Research on Multi-Objective Low-Carbon Flexible Job Shop Scheduling Based on Improved NSGA-II
Abstract
:1. Introduction
2. MOFJSP Scheduling Model
2.1. Description of MOFJSP Problem
2.2. MOFJSP Mathematical Model
2.2.1. The Model of Makespan
2.2.2. The Model of Cost
2.2.3. The Model of Carbon Emission
3. The ASA-NSGA-EE Algorithm
3.1. Population Initialization
3.2. Encoding and Decoding
3.3. Fast Non-Dominated Sorting and Crowding Distance Calculation
3.4. Improved Tournament Selection
3.5. Crossover and Mutation Operation Design Program
3.6. Improved Adaptive Crossover and Mutation Operation
3.7. Improved Elite Retention Strategy
4. Test Simulation
4.1. Performance Evaluation Index of Algorithm
4.2. Enterprise Case
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Notation | Descriptions |
---|---|
Carbon emission factor | |
A large positive number | |
The operation of workpiece | |
Product material cost | |
Machine processing cost | |
Machine processing energy consumption | |
Number of startups and shutdowns for machine | |
Energy consumption during machine startup and shutdown | |
Processing time of the operation of workpiece on machine | |
Machine idle energy consumption | |
The start time of the workpiece on machine | |
Processing cost of the operation of workpiece on machine | |
Energy consumption of machine per unit time during processing | |
Energy consumption of machine during startup and shutdown | |
The completion time of the workpiece on machine k | |
Idle energy consumption of machine per unit of time | |
Whether operation is completed on machine k is 0–1 variable | |
The processing sequence of operation and operation |
Instance | NSGA-II | ASA-NSGA-EE | MOGWO | |||||||
---|---|---|---|---|---|---|---|---|---|---|
IGD | HV | Cov1 | Cov1 | IGD | HV | Cov2 | Cov2 | IGD | HV | |
MK01 | 0.0513 | 0.9565 | 0.152 | 0.649 | 0.0393 | 0.9604 | 0.964 | 0.036 | 0.0702 | 0.9020 |
MK02 | 0.0885 | 0.9632 | 0 | 1 | 0.0077 | 1.1216 | 1 | 0 | 0.0584 | 0.9768 |
MK03 | 0.2093 | 0.8688 | 0 | 0.923 | 0.0406 | 1.2565 | 0.980 | 0 | 0.0914 | 0.9796 |
MK04 | 0.0470 | 0.9700 | 0.124 | 0.734 | 0.0115 | 1.0408 | 0.904 | 0.083 | 0.0451 | 0.9637 |
MK05 | 0.0353 | 0.9930 | 0 | 1 | 0.0011 | 1.0933 | 0.965 | 0 | 0.0271 | 1.0252 |
MK06 | 0.6914 | 0.2734 | 0 | 1 | 0.0199 | 1.3113 | 1 | 0 | 0.1664 | 1.0756 |
MK07 | 0.2416 | 0.8843 | 0 | 1 | 0.0249 | 1.2276 | 0.9808 | 0 | 0.1232 | 0.8893 |
MK08 | 0.0849 | 1.0930 | 0.079 | 0.679 | 0.0162 | 1.1718 | 0.914 | 0.02 | 0.1899 | 0.9055 |
MK09 | 0.3856 | 0.5194 | 0 | 1 | 0.0042 | 1.3017 | 0.930 | 0 | 0.164 | 0.9788 |
MK10 | 0.6309 | 0.3912 | 0 | 1 | 0.0053 | 1.3146 | 1 | 0 | 0.1680 | 1.0337 |
Job No. | Cost | Operation No. | Machine No. | Processing Time/min | Processing Energy/kW |
---|---|---|---|---|---|
Job1 | 250 | 1 | 1, 2, 3 | 10.8, 15, 11.7 | 0.6, 0.88, 0.78 |
2 | 1, 2, 3 | 10, 7.5, 9.2 | 0.6, 0.44, 0.6 | ||
3 | 4, 5 | 25.9, 30 | 2.8, 3.3 | ||
4 | 6, 7 | 55.9, 51.7 | 17.2, 14.5 | ||
5 | 8 | 5.8 | 0.78 | ||
6 | 9, 10 | 23.4, 20 | 8.8, 7 | ||
Job2 | 500 | 1 | 1, 2, 3 | 13.3, 12.5, 14.2 | 0.8, 0.73, 0.95 |
2 | 1, 2, 3 | 11.7, 15, 13.3 | 0.7, 0.9, 0.89 | ||
3 | 4, 5 | 27.5, 30.9 | 3, 3.3 | ||
4 | 6, 7 | 43.4, 46.7 | 13.6, 14.2 | ||
5 | 8 | 7.5 | 0.1 | ||
6 | 9, 10 | 26.7, 25.9 | 10, 9.1 | ||
Job3 | 600 | 1 | 1, 2, 3 | 18.3, 22.5, 20.9 | 1, 1.3, 1.4 |
2 | 1, 2, 3 | 23.4, 25.9, 28.4 | 1.4, 1.5, 1.9 | ||
3 | 4, 5 | 38.4, 33.4 | 4.2, 3.6 | ||
4 | 6, 7 | 55.9, 62.6 | 17.2, 17.4 | ||
5 | 8 | 6.7 | 0.09 | ||
6 | 9, 10 | 34.2, 40.9 | 12.8, 14.3 | ||
Job4 | 700 | 1 | 1, 2, 3 | 20, 23.4, 17.5 | 1.17, 1.37, 1.17 |
2 | 1, 2, 3 | 21.7, 25.9, 18.3 | 1.3, 1.5, 1.2 | ||
3 | 4, 5 | 35, 40.9 | 3.8, 4.4 | ||
4 | 11 | 5 | 1 | ||
5 | 6, 7 | 45, 48.4 | 13.9, 13.3 | ||
6 | 8 | 5 | 0.7 | ||
7 | 10 | 35 | 12.3 | ||
Job5 | 1850 | 1 | 1, 2, 3 | 33.4, 36.7, 35 | 1.9, 2.1, 2.34 |
2 | 1, 2, 3 | 39.2, 38.4, 39.2 | 2.3, 2.24, 2.6 | ||
3 | 4, 5 | 48.4, 53.4 | 5.2, 5.8 | ||
4 | 11 | 32.5 | 6.5 | ||
5 | 6, 7 | 81.8, 90.1 | 25.2, 24.8 | ||
6 | 8 | 5 | 0.7 | ||
7 | 9, 10 | 148.46, 162.6 | 55, 56.9 | ||
Job6 | 1800 | 1 | 8 | 9.2 | 0.12 |
2 | 1, 2, 3 | 34.2, 40, 36.7 | 1.99, 2.3, 2.45 | ||
3 | 1, 2, 3 | 30, 35, 30 | 1.75, 2.04, 2 | ||
4 | 4, 5 | 16.7, 20.9 | 1.8, 1.9 | ||
5 | 11 | 17.5 | 3.5 | ||
6 | 6, 7 | 81.7, 86.7 | 25.1, 23.8 | ||
Job7 | 300 | 1 | 12, 13, 14, 15 | 60, 61.7, 75.9, 80.1 | 7.5, 7.7, 11.4, 12 |
2 | 1, 2, 3 | 15, 18.3, 14.2 | 0.88, 1, 0.95 | ||
3 | 1, 2, 3 | 17.5, 21.7, 18.3 | 1.02, 1.3, 1.2 | ||
4 | 6,7 | 55.9, 61.7 | 17.2, 17 | ||
5 | 12, 13, 14, 15 | 52.5, 55, 70.1, 67.6 | 6.6, 6.89, 10.5, 10 | ||
Job8 | 600 | 1 | 11 | 12.5 | 2.5 |
2 | 1, 2, 3 | 32.5, 38.4, 34.2 | 1.9, 2.2, 2.28 | ||
3 | 8 | 18.3 | 0.2 | ||
4 | 1, 2, 3 | 24.2, 27.5, 22.5 | 1.4, 1.6, 1.5 | ||
5 | 10 | 8.3 | 2.9 | ||
6 | 12, 13, 14, 15 | 94.2, 95.9, 67.6, 71.7 | 11.8, 11.99, 10, 10.8 | ||
Job9 | 600 | 1 | 6, 7 | 75.9, 105.9 | 23.4, 29.1 |
2 | 1, 2, 3 | 35.9, 38.4, 35 | 2.1, 2.24, 2.3 | ||
3 | 8 | 25.9 | 0.3 | ||
4 | 1, 2, 3 | 29.2, 30.9, 25.9 | 1.7, 1.8, 1.7 | ||
5 | 10 | 8.3 | 2.9 | ||
6 | 12, 13, 14, 15 | 103.4, 100.9, 65.9, 77.6 | 12.9, 12.6, 9.88, 11.6 | ||
Job10 | 200 | 1 | 6, 7 | 81.7, 110.1 | 25.2, 30.3 |
2 | 1, 2, 3 | 21.7, 24.2, 25.9 | 1.27, 1.4, 1.7 | ||
3 | 1, 2, 3 | 26.7, 30.9, 27.5 | 1.56, 1.8, 1.8 |
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Mei, Z.; Lu, Y.; Lv, L. Research on Multi-Objective Low-Carbon Flexible Job Shop Scheduling Based on Improved NSGA-II. Machines 2024, 12, 590. https://doi.org/10.3390/machines12090590
Mei Z, Lu Y, Lv L. Research on Multi-Objective Low-Carbon Flexible Job Shop Scheduling Based on Improved NSGA-II. Machines. 2024; 12(9):590. https://doi.org/10.3390/machines12090590
Chicago/Turabian StyleMei, Zheyu, Yujun Lu, and Liye Lv. 2024. "Research on Multi-Objective Low-Carbon Flexible Job Shop Scheduling Based on Improved NSGA-II" Machines 12, no. 9: 590. https://doi.org/10.3390/machines12090590