Journal of System Simulation ›› 2026, Vol. 38 ›› Issue (10): 2980-2996.doi: 10.16182/j.issn1004731x.joss.26-0387
• Complex System Scheduling and Resource Allocation • Previous Articles Next Articles
Zhao Fuqing1, Wu Bin1, Xu Tianpeng1, Zhu Ningning1, Song Houbin2, Yao Yukai1
Received:2026-04-29
Revised:2026-06-30
Online:2026-10-31
Published:2026-10-20
CLC Number:
Zhao Fuqing, Wu Bin, Xu Tianpeng, Zhu Ningning, Song Houbin, Yao Yukai. Scheduling Optimization for Cascaded Hybrid Flow Shop Integrating LLM and RL[J]. Journal of System Simulation, 2026, 38(10): 2980-2996.
Table 3
Comparison between CPLEX and LCES-RL
| 规模 | 完工时间/min | 总能耗/kW | ||
|---|---|---|---|---|
| CPLEX | LCES-RL | CPLEX | LCES-RL | |
| 4-2-1-2 | 172.54 | 172.54 | 13 583.06 | 13 611.03 |
| 4-2-2-2 | 117.98 | 117.98 | 10 583.81 | 10 579.03 |
| 5-2-1-2 | 317.64 | 317.64 | 20 920.04 | 21 098.02 |
| 5-2-2-2 | 231.19 | 231.19 | 20 986.14 | 21 031.85 |
| 5-2-2-3 | 234.40 | 234.40 | 16 099.51 | 16 132.32 |
| 6-2-2-2 | 316.50 | 316.50 | 22 201.08 | 22 633.36 |
| 6-2-2-3 | 270.13 | 270.13 | 23 275.22 | 23 461.93 |
| 6-3-2-2 | 211.16 | 211.16 | 21 489.54 | 21 985.54 |
Table 6
Comparative experimental results
| 实例 | 评价指标 | LCES-RL | NSGA-II | MOEA/D | GATS-IPTSP | NSGA2-MDDQN |
|---|---|---|---|---|---|---|
| (10,2,2) | HV | 0.702 2 | 0.638 5 | 0.719 5 | 0.733 9 | 0.709 4 |
| IGD | 0.023 0 | 0.065 4 | 0.085 3 | 0.021 5 | 0.050 2 | |
| SP | 0.005 8 | 0.008 4 | 0.061 1 | 0.027 3 | 0.015 0 | |
| (10,3,2) | HV | 0.531 9 | 0.492 7 | 0.577 3 | 0.575 1 | 0.560 2 |
| IGD | 0.052 8 | 0.059 6 | 0.093 7 | 0.031 6 | 0.058 4 | |
| SP | 0.006 3 | 0.050 6 | 0.035 1 | 0.048 9 | 0.020 6 | |
| (20,2,2) | HV | 0.574 8 | 0.433 3 | 0.532 4 | 0.548 1 | 0.544 9 |
| IGD | 0.052 6 | 0.087 4 | 0.086 5 | 0.017 7 | 0.070 6 | |
| SP | 0.008 3 | 0.039 1 | 0.065 4 | 0.028 2 | 0.028 8 | |
| (20,3,2) | HV | 0.703 4 | 0.550 7 | 0.692 7 | 0.658 9 | 0.693 8 |
| IGD | 0.047 2 | 0.057 1 | 0.071 4 | 0.030 7 | 0.036 2 | |
| SP | 0.014 1 | 0.059 2 | 0.073 6 | 0.046 7 | 0.020 1 | |
| (40,4,3) | HV | 0.835 0 | 0.603 9 | 0.567 6 | 0.827 6 | 0.634 2 |
| IGD | 0.022 4 | 0.040 8 | 0.140 5 | 0.057 8 | 0.060 9 | |
| SP | 0.002 2 | 0.008 2 | 0.096 7 | 0.074 7 | 0.026 9 | |
| (40,5,3) | HV | 0.885 5 | 0.467 8 | 0.593 7 | 0.826 5 | 0.637 6 |
| IGD | 0.058 8 | 0.078 2 | 0.175 3 | 0.099 1 | 0.092 9 | |
| SP | 0.029 8 | 0.084 4 | 0.108 7 | 0.049 3 | 0.038 1 | |
| (60,4,3) | HV | 0.937 0 | 0.427 3 | 0.339 3 | 0.702 5 | 0.621 8 |
| IGD | 0.069 4 | 0.075 6 | 0.206 9 | 0.077 9 | 0.069 5 | |
| SP | 0.032 2 | 0.040 7 | 0.090 5 | 0.073 8 | 0.033 8 | |
| (60,5,3) | HV | 0.955 5 | 0.184 5 | 0.382 1 | 0.496 7 | 0.495 9 |
| IGD | 0.071 0 | 0.143 1 | 0.230 2 | 0.156 2 | 0.143 9 | |
| SP | 0.045 7 | 0.094 7 | 0.103 2 | 0.083 3 | 0.057 1 | |
| (80,5,4) | HV | 0.971 9 | 0.275 3 | 0.375 1 | 0.484 8 | 0.496 0 |
| IGD | 0.075 9 | 0.112 7 | 0.271 4 | 0.131 7 | 0.103 6 | |
| SP | 0.046 3 | 0.115 5 | 0.147 6 | 0.071 1 | 0.049 2 | |
| (80,6,4) | HV | 0.925 5 | 0.318 2 | 0.418 8 | 0.669 2 | 0.491 9 |
| IGD | 0.084 4 | 0.598 3 | 0.255 6 | 0.131 0 | 0.084 9 | |
| SP | 0.054 7 | 0.023 4 | 0.154 9 | 0.095 1 | 0.047 7 | |
| (100,5,4) | HV | 0.971 1 | 0.180 5 | 0.208 4 | 0.250 7 | 0.218 5 |
| IGD | 0.037 4 | 0.233 2 | 0.273 8 | 0.209 1 | 0.193 5 | |
| SP | 0.026 7 | 0.155 9 | 0.101 8 | 0.052 4 | 0.033 9 | |
| (100,6,4) | HV | 0.886 7 | 0.255 0 | 0.454 6 | 0.468 0 | 0.503 1 |
| IGD | 0.096 8 | 0.153 9 | 0.312 4 | 0.135 6 | 0.104 4 | |
| SP | 0.038 7 | 0.102 5 | 0.157 5 | 0.093 3 | 0.057 4 |
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