A New Multi-Objective Genetic Programming Model for Meteorological Drought Forecasting
Abstract
:1. Introduction
2. Study Area and Data Collection
3. Methods
3.1. The Standardized Precipitation Index
3.2. Overview of GP and MGGP
3.3. State-of-the-Art MOMGGP Algorithm
3.4. Performance Evaluation
4. Results and Discussion
The Best GP, MGGP, and MOMGGP Solutions
- RMSE was applied as the objective function in both tools. The smaller the RMSE, the better the forecasting accuracy;
- arithmetic operations (+, −, ×, and /), exponential function (Exp), three argument addition multiplication, square, and trigonometric functions (including sin and cos) with the same selection probability were used as arbitrary functions;
- SPI lags (from lag 1 to lag 12) together with a set of random numbers in the range of −10 to 10 were used in the terminal set;
- the maximum tree depth for GP and MGGP solution was set to nine and four, respectively;
- the maximum number of genes for MGGP solution was set to five,
- ramped half and half initialization of individuals with the population size of 300 at each run were used;
- the run is configured to proceed for 500 generations or to terminate when a fitness (RMSE) of 0.002 is achieved.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Station | Dataset | Mean | Min | Max | SD * |
---|---|---|---|---|---|
Burdur | Entire | 0.00 | −2.91 | 2.65 | 1.005 |
Training | 0.02 | −2.91 | 2.65 | 0.987 | |
Testing | −0.04 | −2.58 | 2.20 | 1.046 |
State | Threshold |
---|---|
No drought | 0.0 ≤ SPI |
Mild drought | −1.0 ≤ SPI ≤ 0.0 |
Moderate drought | −1.5 ≤ SPI < −1.0 |
Severe drought | −2.0 ≤ SPI < −1.5 |
Extreme drought | SPI < −2.0 |
Training | Testing | ||||
---|---|---|---|---|---|
Models | Complexity | RMSE | NSE | RMSE | NSE |
GP | 190 | 0.550 | 0.689 | 0.548 | 0.726 |
MGGP | 195 | 0.504 | 0.740 | 0.555 | 0.717 |
MOGGP | 128 | 0.522 | 0.721 | 0.542 | 0.731 |
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Reihanifar, M.; Danandeh Mehr, A.; Tur, R.; Ahmed, A.T.; Abualigah, L.; Dąbrowska, D. A New Multi-Objective Genetic Programming Model for Meteorological Drought Forecasting. Water 2023, 15, 3602. https://doi.org/10.3390/w15203602
Reihanifar M, Danandeh Mehr A, Tur R, Ahmed AT, Abualigah L, Dąbrowska D. A New Multi-Objective Genetic Programming Model for Meteorological Drought Forecasting. Water. 2023; 15(20):3602. https://doi.org/10.3390/w15203602
Chicago/Turabian StyleReihanifar, Masoud, Ali Danandeh Mehr, Rifat Tur, Abdelkader T. Ahmed, Laith Abualigah, and Dominika Dąbrowska. 2023. "A New Multi-Objective Genetic Programming Model for Meteorological Drought Forecasting" Water 15, no. 20: 3602. https://doi.org/10.3390/w15203602