo.2020.100688
Hou S, Wen H, Feng S, Wang H, Li Z (2019) Application of layered coding genetic algorithm in optimization of unequal area production facilities layout. Comput Intell Neurosci 2019:1687–5265. https://doi.org/10.1155/2019/3650923
Hunagund I, Pillai V, Kempaiah U (2018) A simulated annealing algorithm for unequal area dynamic facility layout problems with flexible bay structure. Int J Ind Eng Comput 9:307–330. https://doi.org/10.5267/j.ijiec.2017.8.004
Hunagund IB, Pillai VM, Kempaiah UN (2021) Solving unequal area facility layout problems with flexible bay structure by simulated annealing algorithm. In: Advances in production and industrial engineering: select proceedings of ICETMIE 2019. Springer, Singapore, pp 75–101. https://doi.org/10.1007/978-981-15-5519-0_7
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
Kim M, Chae J (2021) A monarch butterfly optimization for an unequal area facility layout problem. Soft Comput 25(23):14933–14953. https://doi.org/10.1007/s00500-021-06076-7
Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680. https://doi.org/10.1126/science.220.4598.671
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, Konak A (2011) Unequal area flexible bay facility layout using ant colony optimisation. Int J Prod Res 49:1877–1902. https://doi.org/10.1080/00207541003614371
Li W, Liang P, Sun B, Sun Y, Huang Y (2023) Reinforcement learning-based particle swarm optimization with neighborhood differential mutation strategy. Swarm Evol Comput 78:101274. https://doi.org/10.1016/j.swevo.2023.101274
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
Liu Y, Lu H, Cheng S, Shi Y (2019) An adaptive online parameter control algorithm for particle swarm optimization based on reinforcement learning. In: 2019 IEEE congress on evolutionary computation (CEC), pp 815–822. https://doi.org/10.1109/CEC.2019.8790035
Mazyavkina N, Sviridov S, Ivanov S, Burnaev E (2021) Reinforcement learning for combinatorial optimization: a survey. Comput Oper Res 134:105400. https://doi.org/10.1016/j.cor.2021.105400
Meller RD, Bozer YA (1992) Solving the facility layout problem with simulated annealing. https://www.researchgate.net/publication/30823106. Accessed 4 Oct 2023
Meller RD, Gau KY (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):117–127. https://doi.org/10.1016/S0167-6377(98)00024-8
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
Raza SM, Sajid M, Singh J (2022) Vehicle routing problem using reinforcement learning: recent advancements. In: Gupta D, Sambyo K, Prasad M, Agarwal S (eds) Advanced machine intelligence and signal processing. Lecture notes in electrical engineering, vol 858. Springer, Singapore. https://doi.org/10.1007/978-981-19-0840-8_20
Scalia G, Micale R, Giallanza A, Marannano G (2019) Firefly algorithm based upon slicing structure encoding for unequal facility layout problem. Int J Ind Eng Comput 10(3):349–360. https://doi.org/10.5267/j.ijiec.2019.2.003
Shin D, Onizawa N, Gross WJ, Hanyu T (2023) Memory-efficient fpga implementation of stochastic simulated annealing. IEEE J Emerg Sel Top Circuits Syst 13(1):108–118. https://doi.org/10.1109/JETCAS.2023.3243260
Tam KY (1992a) A simulated annealing algorithm for allocating space to manufacturing cells. Int J Prod Res 30:63–87. 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
Turgay S (2018) Multi objective simulated annealing approach for facility layout design. Int J Math Eng Manag Sci 3:365–380. https://doi.org/10.33889/IJMEMS.2018.3.4-026
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
Vargas-Martínez M, Rangel-Valdez N, Fernández E, Gómez-Santillán C, Morales-Rodríguez ML (2023) Performance analysis of multiobjective simulated annealing based on decomposition. Math Comput Appl. https://doi.org/10.3390/mca28020038
Wang Y, Chen ZB, Wu ZR, Gao Y (2022) Review of reinforcement learning for combinatorial optimization problem. J Front Comput Sci Technol 16(2):19. https://doi.org/10.3778/j.issn.1673-9418.2107040
Wang T, Lu B, Wang W, Wei W, Yuan X, Li J (2023) Reinforcement learning-based optimization for mobile edge computing scheduling game. IEEE Trans Emerg Top Comput Intell 7(1):55–64. https://doi.org/10.1109/TETCI.2022.3145694
Wu J, Song C, Ma J, Wu J, Han G (2022) Reinforcement learning and particle swarm optimization supporting real-time rescue assignments for multiple autonomous underwater vehicles. IEEE Trans Intell Transp Syst 23(7):6807–6820. https://doi.org/10.1109/TITS.2021.3062500
Yin SY, Jin M, Lu HX, Gong GL, Mao WY, Chen G, Li WC (2023) Reinforcement-learning-based parameter adaptation method for particle swarm optimization. Complex Intell Syst 9:5585–5609. https://doi.org/10.1007/s40747-023-01012-8
Zhan SH, Zhang ZJ, Wang LJ, Zhong YW (2018) List-based simulated annealing algorithm with hybrid greedy repair and optimization operator for 0–1 knapsack problem. IEEE Access 6:54447–54458. https://doi.org/10.1109/ACCESS.2018.2872533
Zhao FQ, Wang ZY, Wang L, Xu TP, Zhu NN, Jonrinaldi (2023) A multi-agent reinforcement learning driven artificial bee colony algorithm with the central controller. Expert Syst Appl 219:119672. https://doi.org/10.1016/j.eswa.2023.119672
Zheng J, He K, Zhou J, Jin Y, Li CM (2023) Reinforced Lin–Kernighan–Helsgaun algorithms for the traveling salesman problems. Knowl Based Syst 260:110144. https://doi.org/10.1016/j.knosys.2022.110144
Acknowledgements
This work is supported by Nature Science Foundation of Fujian Province of People’s Republic of China (Nos. 2020J01570, 2023J01078).
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This work is supported by Nature Science Foundation of Fujian Province of People’s Republic of China (Nos. 2020J01570, 2023J01078).
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All the authors contributed to the study conception and design. The draft of the manuscript was written by JL. AS and LW were responsible for experimental validation and data collation. Material preparation and core code designed was performed by YZ. All the authors read and approved the final manuscript.
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Lin, J., Shen, A., Wu, L. et al. Learning-based simulated annealing algorithm for unequal area facility layout problem. Soft Comput 28, 5667–5682 (2024). https://doi.org/10.1007/s00500-023-09372-6
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DOI: https://doi.org/10.1007/s00500-023-09372-6