Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems
Abstract
:1. Introduction
- A set of jobs , where denotes ith job .
- A set of machines , and denotes jth machine.
- Each job has a specific set of operations , where is the total number of operations in job . Note that operation will be processed only once the operation has been completed in job .
- Each operation is performed independently of the others.
- One job operation cannot begin until all previous operations have been completed.
- Once a processing operation has begun, it will not be interrupted until the procedure is completed.
- It is impossible to handle multiple operations of the same job simultaneously.
- Job operations must wait in line until the next suitable machine is available.
- One machine can only perform one operation at a time.
- During the unallocated period, the machine will remain idle.
2. Related Work
3. Materials and Methods
3.1. Representation of Job-Shop Scheduling Problem
- Each element appearing in a solution represents the job to be processed;
- The number of appearing jobs correlates to the number of machines they must pass through;
- The order of the element in the solution follows the machine sequence that the job must pass through.
Algorithm 1: Coral Reef Optimization (CRO). |
Input: : reef size, : occupation rate, : fraction of broadcast spawners, : fraction of asexual reproduction, : fraction of the worse fitness corals, : the deprecated probability of the worse fitness corals. Output: reasonable solution with best fitness #Initialization—Reef formation phase:
|
3.2. Objective Function
3.3. Local Search: Simulated Annealing (SA)
Algorithm 2: Simulated Annealing |
Input: : temperature, : min temperature,: cooling rate, : fitness function, : solution, : maximum iteration Output: Best_solution #Initialization:
|
3.4. Local Search: Variable Neighborhood Search (VNS)
Algorithm 3: Variable Neighborhood Search |
Input: : index denoting the neighborhood structure, : total number of neighborhood structures,: solution, : fitness function, : solution set in -th neighborhood structure, : computation time Output: Best_solution #Initialization:
|
3.5. Proposal Approaches
Algorithm 4: Hybrid Coral Reef Optimization Algorithms (CROLS1 and CROLS2) |
Input: : reef size, : occupation rate, : fraction of broadcast spawners, : fraction of asexual reproduction, : fraction of the worse fitness corals, : the deprecated probability of the worse fitness corals. Output: Reasonable solution with best fitness #Initialization—Reef formation phase:
|
3.6. Time Complexity
4. Experiment Results and Discussion
4.1. Dataset
4.2. Parameters Used in the Algorithm
4.3. Experiment Results
4.3.1. Search Performance on CRO-Based Algorithm with Different Reef Sizes
4.3.2. Comparison of the Computational Result of CRO-Based Algorithms with Other Implemented Local Search Technique Algorithms
4.3.3. Comparison of the Computational Result of CRO-Based Algorithms with Other Contemporary Algorithms
4.3.4. Improvement of Search Efficiency
4.3.5. Convergence Ability
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Technique | Definition | Range |
---|---|---|---|
CRO | Reef size | ] | |
Iter | CRO | Number of iterations (generations) | |
Fb | CRO | Probability of Broadcast spawning process | |
Fa | CRO | Probability of Budding process | |
r0 | CRO | Initial free/occupied ratio | |
Fd | CRO | Probability of selecting weak individuals from the population | |
Pd | CRO | Probability of removing weak individuals from the population | |
k | CRO | Number of chances for a new coral to colonize a reef | |
ke | CRO | Maximum number of allowed equal corals | |
SA | Min temperature | [0.0001, 1] | |
SA | Cooling rate | [0.7, 0.99] | |
VNS | Solution set in neighborhood structure | [1, L] |
Size | r0 | Fb | Fa | Fd | Pd | k | tmin | α | Nk | |
---|---|---|---|---|---|---|---|---|---|---|
Small | 0.6 | 0.9 | 0.05 | 0.01 | 0.1 | 3 | 0.5 | 0.85 | L | |
Medium | 0.7 | 0.85 | 0.05 | 0.05 | 0.1 | 3 | 0.5 | 0.85 | L | |
Large | 0.7 | 0.85 | 0.1 | 0.1 | 0.1 | 3 | 0.5 | 0.85 | L |
Instance | Size | Reef Size | Method | Opt | Best | Worst | Mean | SD | Time (s) |
---|---|---|---|---|---|---|---|---|---|
LA01 | 10 × 10 | CRO | 666 | 666 | 674 | 668.91 | 2.4 | 128.45 | |
CROLS1 | 666 | 666 | 666 | 666 | 0 | 39.91 | |||
CROLS2 | 666 | 666 | 666 | 666 | 0 | 33.18 | |||
20 × 20 | CRO | 666 | 666 | 671 | 667.73 | 1.58 | 45.09 | ||
CROLS1 | 666 | 666 | 671 | 668.45 | 1.79 | 20.45 | |||
CROLS2 | 666 | 666 | 666 | 666 | 0 | 15.64 | |||
30 × 30 | CRO | 666 | 666 | 674 | 669.55 | 2.7 | 44.27 | ||
CROLS1 | 666 | 666 | 671 | 668.09 | 2 | 20.27 | |||
CROLS2 | 666 | 666 | 671 | 667.45 | 1.91 | 14.64 | |||
LA02 | 10 × 10 | CRO | 655 | 655 | 676 | 664.91 | 6.41 | 118.73 | |
CROLS1 | 655 | 655 | 655 | 655 | 0 | 40.91 | |||
CROLS2 | 655 | 655 | 655 | 655 | 0 | 33.91 | |||
20 × 20 | CRO | 655 | 655 | 671 | 663.73 | 5.68 | 43.82 | ||
CROLS1 | 655 | 655 | 671 | 662.27 | 5.57 | 18.55 | |||
CROLS2 | 655 | 655 | 655 | 655 | 0 | 15.27 | |||
30 × 30 | CRO | 655 | 655 | 676 | 665.36 | 6.62 | 44.55 | ||
CROLS1 | 655 | 655 | 671 | 663.18 | 6.02 | 18.55 | |||
CROLS2 | 655 | 655 | 670 | 661.09 | 6.21 | 14.09 | |||
LA06 | 10 × 10 | CRO | 926 | 926 | 946 | 935.45 | 7.54 | 169.09 | |
CROLS1 | 926 | 926 | 926 | 926 | 0 | 151.82 | |||
CROLS2 | 926 | 926 | 926 | 926 | 0 | 149.73 | |||
20 × 20 | CRO | 926 | 926 | 940 | 931.73 | 4.73 | 125.91 | ||
CROLS1 | 926 | 926 | 940 | 932.36 | 5.46 | 100.73 | |||
CROLS2 | 926 | 926 | 926 | 926 | 0 | 92.45 | |||
30 × 30 | CRO | 926 | 926 | 946 | 935 | 7.82 | 76.36 | ||
CROLS1 | 926 | 926 | 940 | 931.18 | 5.04 | 46.55 | |||
CROLS2 | 926 | 926 | 940 | 933.18 | 5.09 | 41.09 | |||
LA07 | 10 × 10 | CRO | 890 | 899 | 922 | 906.45 | 6.24 | 175.73 | |
CROLS1 | 890 | 890 | 895 | 890.73 | 1.54 | 148.18 | |||
CROLS2 | 890 | 890 | 892 | 890.45 | 0.81 | 133.55 | |||
20 × 20 | CRO | 890 | 895 | 916 | 905.73 | 5.8 | 117.91 | ||
CROLS1 | 890 | 890 | 916 | 907 | 5.04 | 94.82 | |||
CROLS2 | 890 | 890 | 890 | 890 | 0 | 88.73 | |||
30 × 30 | CRO | 890 | 890 | 922 | 908.18 | 7.38 | 78.09 | ||
CROLS1 | 890 | 890 | 916 | 906.91 | 5.29 | 45.91 | |||
CROLS2 | 890 | 890 | 916 | 905.09 | 5.92 | 33.64 | |||
LA11 | 10 × 10 | CRO | 1222 | 1222 | 1257 | 1235.64 | 13.41 | 237.36 | |
CROLS1 | 1222 | 1222 | 1222 | 1222 | 0 | 224.09 | |||
CROLS2 | 1222 | 1222 | 1222 | 1222 | 0 | 229.73 | |||
20 × 20 | CRO | 1222 | 1222 | 1244 | 1228.55 | 7.15 | 166.91 | ||
CROLS1 | 1222 | 1222 | 1244 | 1229.64 | 7.13 | 147.91 | |||
CROLS2 | 1222 | 1222 | 1222 | 1222 | 0 | 136.55 | |||
30 × 30 | CRO | 1222 | 1222 | 1257 | 1233.45 | 12.58 | 128.82 | ||
CROLS1 | 1222 | 1222 | 1244 | 1230.73 | 8.52 | 100.18 | |||
CROLS2 | 1222 | 1222 | 1244 | 1229.91 | 7.89 | 95.72 | |||
LA12 | 10 × 10 | CRO | 1039 | 1039 | 1062 | 1049.55 | 6.96 | 241.45 | |
CROLS1 | 1039 | 1039 | 1042 | 1039.36 | 0.92 | 228.55 | |||
CROLS2 | 1039 | 1039 | 1039 | 1039 | 0 | 217.64 | |||
20 × 20 | CRO | 1039 | 1039 | 1062 | 1049.55 | 6.87 | 164.27 | ||
CROLS1 | 1039 | 1039 | 1062 | 1051.91 | 6.62 | 157.91 | |||
CROLS2 | 1039 | 1039 | 1039 | 1039 | 0 | 149.91 | |||
30 × 30 | CRO | 1039 | 1039 | 1060 | 1048.27 | 7.96 | 120.09 | ||
CROLS1 | 1039 | 1039 | 1043 | 1047.45 | 7.27 | 103.45 | |||
CROLS2 | 1039 | 1039 | 1039 | 1050.91 | 7.01 | 89.91 | |||
LA16 | 10 × 10 | CRO | 945 | 971 | 1024 | 979.27 | 22.73 | 349.64 | |
CROLS1 | 945 | 945 | 979 | 958.91 | 10.69 | 317.73 | |||
CROLS2 | 945 | 945 | 980 | 959.36 | 12.44 | 315.64 | |||
20 × 20 | CRO | 945 | 948 | 1011 | 981.91 | 17.11 | 239.73 | ||
CROLS1 | 945 | 945 | 956 | 949.64 | 4.37 | 212.55 | |||
CROLS2 | 945 | 945 | 955 | 948.91 | 4 | 198.64 | |||
30 × 30 | CRO | 945 | 948 | 1011 | 976.55 | 19.06 | 177.64 | ||
CROLS1 | 945 | 945 | 955 | 947.73 | 2.93 | 125.91 | |||
CROLS2 | 945 | 945 | 955 | 948.73 | 4.13 | 132.55 | |||
LA17 | 10 × 10 | CRO | 784 | 799 | 888 | 833.55 | 31.06 | 337.09 | |
CROLS1 | 784 | 787 | 807 | 795.18 | 7.55 | 309.73 | |||
CROLS2 | 784 | 788 | 807 | 797.91 | 7.79 | 297.55 | |||
20 × 20 | CRO | 784 | 788 | 832 | 811.91 | 13.08 | 252.64 | ||
CROLS1 | 784 | 784 | 788 | 785.36 | 1.69 | 198.55 | |||
CROLS2 | 784 | 784 | 799 | 790.36 | 5.71 | 222.91 | |||
30 × 30 | CRO | 784 | 788 | 832 | 808.27 | 13.51 | 183.18 | ||
CROLS1 | 784 | 784 | 799 | 788.55 | 4.88 | 128.82 | |||
CROLS2 | 784 | 784 | 799 | 787.09 | 4.43 | 130.09 | |||
LA21 | 10 × 10 | CRO | 1046 | 1069 | 1146 | 1105.73 | 79.28 | 553.64 | |
CROLS1 | 1046 | 1056 | 1117 | 1100.64 | 10.07 | 487.18 | |||
CROLS2 | 1046 | 1055 | 1115 | 1099 | 8.29 | 473.09 | |||
20 × 20 | CRO | 1046 | 1069 | 1100 | 1071.45 | 49.41 | 345.91 | ||
CROLS1 | 1046 | 1046 | 1054 | 1048.82 | 3.27 | 269.36 | |||
CROLS2 | 1046 | 1046 | 1066 | 1053.09 | 6.34 | 274.27 | |||
30 × 30 | CRO | 1046 | 1106 | 1250 | 1172.64 | 51.47 | 256.64 | ||
CROLS1 | 1046 | 1046 | 1066 | 1052.55 | 7.76 | 164.36 | |||
CROLS2 | 1046 | 1046 | 1066 | 1052.55 | 6.88 | 165.55 | |||
LA22 | 10 × 10 | CRO | 927 | 978 | 1220 | 1178.36 | 30.51 | 538.45 | |
CROLS1 | 927 | 930 | 1011 | 983.45 | 16.83 | 479.73 | |||
CROLS2 | 927 | 934 | 988 | 976.09 | 8.32 | 464.09 | |||
20 × 20 | CRO | 927 | 944 | 1150 | 1030.64 | 57.45 | 356.27 | ||
CROLS1 | 927 | 927 | 974 | 944.18 | 16.83 | 267.91 | |||
CROLS2 | 927 | 927 | 944 | 932.18 | 4.8 | 265.55 | |||
30 × 30 | CRO | 927 | 935 | 1150 | 1030.09 | 53.54 | 248.27 | ||
CROLS1 | 927 | 927 | 944 | 932.73 | 5.69 | 185.18 | |||
CROLS2 | 927 | 927 | 944 | 934.27 | 6.21 | 174.27 | |||
LA26 | 10 × 10 | CRO | 1218 | 1333 | 1358 | 1349.64 | 22.89 | 759.64 | |
CROLS1 | 1218 | 1246 | 1316 | 1297.09 | 10.72 | 655.82 | |||
CROLS2 | 1218 | 1242 | 1323 | 1305.82 | 12.36 | 651.91 | |||
20 × 20 | CRO | 1218 | 1256 | 1280 | 1263.27 | 45.98 | 536.64 | ||
CROLS1 | 1218 | 1218 | 1253 | 1235.91 | 12.07 | 456.91 | |||
CROLS2 | 1218 | 1218 | 1246 | 1230.27 | 8.97 | 440.36 | |||
30 × 30 | CRO | 1218 | 1226 | 1275 | 1255.82 | 44.37 | 359.91 | ||
CROLS1 | 1218 | 1218 | 1246 | 1229.91 | 10.75 | 281.73 | |||
CROLS2 | 1218 | 1218 | 1246 | 1231.09 | 9.12 | 246.27 | |||
LA27 | 10 × 10 | CRO | 1235 | 1323 | 1495 | 1446.55 | 30.3 | 748.09 | |
CROLS1 | 1235 | 1255 | 1310 | 1275.36 | 8.51 | 688.91 | |||
CROLS2 | 1235 | 1256 | 1304 | 1261.09 | 8.29 | 650.64 | |||
20 × 20 | CRO | 1235 | 1305 | 1415 | 1461.09 | 22.57 | 541.09 | ||
CROLS1 | 1235 | 1235 | 1305 | 1260.55 | 28.95 | 459.45 | |||
CROLS2 | 1235 | 1235 | 1246 | 1239.18 | 4.1 | 447.36 | |||
30 × 30 | CRO | 1235 | 1255 | 1375 | 1359.55 | 25.96 | 336.18 | ||
CROLS1 | 1235 | 1235 | 1246 | 1239.09 | 4.2 | 260.18 | |||
CROLS2 | 1235 | 1235 | 1246 | 1240.27 | 4.09 | 239.27 | |||
LA32 | 10 × 10 | CRO | 1850 | 1934 | 2328 | 2254.91 | 96.2 | 827.91 | |
CROLS1 | 1850 | 1852 | 1896 | 1862.73 | 13.75 | 713.55 | |||
CROLS2 | 1850 | 1850 | 1888 | 1866.73 | 9.77 | 693.09 | |||
20 × 20 | CRO | 1850 | 1932 | 2126 | 2074.85 | 30.69 | 740.73 | ||
CROLS1 | 1850 | 1850 | 1865 | 1855.36 | 5.77 | 646.64 | |||
CROLS2 | 1850 | 1850 | 1856 | 1852.18 | 2.29 | 630.18 | |||
30 × 30 | CRO | 1850 | 1912 | 2105 | 1998.52 | 30.26 | 566.64 | ||
CROLS1 | 1850 | 1850 | 1856 | 1853 | 2.05 | 453.45 | |||
CROLS2 | 1850 | 1850 | 1856 | 1852.18 | 2.33 | 418.45 | |||
LA33 | 10 × 10 | CRO | 1719 | 1865 | 2131 | 2014.73 | 65 | 824.18 | |
CROLS1 | 1719 | 1720 | 1752 | 1732.27 | 12.43 | 726.09 | |||
CROLS2 | 1719 | 1722 | 1752 | 1730.27 | 11.39 | 692.82 | |||
20 × 20 | CRO | 1719 | 1818 | 2056 | 1955.73 | 55.54 | 737.91 | ||
CROLS1 | 1719 | 1719 | 1723 | 1720.45 | 1.56 | 643.09 | |||
CROLS2 | 1719 | 1719 | 1732 | 1723.91 | 5.48 | 617.27 | |||
30 × 30 | CRO | 1719 | 1805 | 2034 | 1934.91 | 60.59 | 557.82 | ||
CROLS1 | 1719 | 1719 | 1732 | 1723.45 | 4.97 | 441.73 | |||
CROLS2 | 1719 | 1719 | 1732 | 1724.18 | 5.14 | 438.82 | |||
LA39 | 10 × 10 | CRO | 1233 | 1388 | 1466 | 1498.82 | 42.44 | 869.09 | |
CROLS1 | 1233 | 1238 | 1316 | 1278.73 | 16.66 | 725.73 | |||
CROLS2 | 1233 | 1274 | 1318 | 1279.82 | 13.48 | 624.45 | |||
20 × 20 | CRO | 1233 | 1368 | 1428 | 1419.36 | 7.61 | 834.09 | ||
CROLS1 | 1233 | 1238 | 1264 | 1241.64 | 27.32 | 675.45 | |||
CROLS2 | 1233 | 1239 | 1264 | 1244.91 | 29.39 | 568.73 | |||
30 × 30 | CRO | 1233 | 1332 | 1403 | 1397.21 | 24.37 | 752.09 | ||
CROLS1 | 1233 | 1233 | 1255 | 1243.09 | 34.44 | 592.64 | |||
CROLS2 | 1233 | 1233 | 1255 | 1237.55 | 13.78 | 502.82 | |||
LA40 | 10 × 10 | CRO | 1222 | 1396 | 1506 | 1451.25 | 49.25 | 875 | |
CROLS1 | 1222 | 1240 | 1336 | 1313.27 | 11.24 | 728.45 | |||
CROLS2 | 1222 | 1269 | 1305 | 1288.45 | 35.41 | 625.36 | |||
20 × 20 | CRO | 1222 | 1364 | 1455 | 1390.35 | 58.7 | 826.82 | ||
CROLS1 | 1222 | 1240 | 1299 | 1270.27 | 35.09 | 674.73 | |||
CROLS2 | 1222 | 1239 | 1299 | 1273.09 | 30.93 | 568.82 | |||
30 × 30 | CRO | 1222 | 1342 | 1424 | 1374.33 | 24.88 | 739.82 | ||
CROLS1 | 1222 | 1228 | 1264 | 1238.25 | 15.89 | 585.45 | |||
CROLS2 | 1222 | 1232 | 1279 | 1248.45 | 23.22 | 495.55 |
Algorithm | Mean Rank | ||
---|---|---|---|
Reef Size 10 × 10 | Reef Size 20 × 20 | Reef Size 30 × 30 | |
CRO | 3.00 | 2.69 | 2.94 |
CROLS1 | 1.56 | 2.06 | 1.47 |
CROLS2 | 1.44 | 1.25 | 1.59 |
Χ2 | ρ | |
---|---|---|
Reef Size 10 × 10 | 25.733 | 0.000003 |
Reef Size 20 × 20 | 16.625 | 0.000245 |
Reef Size 30 × 30 | 21.556 | 0.000021 |
CRO-CROLS1 | CRO-CROLS2 | CROLS1-CROLS2 | |
---|---|---|---|
Z | −3.516 | −3.516 | −1.533 |
p | 0.000438 | 0.000438 | 0.125153 |
Ins. | Size. | Opt. | CRO | CROLS1 | CROLS2 | HGA | MA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
10 × 10 | 20 × 20 | 30 × 30 | 10 × 10 | 20 × 20 | 30 × 30 | 10 × 10 | 20 × 20 | 30 × 30 | |||||
LA01 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | |
LA02 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | |
LA06 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | |
LA07 | 890 | 899 | 895 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | |
LA11 | 1222 | 1228 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | |
LA12 | 1039 | 1042 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | |
LA16 | 945 | 956 | 955 | 955 | 945 | 945 | 945 | 945 | 945 | 945 | 945 | 945 | |
LA17 | 784 | 799 | 788 | 788 | 787 | 784 | 784 | 788 | 784 | 784 | 784 | 784 | |
LA21 | 1046 | 1069 | 1069.9 | 1056 | 1046 | 1046 | 1046 | 1055 | 1046 | 1046 | 1046 | 1055 | |
LA22 | 927 | 978 | 944 | 935 | 930 | 927 | 927 | 934 | 928 | 927 | 935 | 927 | |
LA26 | 1218 | 1333 | 1256 | 1226 | 1246 | 1218 | 1218 | 1242 | 1218 | 1218 | 1218 | 1218 | |
LA27 | 1235 | 1323 | 1305 | 1255 | 1255 | 1235 | 1235 | 1256 | 1246 | 1246 | 1236 | 1261 | |
LA32 | 1850 | 1934 | 1932 | 1912 | 1852 | 1850 | 1850 | 1850 | 1850 | 1850 | 1850 | 1850 | |
LA33 | 1719 | 1865 | 1818 | 1805 | 1720 | 1719 | 1719 | 1722 | 1719 | 1719 | 1719 | 1719 | |
LA39 | 1233 | 1388 | 1368 | 1332 | 1238 | 1238 | 1233 | 1274 | 1239 | 1233 | 1233 | 1241 | |
LA40 | 1222 | 1396 | 1364 | 1342 | 1240 | 1240 | 1228 | 1269 | 1239 | 1232 | 1229 | 1233 |
Instance | Size | BKS | CRO | CROLS1 | CROLS2 | mXLSGA (2020) | NGPSO (2020) | SSS (2020) | GA-CPG-GT (2019) | DWPA (2019) |
---|---|---|---|---|---|---|---|---|---|---|
LA01 | 10 × 5 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 |
LA02 | 10 × 5 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 |
LA06 | 15 × 5 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 |
LA07 | 15 × 5 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 |
LA11 | 20 × 5 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 |
LA12 | 20 × 5 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | - | 1039 | 1039 |
LA16 | 10 × 10 | 945 | 955 | 945 | 945 | 945 | 945 | 947 | 946 | 993 |
LA17 | 10 × 10 | 784 | 788 | 784 | 784 | 784 | 794 | - | 784 | 793 |
LA21 | 15 × 10 | 1046 | 1056 | 1046 | 1046 | 1059 | 1183 | 1076 | 1090 | 1105 |
LA22 | 15 × 10 | 927 | 935 | 927 | 927 | 935 | 927 | - | 954 | 989 |
LA26 | 20 × 10 | 1218 | 1226 | 1218 | 1218 | 1218 | 1218 | - | 1237 | 1303 |
LA27 | 20 × 10 | 1235 | 1255 | 1235 | 1246 | 1269 | 1394 | - | 1313 | 1346 |
LA32 | 30 × 10 | 1850 | 1912 | 1850 | 1850 | 1850 | 1850 | - | 1850 | 1850 |
LA33 | 30 × 10 | 1719 | 1805 | 1719 | 1719 | 1719 | 1719 | - | 1719 | 1719 |
LA39 | 15 × 15 | 1233 | 1332 | 1233 | 1233 | 1258 | 1662 | - | 1290 | 1334 |
LA40 | 15 × 15 | 1222 | 1342 | 1228 | 1232 | 1243 | 1222 | 1252 | 1252 | 1347 |
FT06 | 6 × 6 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | - |
FT10 | 10 × 10 | 930 | 934 | 930 | 930 | 930 | 930 | 936 | 935 | - |
FT20 | 20 × 5 | 1165 | 1197 | 1174 | 1170 | 1165 | 1210 | 1165 | 1180 | - |
ABZ05 | 10 × 10 | 1234 | 1255 | 1234 | 1234 | 1234 | 1234 | - | 1238 | - |
ABZ06 | 10 × 10 | 943 | 988 | 943 | 943 | 943 | 943 | - | 947 | - |
ABZ07 | 20 × 15 | 656 | 755 | 731 | 727 | 695 | 713 | - | - | - |
ABZ08 | 20 × 15 | 665 | 720 | 709 | 705 | 713 | 729 | - | - | - |
ABZ09 | 20 × 15 | 679 | 817 | 707 | 711 | 721 | 930 | - | - | - |
ORB01 | 10 × 10 | 1059 | 1120 | 1070 | 1072 | 1068 | 1174 | - | 1084 | - |
ORB02 | 10 × 10 | 888 | 927 | 899 | 895 | 889 | 913 | - | 890 | - |
ORB03 | 10 × 10 | 1005 | 1097 | 1021 | 1023 | 1023 | 1104 | - | 1037 | - |
ORB04 | 10 × 10 | 1005 | 1121 | 1005 | 1005 | 1005 | 1005 | - | 1028 | - |
ORB05 | 10 × 10 | 887 | 904 | 890 | 894 | 889 | 887 | - | 894 | - |
ORB06 | 10 × 10 | 1010 | 1085 | 1020 | 1023 | 1019 | 1124 | - | 1035 | - |
ORB07 | 10 × 10 | 397 | 418 | 397 | 397 | 397 | 397 | - | 404 | - |
ORB08 | 10 × 10 | 899 | 988 | 912 | 907 | 907 | 1020 | - | 937 | - |
ORB09 | 10 × 10 | 934 | 955 | 938 | 940 | 940 | 980 | - | 943 | - |
ORB10 | 10 × 10 | 944 | 1010 | 967 | 950 | 944 | 1027 | - | 967 | - |
Instance | Size | CROLS1 | CROLS2 | ||||
---|---|---|---|---|---|---|---|
10 × 10 | 20 × 20 | 30 × 30 | 10 × 10 | 20 × 20 | 30 × 30 | ||
LA01 | 0 | 0 | 0 | 0 | 0 | 0 | |
LA02 | 1.68 | 0.46 | 0.15 | 1.68 | 0.46 | 0.15 | |
LA06 | 0 | 0 | 0 | 0 | 0 | 0 | |
LA07 | 1.01 | 0.56 | 0 | 1.01 | 0.56 | 0 | |
LA11 | 0.49 | 0 | 0 | 0.49 | 0 | 0 | |
LA12 | 0.29 | 0 | 0 | 0.29 | 0 | 0 | |
LA16 | 2.43 | 0.32 | 0.32 | 2.75 | 0.32 | 0.32 | |
LA17 | 1.53 | 0.51 | 0.51 | 1.4 | 0.51 | 0.51 | |
LA21 | 2.2 | 2.28 | 0.96 | 1.34 | 2.28 | 0.96 | |
LA22 | 5.18 | 1.83 | 0.86 | 4.75 | 1.73 | 0.86 | |
LA26 | 7.14 | 3.12 | 0.66 | 7.47 | 3.12 | 0.66 | |
LA27 | 5.51 | 5.67 | 1.62 | 5.43 | 4.78 | 0.73 | |
LA32 | 4.43 | 4.43 | 3.35 | 4.54 | 4.43 | 3.35 | |
LA33 | 8.44 | 5.76 | 5 | 8.32 | 5.76 | 5 | |
LA39 | 12.17 | 10.54 | 8.03 | 9.25 | 10.46 | 8.03 | |
LA40 | 12.77 | 10.15 | 9.33 | 10.39 | 10.23 | 9 |
Reef Size | 10 × 10 | 20 × 20 | 30 × 30 |
---|---|---|---|
CRO | 150.5 | 42.2 | 30.4 |
CROLS1 | 13.4 | 10.6 | 10.4 |
CROLS2 | 12.2 | 8 | 6.4 |
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Shieh, C.-S.; Nguyen, T.-T.; Lin, W.-W.; Nguyen, D.-C.; Horng, M.-F. Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems. Appl. Sci. 2022, 12, 9867. https://doi.org/10.3390/app12199867
Shieh C-S, Nguyen T-T, Lin W-W, Nguyen D-C, Horng M-F. Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems. Applied Sciences. 2022; 12(19):9867. https://doi.org/10.3390/app12199867
Chicago/Turabian StyleShieh, Chin-Shiuh, Thanh-Tuan Nguyen, Wan-Wei Lin, Dinh-Cuong Nguyen, and Mong-Fong Horng. 2022. "Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems" Applied Sciences 12, no. 19: 9867. https://doi.org/10.3390/app12199867
APA StyleShieh, C.-S., Nguyen, T.-T., Lin, W.-W., Nguyen, D.-C., & Horng, M.-F. (2022). Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems. Applied Sciences, 12(19), 9867. https://doi.org/10.3390/app12199867