A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility
Abstract
:1. Introduction
2. Problem Description
3. CSFLA for DAHFSP with Factory Eligibility
3.1. Initialization
Algorithm 1 Decoding |
|
3.2. Two Cooperations in the Search Process of Group 1
Algorithm 2 Cooperation within group 1 |
|
Algorithm 3 Reinforcement search process in group 1 |
|
3.3. Cooperation-Based Search Process of Group 2
Algorithm 4 Cooperation-based search process of group 2 |
|
3.4. Algorithm Description
Algorithm 5 CSFLA |
|
4. Computational Experiments
4.1. Test Instances and Comparative Algorithms
4.2. Parameter Settings
4.3. Results and Discussions
5. Conclusions and Future Topics
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
SDST | sequence-dependent setup time |
the best solution of population | |
the start time of the fabfication of at stage l in factory f | |
the end time of the fabfication of at stage l in factory f | |
the start time of transportation of producth i in factory f | |
the end time of transportation of producth i in factory f | |
the start time of assembly of product i in factory f | |
the end time of assembly of product i in factory f | |
U | a large positive number |
decision variable, if is allocated in factory f, = 1; | |
otherwise = 0 | |
decision variable, if is allocated in , = 1; | |
otherwise = 0 | |
decision variable, if is processed before at stage l in factory f, | |
= 1; otherwise = 0 | |
decision variable, if product i is transported by , = 1; otherwise = 0 | |
decision variable, if product i is transported before product in factory f, = 1; | |
otherwise = 0 | |
decision variable, if product i is assembled before product in factory f, = 1; | |
otherwise = 0 | |
decision variable, if product i is assembled by , = 1; otherwise = 0 |
References
- Hao, J.H.; Li, J.Q.; Du, Y.; Song, M.X.; Duan, P.; Zhang, Y.Y. Solving distributed hybrid flowshop scheduling problems by a hybrid brain storm optimization algorithm. IEEE Access 2019, 7, 68879–68894. [Google Scholar] [CrossRef]
- Zheng, J.; Wang, L.; Wang, J.J. A cooperative coevolution algorithm for multi-objective fuzzy distributed hybrid flow shop. Knowl. Based Syst. 2020, 194, 105536. [Google Scholar] [CrossRef]
- Shao, W.S.; Shao, Z.S.; Pi, D.C. Modeling and multi-neighborhood iterated greedy algorithm for distributed hybrid flow shop scheduling problem. Knowl. Based Syst. 2020, 194, 105527. [Google Scholar] [CrossRef]
- Shao, W.S.; Shao, Z.S.; Pi, D.C. Effective constructive heuristics for distributed no-wait flexible flow shop scheduling problem. Comput. Oper. Res. 2021, 136, 105482. [Google Scholar] [CrossRef]
- Shao, W.S.; Shao, Z.S.; Pi, D.C. Multi-objective evolutionary algorithm based on multiple neighborhoods local search for multi-objective distributed hybrid flow shop scheduling problem. Expert Syst. Appl. 2021, 183, 115453. [Google Scholar] [CrossRef]
- Li, Y.L.; Li, X.Y.; Gao, L.; Zhang, B.; Pan, Q.K.; Tasgetiren, F.; Meng, L.L. A discrete artificial bee colony algorithm for distributed hybrid flowshop scheduling problem with sequence-dependent setup times. Int. J. Prod. Res. 2021, 59, 3880–3899. [Google Scholar] [CrossRef]
- Wang, J.J.; Wang, L. A cooperative memetic algorithm with learning-based agent for energy-aware distributed hybrid flow-shop scheduling. IEEE Trans. Evol. Comput. 2022, 26, 461–475. [Google Scholar] [CrossRef]
- Geng, K.F.; Ye, C.M. A memetic algorithm for energy-efficient distributed re-entrant hybrid flow shop scheduling problem. J. Intell. Fuzzy Syst. 2021, 41, 3951–3971. [Google Scholar] [CrossRef]
- Qin, H.; Li, T.; Teng, Y.; Wang, K. Integrated production and distribution scheduling in distributed hybrid flow shops. Memet. Comput. 2021, 13, 185–202. [Google Scholar] [CrossRef]
- Shao, Z.S.; Shao, W.S.; Pi, D.C. A learning-Based Selection Hyper-Heuristic for Distributed Heterogeneous Hybrid Blocking Flow-shop Scheduling. IEEE Trans. Emerg. Top. Comput. Intell. 2022. Available online: https://ieeexplore.ieee.org/abstract/document/9782097 (accessed on 22 February 2023). [CrossRef]
- Qin, H.X.; Han, Y.Y. A collaborative iterative greedy algorithm for the scheduling of distributed heterogeneous hybrid flow shop with blocking constraints. Expert Syst. Appl. 2022, 201, 117256. [Google Scholar] [CrossRef]
- Cai, J.C.; Lei, D.M.; Wang, J.; Wang, L. A novel shuffled frog-leaping algorithm with reinforcement learning for distributed assembly hybrid flow shop scheduling. Int. J. Prod. Res. 2022. Available online: https://www.tandfonline.com/doi/abs/10.1080/00207543.2022.2031331 (accessed on 22 February 2023). [CrossRef]
- Ying, K.C.; Lin, S.W. Minimizing makespan for the distributed hybrid flowshop scheduling problem with multiprocessor tasks. Expert Syst. Appl. 2018, 92, 132–141. [Google Scholar] [CrossRef]
- Cai, J.C.; Zhou, R.; Lei, D.M. Dynamic shuffled frog-leaping algorithm for distributed hybrid flow shop scheduling with multiprocessor tasks. Eng. Appl. Artif. Intell. 2020, 90, 103540. [Google Scholar] [CrossRef]
- Jiang, E.D.; Wang, L.; Wang, J.J. Decomposition-based multi-objective optimization for energy-aware distributed hybrid flow shop scheduling with multiprocessor tasks. Tsinghua Sci. Technol. 2021, 26, 646–663. [Google Scholar] [CrossRef]
- Li, Y.L.; Li, X.Y.; Gao, L.; Meng, L.L. An improved artificial bee colony algorithm for distributed heterogeneous hybrid flow-shop scheduling problem with sequence-dependent setup times. Comput. Ind. Eng. 2020, 147, 106638. [Google Scholar] [CrossRef]
- Cai, J.C.; Lei, D.M.; Li, M. A shuffled frog-leaping algorithm with memeplex quality for bi-objective distributed scheduling in hybrid flow shop. Int. J. Prod. Res. 2021, 59, 5404–5421. [Google Scholar] [CrossRef]
- Lei, D.M.; Wang, T. Solving distributed two-stage hybrid flow-shop scheduling using a shuffled frog-leaping algorithm with memeplex grouping. Eng. Optimiz. 2020, 52, 1461–1474. [Google Scholar] [CrossRef]
- Lei, D.M.; Xi, B.J. Diversified teaching-learning-based optimization for fuzzy two-stage hybrid flow shop scheduling with setup time. J. Intell. Fuzzy Syst. 2021, 41, 4159–4173. [Google Scholar] [CrossRef]
- Hatami, S.; Ruiz, R.; Carlos, A.R. The distributed assembly permutation flowshop scheduling problem. Int. J. Prod. Res. 2013, 51, 5292–5308. [Google Scholar] [CrossRef] [Green Version]
- Xiong, F.L.; Xing, K.Y.; Wang, F.; Lei, H.; Han, L.B. Minimizing the total completion time in a distributed two stage assembly system with setup times. Comput. Oper. Res. 2014, 47, 92–105. [Google Scholar] [CrossRef]
- Zhang, G.H.; Xing, K.Y. Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment. Comput. Ind. Eng. 2018, 125, 423–433. [Google Scholar] [CrossRef]
- Zhang, Z.Q.; Qian, B.; Hu, R.; Jin, H.P.; Wang, L. A matrix-cube-based estimation of distribution algorithm for the distributed assembly permutation flow-shop scheduling problem. Swarm Evol. Comput. 2021, 60, 100785. [Google Scholar] [CrossRef]
- Wang, J.; Lei, D.M.; Cai, J.C. An adaptive artificial bee colony with reinforcement learning for distributed three-stage assembly scheduling with maintenance. Appl. Soft. Comput. 2022, 117, 108371. [Google Scholar] [CrossRef]
- Huang, J.L.; Gu, X.S. Distributed assembly permutation flow-shop scheduling problem with sequence-dependent set-up times using a novel biogeography-based optimization algorithm. Eng. Optimiz. 2022, 54, 593–613. [Google Scholar] [CrossRef]
- Eusuff, M.; Lansey, K.; Pasha, F. Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization. Eng. Optimiz. 2006, 38, 129–154. [Google Scholar] [CrossRef]
- Cai, J.C.; Lei, D.M. A cooperated shuffled frog-leaping algorithm for distributed energy-efficient hybrid flow shop scheduling with fuzzy processing time. Complex Intell. Syst. 2021, 7, 2235–2253. [Google Scholar] [CrossRef]
- Rahimi-Vahed, A.; Mirzaei, A.H. Solving a bi-criteria permutation flow-shop problem using shuffled frog-leaping algorithm. Soft Comput. 2008, 12, 435–452. [Google Scholar] [CrossRef]
- Pan, Q.K.; Wang, L.; Gao, L.; Li, J.Q. An effective shuffled frog-leaping algorithm for lot-streaming flow shop scheduling problem. Int. J. Adv. Manuf. Technol. 2011, 52, 699–713. [Google Scholar] [CrossRef]
- Xu, Y.; Wang, L.; Wang, S.Y.; Liu, M. An effective shuffled frog-leaping algorithm for solving the hybrid flow-shop scheduling problem with identical parallel machines. Eng. Optimiz. 2013, 45, 1409–1430. [Google Scholar] [CrossRef]
- Wang, L.; Li, D.D. Fuzzy distributed hybrid flow shop scheduling problem with heterogeneous factory and unrelated parallel machine: A shuffled frog leaping algorithm with collaboration of multiple search strategies. IEEE Access. 2020, 8, 191191–191203. [Google Scholar] [CrossRef]
- Li, X.; Luo, J.P.; Chen, M.R.; Wang, N. An improved shuffled frog-leaping algorithm with extremal optimisation for continuous optimisation. Inf. Sci. 2012, 192, 143–151. [Google Scholar] [CrossRef]
- Zhang, X.X.; Ji, Z.C.; Wang, Y. An improved SFLA for flexible job shop scheduling problem considering energy consumption. Mod. Phys. Lett. B 2018, 32, 1840112. [Google Scholar] [CrossRef]
- Zhang, H.; Liu, S.; Moraca, S.; Ojstersek, R. An effective use of hybrid metaheuristics algorithm for job shop scheduling problem. Int. J. Simul. Model. 2018, 16, 644–657. [Google Scholar] [CrossRef]
- Kong, M.; Liu, X.B.; Pei, J.; Pardalos, P.M.; Mladenovic, N. Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines. J. Glob. Optim. 2020, 78, 693–715. [Google Scholar] [CrossRef]
- Xu, Y.; Wang, L.; Liu, M.; Wang, S.Y. An effective shuffled frog-leaping algorithm for hybrid flow-shop scheduling with multiprocessor tasks. Int. J. Adv. Manuf. Technol. 2013, 68, 1529–1537. [Google Scholar] [CrossRef]
- Zhang, G.H.; Xing, K.Y.; Cao, F. Scheduling distributed flowshops with flexible assembly and set-up time to minimise makespan. Int. J. Prod. Res. 2018, 56, 3226–3244. [Google Scholar] [CrossRef]
- Komaki, G.M.; Teymourian, E.; Kayvanfar, V.; Booyavi, Z. Improved discrete cuckoo optimization algorithm for the three-stage assembly flowshop scheduling problem. Comput. Ind. Eng. 2017, 105, 158–173. [Google Scholar] [CrossRef]
- Li, Q.H.; Li, J.Q.; Zhang, Q.K.; Duan, P.; Meng, T. An improved whale optimisation algorithm for distributed assembly flow shop with crane transportation. Int. J. Autom. Control. 2021, 15, 710–743. [Google Scholar] [CrossRef]
- Montgomery, D.C. Design and Analysis of Experiments; Wiley: Hoboken, NJ, USA, 2008. [Google Scholar]
Product i | |||
---|---|---|---|
Factory 1: /Factory 2: | Factory 1: /Factory 2: | ||
1 | 4 | 25/21 | 54/58 |
2 | 2 | 34/38 | 92/100 |
3 | 3 | 49/55 | 19/29 |
4 | 2 | 88/84 | 37/39 |
5 | 4 | 95/96 | 36/41 |
Product i | 1 | 2 | 3 | 4 | 5 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 1 | 2 | 1 | 2 | 3 | 1 | 2 | 1 | 2 | 3 | 4 | ||
Factory 1: | 43 | 93 | 22 | 19 | 40 | 75 | 70 | 68 | 36 | 41 | 34 | 73 | 45 | 43 | 50 | |
54 | 83 | 47 | 96 | 34 | 41 | 43 | 100 | 95 | 49 | 25 | 69 | 57 | 78 | 33 | ||
Factory 2: | 55 | 87 | 24 | 20 | 48 | 72 | 73 | 66 | 42 | 44 | 23 | 74 | 42 | 54 | 48 | |
46 | 91 | 48 | 92 | 27 | 39 | 49 | 94 | 99 | 42 | 34 | 65 | 42 | 69 | 45 |
Parameters | Factor Level | |||
---|---|---|---|---|
1 | 2 | 3 | 4 | |
N | 60 | 90 | 120 | 150 |
s | 5 | 6 | 10 | 15 |
30 | 40 | 50 | 60 | |
T | 2 | 3 | 4 | 5 |
V | 3 | 4 | 5 | 6 |
Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA | Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA |
---|---|---|---|---|---|---|---|---|---|---|---|
20 × 2 × 2 | 664.0 | 722.0 | 689.0 | 699.0 | 702.0 | 60 × 4 × 2 | 1033.0 | 1148.0 | 1055.0 | 1078.0 | 1098.0 |
20 × 2 × 4 | 1071.0 | 1161.0 | 1099.0 | 1105.0 | 1103.0 | 60 × 4 × 4 | 1651.0 | 1798.0 | 1687.0 | 1719.0 | 1757.0 |
20 × 2 × 6 | 1351.0 | 1418.0 | 1372.0 | 1377.0 | 1399.0 | 60 × 4 × 6 | 1229.0 | 1381.0 | 1264.0 | 1319.0 | 1338.0 |
20 × 2 × 8 | 1499.0 | 1639.0 | 1537.0 | 1563.0 | 1574.0 | 60 × 4 × 8 | 1705.0 | 1840.0 | 1730.0 | 1760.0 | 1764.0 |
20 × 3 × 2 | 711.0 | 769.0 | 730.0 | 741.0 | 765.0 | 60 × 5 × 2 | 1172.0 | 1274.0 | 1186.0 | 1284.0 | 1260.0 |
20 × 3 × 4 | 903.0 | 994.0 | 932.0 | 922.0 | 953.0 | 60 × 5 × 4 | 1271.0 | 1399.0 | 1292.0 | 1313.0 | 1344.0 |
20 × 3 × 6 | 846.0 | 904.0 | 860.0 | 881.0 | 907.0 | 60 × 5 × 6 | 1483.0 | 1650.0 | 1537.0 | 1579.0 | 1628.0 |
20 × 3 × 8 | 1158.0 | 1245.0 | 1179.0 | 1174.0 | 1223.0 | 60 × 5 × 8 | 1609.0 | 1745.0 | 1619.0 | 1766.0 | 1706.0 |
20 × 4 × 2 | 405.0 | 455.0 | 414.0 | 426.0 | 434.0 | 80 × 2 × 2 | 3846.0 | 3915.0 | 3850.0 | 3895.0 | 3872.0 |
20 × 4 × 4 | 579.0 | 670.0 | 603.0 | 616.0 | 649.0 | 80 × 2 × 4 | 2624.0 | 2764.0 | 2627.0 | 2674.0 | 2719.0 |
20 × 4 × 6 | 816.0 | 872.0 | 841.0 | 849.0 | 844.0 | 80 × 2 × 6 | 3715.0 | 3910.0 | 3741.0 | 3767.0 | 3855.0 |
20 × 4 × 8 | 916.0 | 1001.0 | 917.0 | 946.0 | 969.0 | 80 × 2 × 8 | 4184.0 | 4421.0 | 4230.0 | 4247.0 | 4372.0 |
20 × 5 × 2 | 455.0 | 526.0 | 476.0 | 499.0 | 520.0 | 80 × 3 × 2 | 1446.0 | 1572.0 | 1480.0 | 1476.0 | 1537.0 |
20 × 5 × 4 | 608.0 | 694.0 | 617.0 | 668.0 | 659.0 | 80 × 3 × 4 | 1548.0 | 1675.0 | 1556.0 | 1611.0 | 1641.0 |
20 × 5 × 6 | 808.0 | 898.0 | 814.0 | 849.0 | 876.0 | 80 × 3 × 6 | 2603.0 | 2715.0 | 2610.0 | 2666.0 | 2690.0 |
20 × 5 × 8 | 874.0 | 955.0 | 882.0 | 918.0 | 908.0 | 80 × 3 × 8 | 2753.0 | 2933.0 | 2782.0 | 2800.0 | 2818.0 |
40 × 2 × 2 | 1356.0 | 1423.0 | 1362.0 | 1370.0 | 1407.0 | 80 × 4 × 2 | 1885.0 | 1944.0 | 1895.0 | 1962.0 | 1939.0 |
40 × 2 × 4 | 1887.0 | 1982.0 | 1902.0 | 1913.0 | 1950.0 | 80 × 4 × 4 | 1994.0 | 2155.0 | 2035.0 | 2093.0 | 2083.0 |
40 × 2 × 6 | 1629.0 | 1775.0 | 1655.0 | 1655.0 | 1737.0 | 80 × 4 × 6 | 2203.0 | 2437.0 | 2261.0 | 2324.0 | 2295.0 |
40 × 2 × 8 | 2285.0 | 2395.0 | 2323.0 | 2323.0 | 2380.0 | 80 × 4 × 8 | 2230.0 | 2388.0 | 2253.0 | 2372.0 | 2361.0 |
40 × 3 × 2 | 930.0 | 1031.0 | 951.0 | 944.0 | 961.0 | 80 × 5 × 2 | 978.0 | 1120.0 | 1010.0 | 1028.0 | 1067.0 |
40 × 3 × 4 | 1427.0 | 1562.0 | 1456.0 | 1473.0 | 1502.0 | 80 × 5 × 4 | 1703.0 | 1864.0 | 1739.0 | 1782.0 | 1799.0 |
40 × 3 × 6 | 1568.0 | 1695.0 | 1583.0 | 1592.0 | 1626.0 | 80 × 5 × 6 | 1747.0 | 1946.0 | 1808.0 | 1886.0 | 1881.0 |
40 × 3 × 8 | 1564.0 | 1691.0 | 1571.0 | 1600.0 | 1623.0 | 80 × 5 × 8 | 1826.0 | 2011.0 | 1850.0 | 1942.0 | 1930.0 |
40 × 4 × 2 | 885.0 | 979.0 | 919.0 | 926.0 | 939.0 | 100 × 2 × 2 | 3080.0 | 3135.0 | 3086.0 | 3117.0 | 3136.0 |
40 × 4 × 4 | 1137.0 | 1219.0 | 1142.0 | 1188.0 | 1202.0 | 100 × 2 × 4 | 4874.0 | 4970.0 | 4866.0 | 4929.0 | 4936.0 |
40 × 4 × 6 | 1184.0 | 1282.0 | 1218.0 | 1239.0 | 1258.0 | 100 × 2 × 6 | 4711.0 | 4870.0 | 4755.0 | 4819.0 | 4822.0 |
40 × 4 × 8 | 1336.0 | 1497.0 | 1384.0 | 1428.0 | 1420.0 | 100 × 2 × 8 | 4866.0 | 5075.0 | 4891.0 | 4913.0 | 4986.0 |
40 × 5 × 2 | 635.0 | 724.0 | 673.0 | 690.0 | 706.0 | 100 × 3 × 2 | 2074.0 | 2226.0 | 2103.0 | 2105.0 | 2148.0 |
40 × 5 × 4 | 934.0 | 1084.0 | 966.0 | 973.0 | 1026.0 | 100 × 3 × 4 | 3189.0 | 3375.0 | 3216.0 | 3288.0 | 3287.0 |
40 × 5 × 6 | 1122.0 | 1283.0 | 1160.0 | 1162.0 | 1218.0 | 100 × 3 × 6 | 3035.0 | 3173.0 | 3070.0 | 3126.0 | 3101.0 |
40 × 5 × 8 | 1299.0 | 1462.0 | 1327.0 | 1332.0 | 1387.0 | 100 × 3 × 8 | 3591.0 | 3809.0 | 3664.0 | 3710.0 | 3752.0 |
60 × 2 × 2 | 1646.0 | 1749.0 | 1657.0 | 1676.0 | 1702.0 | 100 × 4 × 2 | 1613.0 | 1733.0 | 1650.0 | 1698.0 | 1670.0 |
60 × 2 × 4 | 2808.0 | 2920.0 | 2824.0 | 2863.0 | 2890.0 | 100 × 4 × 4 | 2568.0 | 2724.0 | 2580.0 | 2613.0 | 2647.0 |
60 × 2 × 6 | 3027.0 | 3195.0 | 3037.0 | 3065.0 | 3170.0 | 100 × 4 × 6 | 2676.0 | 2870.0 | 2709.0 | 2773.0 | 2772.0 |
60 × 2 × 8 | 2863.0 | 3001.0 | 2891.0 | 2927.0 | 2941.0 | 100 × 4 × 8 | 2526.0 | 2733.0 | 2572.0 | 2686.0 | 2693.0 |
60 × 3 × 2 | 2015.0 | 2096.0 | 2023.0 | 2047.0 | 2054.0 | 100 × 5 × 2 | 1869.0 | 2027.0 | 1880.0 | 1965.0 | 1889.0 |
60 × 3 × 4 | 2099.0 | 2278.0 | 2126.0 | 2148.0 | 2215.0 | 100 × 5 × 4 | 1374.0 | 1466.0 | 1399.0 | 1449.0 | 1419.0 |
60 × 3 × 6 | 2211.0 | 2339.0 | 2222.0 | 2273.0 | 2294.0 | 100 × 5 × 6 | 1684.0 | 1851.0 | 1738.0 | 1862.0 | 1765.0 |
60 × 3 × 8 | 2331.0 | 2457.0 | 2344.0 | 2378.0 | 2403.0 | 100 × 5 × 8 | 2205.0 | 2434.0 | 2252.0 | 2365.0 | 2312.0 |
120 × 2 × 2 | 3422.0 | 3479.0 | 3463.0 | 3433.0 | 3476.0 | 140 × 2 × 2 | 4265.0 | 4358.0 | 4364.0 | 4271.0 | 4321.0 |
120 × 2 × 4 | 5671.0 | 5720.0 | 5701.0 | 5683.0 | 5694.0 | 140 × 2 × 4 | 6415.0 | 6504.0 | 6590.0 | 6425.0 | 6507.0 |
120 × 2 × 6 | 5951.0 | 6040.0 | 6043.0 | 5954.0 | 6031.0 | 140 × 2 × 6 | 6614.0 | 6706.0 | 6677.0 | 6625.0 | 6665.0 |
120 × 2 × 8 | 5704.0 | 5787.0 | 5775.0 | 5712.0 | 5788.0 | 140 × 2 × 8 | 6533.0 | 6610.0 | 6600.0 | 6535.0 | 6622.0 |
120 × 3 × 2 | 2229.0 | 2253.0 | 2263.0 | 2202.0 | 2238.0 | 140 × 3 × 2 | 2563.0 | 2619.0 | 2609.0 | 2557.0 | 2600.0 |
120 × 3 × 4 | 2411.0 | 2496.0 | 2489.0 | 2444.0 | 2483.0 | 140 × 3 × 4 | 2698.0 | 2757.0 | 2773.0 | 2673.0 | 2758.0 |
120 × 3 × 6 | 3846.0 | 3997.0 | 3941.0 | 3802.0 | 3911.0 | 140 × 3 × 6 | 4638.0 | 4664.0 | 4690.0 | 4655.0 | 4673.0 |
120 × 3 × 8 | 4265.0 | 4428.0 | 4382.0 | 4272.0 | 4381.0 | 140 × 3 × 8 | 3438.0 | 3530.0 | 3569.0 | 3451.0 | 3526.0 |
120 × 4 × 2 | 1741.0 | 1785.0 | 1747.0 | 1771.0 | 1767.0 | 140 × 4 × 2 | 2002.0 | 2016.0 | 2035.0 | 1964.0 | 1988.0 |
120 × 4 × 4 | 2145.0 | 2238.0 | 2195.0 | 2146.0 | 2203.0 | 140 × 4 × 4 | 2425.0 | 2482.0 | 2433.0 | 2486.0 | 2481.0 |
120 × 4 × 6 | 2258.0 | 2378.0 | 2376.0 | 2272.0 | 2383.0 | 140 × 4 × 6 | 3517.0 | 3562.0 | 3619.0 | 3573.0 | 3588.0 |
120 × 4 × 8 | 3146.0 | 3209.0 | 3184.0 | 3150.0 | 3151.0 | 140 × 4 × 8 | 3839.0 | 3937.0 | 3912.0 | 3842.0 | 3915.0 |
120 × 5 × 2 | 2317.0 | 2358.0 | 2363.0 | 2329.0 | 2350.0 | 140 × 5 × 2 | 1904.0 | 1941.0 | 1915.0 | 1959.0 | 1925.0 |
120 × 5 × 4 | 2558.0 | 2606.0 | 2581.0 | 2616.0 | 2633.0 | 140 × 5 × 4 | 2875.0 | 2949.0 | 2954.0 | 2882.0 | 2952.0 |
120 × 5 × 6 | 2601.0 | 2608.0 | 2651.0 | 2585.0 | 2648.0 | 140 × 5 × 6 | 3142.0 | 3297.0 | 3198.0 | 3315.0 | 3211.0 |
120 × 5 × 8 | 2655.0 | 2690.0 | 2724.0 | 2747.0 | 2729.0 | 140 × 5 × 8 | 3245.0 | 3405.0 | 3359.0 | 3199.0 | 3317.0 |
Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA | Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA |
---|---|---|---|---|---|---|---|---|---|---|---|
20 × 2 × 2 | 691.0 | 790.0 | 726.0 | 760.0 | 824.0 | 60 × 4 × 2 | 1064.0 | 1218.0 | 1085.0 | 1238.0 | 1181.0 |
20 × 2 × 4 | 1099.0 | 1205.0 | 1124.0 | 1150.0 | 1225.0 | 60 × 4 × 4 | 1692.0 | 1923.0 | 1723.0 | 2223.0 | 1834.0 |
20 × 2 × 6 | 1374.0 | 1470.0 | 1414.0 | 1430.0 | 1458.0 | 60 × 4 × 6 | 1285.0 | 1452.0 | 1311.0 | 1495.0 | 1462.0 |
20 × 2 × 8 | 1554.0 | 1754.0 | 1600.0 | 1642.0 | 1735.0 | 60 × 4 × 8 | 1754.0 | 1924.0 | 1773.0 | 2236.0 | 1920.0 |
20 × 3 × 2 | 728.0 | 857.0 | 758.0 | 853.0 | 815.0 | 60 × 5 × 2 | 1239.0 | 1448.0 | 1241.0 | 1551.0 | 1304.0 |
20 × 3 × 4 | 938.0 | 1072.0 | 978.0 | 1116.0 | 1113.0 | 60 × 5 × 4 | 1289.0 | 1514.0 | 1328.0 | 1789.0 | 1451.0 |
20 × 3 × 6 | 895.0 | 1000.0 | 906.0 | 1054.0 | 1047.0 | 60 × 5 × 6 | 1532.0 | 1809.0 | 1568.0 | 2073.0 | 1725.0 |
20 × 3 × 8 | 1192.0 | 1354.0 | 1236.0 | 1285.0 | 1350.0 | 60 × 5 × 8 | 1663.0 | 1886.0 | 1698.0 | 1997.0 | 1807.0 |
20 × 4 × 2 | 425.0 | 493.0 | 438.0 | 476.0 | 465.0 | 80 × 2 × 2 | 3869.0 | 3986.0 | 3892.0 | 3960.0 | 4006.0 |
20 × 4 × 4 | 611.0 | 714.0 | 640.0 | 665.0 | 758.0 | 80 × 2 × 4 | 2655.0 | 2844.0 | 2691.0 | 2770.0 | 2818.0 |
20 × 4 × 6 | 844.0 | 1004.0 | 872.0 | 1020.0 | 1002.0 | 80 × 2 × 6 | 3765.0 | 3987.0 | 3791.0 | 3944.0 | 3953.0 |
20 × 4 × 8 | 954.0 | 1082.0 | 959.0 | 1103.0 | 1051.0 | 80 × 2 × 8 | 4262.0 | 4574.0 | 4295.0 | 4496.0 | 4508.0 |
20 × 5 × 2 | 487.0 | 611.0 | 523.0 | 672.0 | 571.0 | 80 × 3 × 2 | 1482.0 | 1674.0 | 1520.0 | 1784.0 | 1613.0 |
20 × 5 × 4 | 633.0 | 750.0 | 650.0 | 889.0 | 734.0 | 80 × 3 × 4 | 1581.0 | 1774.0 | 1610.0 | 1740.0 | 1727.0 |
20 × 5 × 6 | 838.0 | 988.0 | 890.0 | 1037.0 | 991.0 | 80 × 3 × 6 | 2648.0 | 2836.0 | 2664.0 | 2846.0 | 2740.0 |
20 × 5 × 8 | 909.0 | 1031.0 | 935.0 | 1090.0 | 1052.0 | 80 × 3 × 8 | 2817.0 | 3031.0 | 2843.0 | 2894.0 | 2947.0 |
40 × 2 × 2 | 1372.0 | 1483.0 | 1391.0 | 1471.0 | 1533.0 | 80 × 4 × 2 | 1909.0 | 2102.0 | 1942.0 | 2425.0 | 2124.0 |
40 × 2 × 4 | 1922.0 | 2061.0 | 1930.0 | 2013.0 | 2046.0 | 80 × 4 × 4 | 2029.0 | 2272.0 | 2061.0 | 2518.0 | 2197.0 |
40 × 2 × 6 | 1696.0 | 1860.0 | 1695.0 | 1737.0 | 1803.0 | 80 × 4 × 6 | 2273.0 | 2517.0 | 2303.0 | 2511.0 | 2457.0 |
40 × 2 × 8 | 2350.0 | 2497.0 | 2358.0 | 2421.0 | 2460.0 | 80 × 4 × 8 | 2279.0 | 2528.0 | 2322.0 | 2589.0 | 2469.0 |
40 × 3 × 2 | 962.0 | 1086.0 | 986.0 | 1019.0 | 1047.0 | 80 × 5 × 2 | 1035.0 | 1172.0 | 1043.0 | 1315.0 | 1136.0 |
40 × 3 × 4 | 1463.0 | 1684.0 | 1505.0 | 1581.0 | 1636.0 | 80 × 5 × 4 | 1747.0 | 1986.0 | 1777.0 | 2303.0 | 1876.0 |
40 × 3 × 6 | 1608.0 | 1777.0 | 1641.0 | 1728.0 | 1729.0 | 80 × 5 × 6 | 1818.0 | 2096.0 | 1856.0 | 2472.0 | 2017.0 |
40 × 3 × 8 | 1610.0 | 1775.0 | 1621.0 | 1939.0 | 1756.0 | 80 × 5 × 8 | 1860.0 | 2121.0 | 1904.0 | 2279.0 | 2002.0 |
40 × 4 × 2 | 917.0 | 1083.0 | 949.0 | 1072.0 | 1040.0 | 100 × 2 × 2 | 3107.0 | 3253.0 | 3132.0 | 3245.0 | 3202.0 |
40 × 4 × 4 | 1160.0 | 1290.0 | 1193.0 | 1289.0 | 1296.0 | 100 × 2 × 4 | 4912.0 | 5041.0 | 4944.0 | 5020.0 | 5003.0 |
40 × 4 × 6 | 1222.0 | 1392.0 | 1244.0 | 1434.0 | 1348.0 | 100 × 2 × 6 | 4782.0 | 5038.0 | 4819.0 | 4929.0 | 4932.0 |
40 × 4 × 8 | 1374.0 | 1590.0 | 1422.0 | 1701.0 | 1524.0 | 100 × 2 × 8 | 4919.0 | 5214.0 | 4954.0 | 5043.0 | 5107.0 |
40 × 5 × 2 | 677.0 | 798.0 | 705.0 | 869.0 | 757.0 | 100 × 3 × 2 | 2101.0 | 2320.0 | 2140.0 | 2251.0 | 2239.0 |
40 × 5 × 4 | 970.0 | 1179.0 | 1002.0 | 1214.0 | 1126.0 | 100 × 3 × 4 | 3237.0 | 3510.0 | 3296.0 | 3460.0 | 3415.0 |
40 × 5 × 6 | 1160.0 | 1344.0 | 1214.0 | 1419.0 | 1322.0 | 100 × 3 × 6 | 3098.0 | 3302.0 | 3114.0 | 3332.0 | 3244.0 |
40 × 5 × 8 | 1349.0 | 1537.0 | 1375.0 | 1642.0 | 1581.0 | 100 × 3 × 8 | 3683.0 | 3933.0 | 3726.0 | 4198.0 | 3925.0 |
60 × 2 × 2 | 1699.0 | 1803.0 | 1721.0 | 1843.0 | 1756.0 | 100 × 4 × 2 | 1649.0 | 1798.0 | 1696.0 | 1974.0 | 1748.0 |
60 × 2 × 4 | 2873.0 | 3076.0 | 2880.0 | 3032.0 | 2988.0 | 100 × 4 × 4 | 2609.0 | 2894.0 | 2650.0 | 2886.0 | 2753.0 |
60 × 2 × 6 | 3072.0 | 3372.0 | 3107.0 | 3221.0 | 3250.0 | 100 × 4 × 6 | 2738.0 | 3017.0 | 2778.0 | 3105.0 | 2948.0 |
60 × 2 × 8 | 2922.0 | 3079.0 | 2949.0 | 3029.0 | 3028.0 | 100 × 4 × 8 | 2605.0 | 2892.0 | 2655.0 | 2863.0 | 2803.0 |
60 × 3 × 2 | 2039.0 | 2206.0 | 2042.0 | 2244.0 | 2161.0 | 100 × 5 × 2 | 1903.0 | 2101.0 | 1921.0 | 2357.0 | 2044.0 |
60 × 3 × 4 | 2145.0 | 2378.0 | 2186.0 | 2328.0 | 2293.0 | 100 × 5 × 4 | 1414.0 | 1582.0 | 1448.0 | 1718.0 | 1583.0 |
60 × 3 × 6 | 2255.0 | 2455.0 | 2273.0 | 2832.0 | 2429.0 | 100 × 5 × 6 | 1732.0 | 1952.0 | 1779.0 | 2191.0 | 1889.0 |
60 × 3 × 8 | 2366.0 | 2545.0 | 2412.0 | 2463.0 | 2490.0 | 100 × 5 × 8 | 2264.0 | 2528.0 | 2313.0 | 2782.0 | 2415.0 |
120 × 2 × 2 | 3536.0 | 3549.0 | 3551.0 | 3524.0 | 3519.0 | 140 × 2 × 2 | 4400.0 | 4449.0 | 4488.0 | 4414.0 | 4424.0 |
120 × 2 × 4 | 5766.0 | 5770.0 | 5788.0 | 5776.0 | 5773.0 | 140 × 2 × 4 | 6539.0 | 6550.0 | 6552.0 | 6541.0 | 6551.0 |
120 × 2 × 6 | 6069.0 | 6083.0 | 6107.0 | 6033.0 | 6085.0 | 140 × 2 × 6 | 6771.0 | 6832.0 | 6800.0 | 6697.0 | 6864.0 |
120 × 2 × 8 | 5861.0 | 5883.0 | 5864.0 | 5869.0 | 5880.0 | 140 × 2 × 8 | 6671.0 | 6747.0 | 6714.0 | 6699.0 | 6710.0 |
120 × 3 × 2 | 2359.0 | 2367.0 | 2365.0 | 2393.0 | 2370.0 | 140 × 3 × 2 | 2632.0 | 2684.0 | 2698.0 | 2637.0 | 2681.0 |
120 × 3 × 4 | 2570.0 | 2602.0 | 2605.0 | 2632.0 | 2564.0 | 140 × 3 × 4 | 2795.0 | 2927.0 | 2864.0 | 2796.0 | 2852.0 |
120 × 3 × 6 | 4061.0 | 4091.0 | 4089.0 | 4344.0 | 4069.0 | 140 × 3 × 6 | 4805.0 | 4820.0 | 4786.0 | 5284.0 | 4813.0 |
120 × 3 × 8 | 4455.0 | 4506.0 | 4496.0 | 4628.0 | 4515.0 | 140 × 3 × 8 | 3565.0 | 3694.0 | 3654.0 | 3582.0 | 3640.0 |
120 × 4 × 2 | 1865.0 | 1907.0 | 1914.0 | 2013.0 | 1862.0 | 140 × 4 × 2 | 2072.0 | 2079.0 | 2086.0 | 2531.0 | 2096.0 |
120 × 4 × 4 | 2235.0 | 2331.0 | 2285.0 | 2533.0 | 2237.0 | 140 × 4 × 4 | 2605.0 | 2656.0 | 2619.0 | 2754.0 | 2557.0 |
120 × 4 × 6 | 2420.0 | 2472.0 | 2492.0 | 2507.0 | 2479.0 | 140 × 4 × 6 | 3705.0 | 3707.0 | 3779.0 | 4378.0 | 3715.0 |
120 × 4 × 8 | 3322.0 | 3295.0 | 3304.0 | 3547.0 | 3307.0 | 140 × 4 × 8 | 4003.0 | 4008.0 | 4069.0 | 4196.0 | 4066.0 |
120 × 5 × 2 | 2472.0 | 2501.0 | 2525.0 | 3110.0 | 2474.0 | 140 × 5 × 2 | 2022.0 | 2066.0 | 2055.0 | 2272.0 | 2027.0 |
120 × 5 × 4 | 2757.0 | 2834.0 | 2766.0 | 3245.0 | 2743.0 | 140 × 5 × 4 | 3052.0 | 3057.0 | 3110.0 | 3448.0 | 3102.0 |
120 × 5 × 6 | 2719.0 | 2841.0 | 2809.0 | 3184.0 | 2729.0 | 140 × 5 × 6 | 3368.0 | 3423.0 | 3431.0 | 3736.0 | 3378.0 |
120 × 5 × 8 | 2806.0 | 2825.0 | 2859.0 | 3232.0 | 2844.0 | 140 × 5 × 8 | 3502.0 | 3508.0 | 3514.0 | 3949.0 | 3532.0 |
Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA | Instance | CSFLA | SFLA | IDCOA | HVNS | IWOA |
---|---|---|---|---|---|---|---|---|---|---|---|
20 × 2 × 2 | 677.6 | 758.8 | 702.3 | 725.2 | 738.4 | 60 × 4 × 2 | 1051.7 | 1182.7 | 1073.3 | 1150.5 | 1135.8 |
20 × 2 × 4 | 1086.9 | 1192.0 | 1113.0 | 1126.1 | 1157.8 | 60 × 4 × 4 | 1674.2 | 1859.6 | 1705.0 | 1840.2 | 1794.1 |
20 × 2 × 6 | 1361.6 | 1448.6 | 1393.0 | 1396.6 | 1430.2 | 60 × 4 × 6 | 1265.0 | 1420.1 | 1295.2 | 1391.8 | 1370.5 |
20 × 2 × 8 | 1535.6 | 1702.1 | 1564.4 | 1594.0 | 1655.6 | 60 × 4 × 8 | 1725.5 | 1890.4 | 1752.8 | 1919.3 | 1830.2 |
20 × 3 × 2 | 718.9 | 817.6 | 741.6 | 791.2 | 786.8 | 60 × 5 × 2 | 1193.9 | 1351.5 | 1222.1 | 1423.6 | 1281.7 |
20 × 3 × 4 | 919.2 | 1039.2 | 954.4 | 979.2 | 1015.8 | 60 × 5 × 4 | 1283.0 | 1480.7 | 1307.1 | 1496.2 | 1396.0 |
20 × 3 × 6 | 867.2 | 961.8 | 884.1 | 939.5 | 953.2 | 60 × 5 × 6 | 1513.2 | 1718.9 | 1553.3 | 1780.4 | 1651.9 |
20 × 3 × 8 | 1173.7 | 1310.1 | 1200.2 | 1219.9 | 1283.5 | 60 × 5 × 8 | 1634.9 | 1834.1 | 1674.7 | 1858.5 | 1766.4 |
20 × 4 × 2 | 413.0 | 472.7 | 430.3 | 442.7 | 452.2 | 80 × 2 × 2 | 3858.1 | 3936.8 | 3868.0 | 3920.1 | 3904.2 |
20 × 4 × 4 | 594.4 | 687.9 | 615.1 | 641.8 | 684.3 | 80 × 2 × 4 | 2640.7 | 2806.6 | 2661.9 | 2720.8 | 2762.9 |
20 × 4 × 6 | 830.9 | 942.0 | 857.4 | 895.2 | 921.3 | 80 × 2 × 6 | 3746.5 | 3959.1 | 3764.6 | 3845.6 | 3894.4 |
20 × 4 × 8 | 933.8 | 1038.5 | 944.2 | 1005.9 | 1009.9 | 80 × 2 × 8 | 4218.4 | 4510.8 | 4267.7 | 4343.0 | 4418.1 |
20 × 5 × 2 | 470.4 | 571.9 | 496.3 | 571.4 | 541.0 | 80 × 3 × 2 | 1464.1 | 1606.9 | 1496.4 | 1619.0 | 1572.1 |
20 × 5 × 4 | 621.1 | 713.6 | 631.6 | 748.4 | 682.6 | 80 × 3 × 4 | 1566.7 | 1712.7 | 1595.7 | 1662.2 | 1672.0 |
20 × 5 × 6 | 825.1 | 948.4 | 843.9 | 928.2 | 916.2 | 80 × 3 × 6 | 2624.5 | 2776.4 | 2640.5 | 2746.8 | 2715.6 |
20 × 5 × 8 | 889.0 | 997.8 | 906.6 | 981.9 | 965.2 | 80 × 3 × 8 | 2780.4 | 2986.7 | 2816.1 | 2862.8 | 2900.0 |
40 × 2 × 2 | 1363.2 | 1446.2 | 1380.1 | 1409.9 | 1437.8 | 80 × 4 × 2 | 1901.0 | 2014.4 | 1915.4 | 2132.3 | 2001.0 |
40 × 2 × 4 | 1903.0 | 2017.3 | 1919.7 | 1949.8 | 1985.5 | 80 × 4 × 4 | 2013.7 | 2212.1 | 2049.9 | 2260.0 | 3132.7 |
40 × 2 × 6 | 1658.3 | 1813.4 | 1674.6 | 1705.0 | 1775.6 | 80 × 4 × 6 | 2242.2 | 2476.3 | 2284.6 | 2412.5 | 2354.8 |
40 × 2 × 8 | 2308.1 | 2442.8 | 2336.2 | 2359.5 | 2413.3 | 80 × 4 × 8 | 2254.8 | 2462.0 | 2290.3 | 2480.8 | 2405.9 |
40 × 3 × 2 | 938.4 | 1060.2 | 967.2 | 986.8 | 1014.7 | 80 × 5 × 2 | 999.7 | 1142.8 | 1030.2 | 1177.4 | 1098.4 |
40 × 3 × 4 | 1446.1 | 1605.9 | 1477.9 | 1516.4 | 1554.3 | 80 × 5 × 4 | 1724.0 | 1927.6 | 1755.0 | 1955.9 | 1835.9 |
40 × 3 × 6 | 1588.9 | 1736.5 | 1605.7 | 1650.1 | 1683.9 | 80 × 5 × 6 | 1787.3 | 2015.1 | 1826.3 | 2110.1 | 1929.8 |
40 × 3 × 8 | 1579.6 | 1725.6 | 1598.5 | 1702.2 | 1683.2 | 80 × 5 × 8 | 1845.6 | 2055.2 | 1883.2 | 2084.2 | 1952.3 |
40 × 4 × 2 | 903.4 | 1026.1 | 930.5 | 983.1 | 986.3 | 100 × 2 × 2 | 3094.1 | 3212.9 | 3105.0 | 3163.8 | 3166.5 |
40 × 4 × 4 | 1149.4 | 1268.6 | 1171.3 | 1240.6 | 1236.2 | 100 × 2 × 4 | 4898.9 | 5010.3 | 4904.5 | 4978.6 | 4968.6 |
40 × 4 × 6 | 1199.8 | 1353.3 | 1232.6 | 1326.0 | 1303.3 | 100 × 2 × 6 | 4749.8 | 4960.7 | 4784.4 | 4869.0 | 4885.1 |
40 × 4 × 8 | 1357.0 | 1531.6 | 1399.9 | 1535.4 | 1470.2 | 100 × 2 × 8 | 4895.7 | 5138.5 | 4938.7 | 4971.6 | 5037.0 |
40 × 5 × 2 | 661.1 | 765.6 | 688.3 | 771.1 | 735.3 | 100 × 3 × 2 | 2088.2 | 2254.8 | 2118.2 | 2175.5 | 2194.6 |
40 × 5 × 4 | 957.1 | 1119.3 | 989.8 | 1108.9 | 1063.1 | 100 × 3 × 4 | 3212.3 | 3441.0 | 3254.6 | 3356.5 | 3347.7 |
40 × 5 × 6 | 1148.0 | 1315.6 | 1180.3 | 1259.1 | 1263.1 | 100 × 3 × 6 | 3072.9 | 3239.3 | 3092.9 | 3186.2 | 3178.1 |
40 × 5 × 8 | 1322.7 | 1494.5 | 1346.1 | 1455.9 | 1458.5 | 100 × 3 × 8 | 3648.3 | 3889.2 | 3697.0 | 3843.5 | 3833.0 |
60 × 2 × 2 | 1673.9 | 1784.6 | 1691.3 | 1739.3 | 1730.9 | 100 × 4 × 2 | 1636.4 | 1769.4 | 1663.1 | 1789.0 | 1724.0 |
60 × 2 × 4 | 2829.7 | 3009.9 | 2860.1 | 2934.4 | 2947.4 | 100 × 4 × 4 | 2585.6 | 2789.4 | 2619.0 | 2743.0 | 2694.6 |
60 × 2 × 6 | 3048.1 | 3272.0 | 3074.1 | 3127.7 | 3214.0 | 100 × 4 × 6 | 2707.3 | 2954.7 | 2745.1 | 2893.4 | 2864.1 |
60 × 2 × 8 | 2894.7 | 3037.8 | 2911.2 | 2965.2 | 2983.3 | 100 × 4 × 8 | 2570.6 | 2796.7 | 2607.4 | 2754.7 | 2730.0 |
60 × 3 × 2 | 2024.4 | 2139.1 | 2033.2 | 2118.5 | 2098.8 | 100 × 5 × 2 | 1882.9 | 2063.9 | 1901.8 | 2113.7 | 1969.3 |
60 × 3 × 4 | 2127.4 | 2321.2 | 2159.4 | 2237.9 | 2258.6 | 100 × 5 × 4 | 1399.4 | 1543.3 | 1427.8 | 1586.0 | 1492.3 |
60 × 3 × 6 | 2232.9 | 2389.7 | 2247.4 | 2384.2 | 2352.9 | 100 × 5 × 6 | 1702.3 | 1901.0 | 1751.8 | 1945.8 | 1825.3 |
60 × 3 × 8 | 2351.6 | 2501.4 | 2384.5 | 2430.6 | 2451.5 | 100 × 5 × 8 | 2242.1 | 2483.8 | 2287.9 | 2504.7 | 2370.5 |
120 × 2 × 2 | 3465.1 | 3526.3 | 3513.7 | 3465.3 | 3501.8 | 140 × 2 × 2 | 4347.9 | 4406.0 | 4403.7 | 4341.4 | 4379.8 |
120 × 2 × 4 | 5718.8 | 5746.6 | 5749.7 | 5730.2 | 5740.3 | 140 × 2 × 4 | 6481.8 | 6527.7 | 6527.0 | 6484.7 | 6536.4 |
120 × 2 × 6 | 6004.3 | 6058.6 | 6067.9 | 5996.2 | 6054.9 | 140 × 2 × 6 | 6659.5 | 6791.3 | 6742.4 | 6670.5 | 6763.9 |
120 × 2 × 8 | 5774.9 | 5823.3 | 5817.8 | 5778.2 | 5822.5 | 140 × 2 × 8 | 6591.9 | 6677.5 | 6665.9 | 6597.7 | 6665.3 |
120 × 3 × 2 | 2254.5 | 2319.6 | 2320.8 | 2251.9 | 2304.8 | 140 × 3 × 2 | 2579.2 | 2654.2 | 2651.9 | 2587.7 | 2641.8 |
120 × 3 × 4 | 2497.0 | 2533.4 | 2526.2 | 2537.4 | 2534.8 | 140 × 3 × 4 | 2738.7 | 2831.5 | 2805.4 | 2746.7 | 2805.9 |
120 × 3 × 6 | 3967.7 | 4044.4 | 4006.5 | 4036.4 | 3972.4 | 140 × 3 × 6 | 4734.6 | 4752.2 | 4751.4 | 4807.3 | 4745.0 |
120 × 3 × 8 | 4378.2 | 4473.7 | 4453.6 | 4435.5 | 4459.2 | 140 × 3 × 8 | 3501.2 | 3605.0 | 3613.3 | 3512.4 | 3585.5 |
120 × 4 × 2 | 1799.1 | 1852.3 | 1837.5 | 1877.7 | 1818.5 | 140 × 4 × 2 | 2037.9 | 2058.0 | 2060.4 | 2202.6 | 2034.0 |
120 × 4 × 4 | 2203.7 | 2273.2 | 2243.1 | 2327.0 | 2220.8 | 140 × 4 × 4 | 2512.0 | 2532.8 | 2530.0 | 2593.1 | 2511.6 |
120 × 4 × 6 | 2388.6 | 2428.9 | 2453.9 | 2424.8 | 2425.8 | 140 × 4 × 6 | 3609.3 | 3648.7 | 3684.9 | 3857.9 | 3658.4 |
120 × 4 × 8 | 3233.4 | 3243.3 | 3235.2 | 3327.4 | 3236.9 | 140 × 4 × 8 | 3933.7 | 3966.3 | 4004.6 | 3946.3 | 3994.4 |
120 × 5 × 2 | 2397.5 | 2443.3 | 2424.1 | 2673.7 | 2415.5 | 140 × 5 × 2 | 1969.6 | 1999.7 | 1981.8 | 2038.5 | 1977.3 |
120 × 5 × 4 | 2635.4 | 2693.5 | 2702.9 | 2928.0 | 2689.8 | 140 × 5 × 4 | 2957.1 | 3015.5 | 3056.7 | 3107.6 | 3023.7 |
120 × 5 × 6 | 2678.0 | 2706.5 | 2725.4 | 2864.0 | 2693.7 | 140 × 5 × 6 | 3289.5 | 3340.7 | 3349.8 | 3477.8 | 3304.2 |
120 × 5 × 8 | 2739.1 | 2771.3 | 2777.6 | 2919.0 | 2782.5 | 140 × 5 × 8 | 3378.6 | 3467.8 | 3429.6 | 3466.8 | 3420.0 |
Wilcoxon-Test | MIN | MAX | AVG |
---|---|---|---|
Wilcoxon test (CSFLA, SFLA) | 0.000 | 0.000 | 0.000 |
Wilcoxon test (CSFLA, IDCOA) | 0.000 | 0.000 | 0.000 |
Wilcoxon test (CSFLA, HVNS) | 0.000 | 0.000 | 0.000 |
Wilcoxon test (CSFLA, IWOA) | 0.000 | 0.000 | 0.000 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lei, D.; Dai, T. A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility. Symmetry 2023, 15, 786. https://doi.org/10.3390/sym15040786
Lei D, Dai T. A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility. Symmetry. 2023; 15(4):786. https://doi.org/10.3390/sym15040786
Chicago/Turabian StyleLei, Deming, and Tao Dai. 2023. "A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility" Symmetry 15, no. 4: 786. https://doi.org/10.3390/sym15040786
APA StyleLei, D., & Dai, T. (2023). A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility. Symmetry, 15(4), 786. https://doi.org/10.3390/sym15040786