Enhancing NSGA-II Algorithm through Hybrid Strategy for Optimizing Maize Water and Fertilizer Irrigation Simulation
Abstract
:1. Introduction
2. Related Works
2.1. Multi-Objective Algorithm NSGA-II
2.2. Problems in CD Sorting of NSGA-II
3. The Proposed NDE-NSGA-II
3.1. Initializing Population with Tent Mapping
Algorithm 1 Tent Chaos Initialization |
|
3.2. Local Search Strategy
Algorithm 2 The local searching strategy |
|
3.3. Convergence and Diversity Measures
Algorithm 3 Elitist selection |
|
4. Algorithm Comparison
4.1. Indicators for Evaluation
4.2. Convergence Evaluation of Different Algorithms on ZDT and DTLZ Test Problems
4.3. Diversity Evaluation of Different Algorithms on ZDT and DTLZ Test Problems
4.4. Comprehensive Evaluation of Different Algorithms on ZDT and DTLZ Test Problems
4.5. Quantify the Number of Mutation Strategies across Different Algorithms and Test Functions
5. Experiments and Analysis of Results
5.1. Study Area
5.2. Objective Function
5.3. Optimization Strategies and Configuration
5.4. Result and Analysis
6. Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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D | NSGA-II | MOEA/D | SPEA2 | CDE-NSGA-II | CMWOA | NDE-NSGA-II | |
---|---|---|---|---|---|---|---|
ZDT1 | 30 | ||||||
()− | ()− | ()− | ()− | ()+ | () | ||
ZDT2 | 30 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
ZDT3 | 30 | ||||||
()− | ()− | ()+ | ()− | ()+ | () | ||
ZDT4 | 10 | ||||||
()− | ()− | ()− | ()= | ()− | () | ||
ZDT6 | 10 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ1 | 7 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ2 | 12 | ||||||
()= | ()+ | ()− | ()= | ()− | () | ||
DTLZ3 | 12 | ||||||
()+ | ()− | ()− | ()− | ()− | ( | ||
DTLZ4 | 12 | ||||||
()= | ()+ | ()− | ()− | ()− | () | ||
DTLZ5 | 12 | ||||||
()= | ()+ | ()− | ()= | ()− | () | ||
DTLZ6 | 12 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ7 | 12 | ||||||
()+ | ()+ | ()+ | ()− | ()+ | () | ||
+/−/= | 2/7/3 | 4/8/0 | 2/10/0 | 0/9/3 | 3/9/0 |
D | NSGA-II | MOEA/D | SPEA2 | CDE-NSGA-II | CMWOA | NDE-NSGA-II | |
---|---|---|---|---|---|---|---|
ZDT1 | 30 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
ZDT2 | 30 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
ZDT3 | 30 | ||||||
()+ | ()− | ()+ | ()= | ()+ | () | ||
ZDT4 | 10 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
ZDT6 | 10 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ1 | 7 | ||||||
()− | ()+ | ()− | ()− | ()− | () | ||
DTLZ2 | 12 | ||||||
()− | ()+ | ()+ | ()− | ()+ | () | ||
DTLZ3 | 12 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ4 | 12 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
DTLZ5 | 12 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ6 | 12 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ7 | 12 | ||||||
()+ | ()= | ()+ | ()− | ()+ | () | ||
+/−/= | 2/10/0 | 2/9/1 | 3/9/0 | 0/11/1 | 3/6/3 |
D | NSGA-II | MOEA/D | SPEA2 | CDE-NSGA-II | CMWOA | NDE-NSGA-II | |
---|---|---|---|---|---|---|---|
ZDT1 | 30 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
ZDT2 | 30 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
ZDT3 | 30 | ||||||
()= | ()− | ()+ | ()= | ()+ | () | ||
ZDT4 | 10 | ||||||
()− | ()− | ()− | ()= | ()− | () | ||
ZDT6 | 10 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
DTLZ1 | 7 | ||||||
()− | ()= | ()− | ()− | ()− | () | ||
DTLZ2 | 12 | ||||||
()− | ()+ | ()= | ()− | ()− | () | ||
DTLZ3 | 12 | ||||||
()+ | ()− | ()− | ()− | ()− | () | ||
DTLZ4 | 12 | ||||||
()− | ()− | ()− | ()− | ()− | () | ||
DTLZ5 | 12 | ||||||
()= | ()− | ()= | ()= | ()− | () | ||
DTLZ6 | 12 | ||||||
()− | ()− | ()− | ()− | ()= | () | ||
DTLZ7 | 12 | ||||||
()+ | ()+ | ()+ | ()− | ()+ | () | ||
+/−/= | 2/8/2 | 2/9/1 | 2/8/2 | 0/9/3 | 2/6/4 |
D | NSGA-II | MOEA/D | SPEA2 | CDE-NSGA-II | CMWOA | NDE-NSGA-II | |
---|---|---|---|---|---|---|---|
ZDT1 | 30 | 127/299 | 291/633 | 161/303 | 134/318 | 122/314 | 98/310 |
ZDT2 | 30 | 129/302 | 315/594 | 152/318 | 133/302 | 137/295 | 125/312 |
ZDT3 | 30 | 163/269 | 388/633 | 142/325 | 145/295 | 147/311 | 120/328 |
ZDT4 | 10 | 82/103 | 216/407 | 76/100 | 89/111 | 89/94 | 105/189 |
ZDT6 | 10 | 58/101 | 121/219 | 53/95 | 54/102 | 41/94 | 65/106 |
DTLZ1 | 7 | 8/70 | 36/237 | 8/69 | 10/75 | 20/73 | 8/77 |
DTLZ2 | 12 | 4/132 | 36/382 | 6/123 | 3/115 | 4/102 | 2/121 |
DTLZ3 | 12 | 44/126 | 43/347 | 33/117 | 28/113 | 28/108 | 16/126 |
DTLZ4 | 12 | 14/103 | 26/268 | 7/124 | 16/132 | 11/113 | 2/120 |
DTLZ5 | 12 | 7/122 | 13/343 | 9/113 | 11/126 | 13/120 | 6/134 |
DTLZ6 | 12 | 85/115 | 48/339 | 11/133 | 11/115 | 2/106 | 6/132 |
DTLZ7 | 12 | 102/193 | 298/587 | 103/222 | 90/230 | 80/233 | 123/241 |
N1 Costs (Yuan/kg) | N2 Costs (Yuan/kg) | N3 Costs (Yuan/kg) |
---|---|---|
3.98 | 2.65 | 3.82 |
Yield (kg/ha) | Yield Increase (%) | Total Irrigation (mm) | Irrigation Reduction (%) | Total Nitrogen (kg/ha) | Fertilization Reduction (%) | ||||
---|---|---|---|---|---|---|---|---|---|
Practices | Optimized Results | Practices | Optimized Results | Practices | Optimized Results | ||||
N1 | 12,836 | 13,585 | 5.8% | 80 | 55 | 31.3% | 300 | 375 | −25% |
N2 | 13,589 | 5.9% | 50 | 37.5% | 275 | 8.3% | |||
N3 | 13,587 | 5.5% | 62 | 22.5% | 277 | 7.7% |
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Du, J.; Liu, R.; Cheng, D.; Wang, X.; Zhang, T.; Yu, F. Enhancing NSGA-II Algorithm through Hybrid Strategy for Optimizing Maize Water and Fertilizer Irrigation Simulation. Symmetry 2024, 16, 1062. https://doi.org/10.3390/sym16081062
Du J, Liu R, Cheng D, Wang X, Zhang T, Yu F. Enhancing NSGA-II Algorithm through Hybrid Strategy for Optimizing Maize Water and Fertilizer Irrigation Simulation. Symmetry. 2024; 16(8):1062. https://doi.org/10.3390/sym16081062
Chicago/Turabian StyleDu, Jinyang, Renyun Liu, Du Cheng, Xu Wang, Tong Zhang, and Fanhua Yu. 2024. "Enhancing NSGA-II Algorithm through Hybrid Strategy for Optimizing Maize Water and Fertilizer Irrigation Simulation" Symmetry 16, no. 8: 1062. https://doi.org/10.3390/sym16081062