Multi-Reservoir Flood Control Operation Using Improved Bald Eagle Search Algorithm with ε Constraint Method (original) (raw)

Abstract

The reservoir flood control operation problem has the characteristics of multiconstraint, high-dimension, nonlinearity, and being difficult to solve. In order to better solve this problem, this paper proposes an improved bald eagle search algorithm (CABES) coupled with ε-constraint method (ε-CABES). In order to test the performance of the CABES algorithm, a typical test function is used to simulate and verify CABES. The results are compared with the bald eagle algorithm and particle swarm optimization algorithm to verify its superiority. In order to further test the rationality and effectiveness of the CABES method, two single reservoirs and a multi-reservoir system are selected for flood control operation, and the ε constraint method and the penalty function method (CF-CABES) are compared, respectively. Results show that peak clipping rates of ε-CABES and CF-CABES are both 60.28% for Shafan Reservoir and 52.03% for Dahuofang Reservoir, respectively. When solving the multi-reservoir joint flood control operation system, only ε-CABES flood control operation is successful, and the peak clipping rate is 51.76%. Therefore, in the single-reservoir flood control operation, the penalty function method and the ε constraint method have similar effects. However, in multi-reservoir operation, the ε constraint method is better than the penalty function method. In summary, the ε-CABES algorithm is more reliable and effective, which provides a new method for solving the joint flood control scheduling problem of large reservoirs.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (59)

  1. Table 7. Comparison of operation results of different algorithms for Dahuofang Reservoir. Algorithm ε-CABES ε-BES CF-CABES CF-BES 30,737,530.83 30,737,888.76 30,737,530.88 30,737,817.37 30,737,532.02 30,737,871.90 30,737,532.03 30,737,731.38 30,737,531.31 30,737,852.62 30,737,530.82 30,737,731.27 30,737,532.18 30,737,577.04 30,737,530.95 30,737,782.44 30,737,531.09 30,738,027.34 30,737,537.61 30,774,732.07 30,737,530.96 30,737,649.03 30,737,530.90 30,737,576.15 30,737,530.85 30,738,846.39 30,737,531.89 30,737,736.26 30,737,533.62 30,738,133.48 30,737,531.25 30,737,633.93 30,737,530.95 30,737,944.77 30,737,530.82 30,737,844.28 30,737,531.10 30,737,641.22 30,737,531.16 30,737,681.17
  2. Table 8. Operation results of reservoirs in Luanhe River Basin using different methods. Algorithm ε-CABES 1,176,703,090.13 1,177,927,824.01 1,176,640,533.05 1,175,832,077.13 1,177,365,505.25 1,177,167,086.15 1,177,890,549.69 1,176,890,264.34 1,177,026,241.21 1,182,787,126.17
  3. Minimum 1,175,832,077.13
  4. Mean 1,177,623,029.71
  5. Median 1,177,096,663.68
  6. Maximum 1,182,787,126.17 Standard deviation 1,175,832,077.13 Iteration duration (s)
  7. Blöschl, G.; Hall, J.; Viglione, A.; Perdigão, R.A.P.; Parajka, J.; Merz, B.; Lun, D.; Arheimer, B.; Aronica, G.T.; Bilibashi, A.; et al. Changing climate both increases and decreases European river floods. Nature 2019, 573, 108-111. https://doi.org/10.1038/s41586- 019-1495-6.
  8. Iyakaremye, V.; Zeng, G.; Yang, X.; Zhang, G.; Ullah, I.; Gahigi, A.; Vuguziga, F.; Asfaw, T.G.; Ayugi, B. Increased high- temperature extremes and associated population exposure in Africa by the mid-21st century. Sci. Total Environ. 2021, 790, 148162. https://doi.org/10.1016/j.scitotenv.2021.148162.
  9. Sein, Z.M.M.; Zhi, X.; Ullah, I.; Azam, K.; Ngoma, H.; Saleem, F.; Xing, Y.; Iyakaremye, V.; Syed, S.; Hina, S.; et al. Recent variability of sub-seasonal monsoon precipitation and its potential drivers in Myanmar using in-situ observation during 1981- 2020. Int. J. Climatol. 2022, 42, 3341-3359. https://doi.org/10.1002/joc.7419.
  10. Xing, Y.; Shao, D.; Liang, Q.; Chen, H.; Ma, X.; Ullah, I. Investigation of the drainage loss effects with a street view based drainage calculation method in hydrodynamic modelling of pluvial floods in urbanized area. J. Hydrol. 2022, 605, 127365. https://doi.org/10.1016/j.jhydrol.2021.127365.
  11. Kundzewicz, Z.W.; Su, B.; Wang, Y.; Xia, J.; Huang, J.; Jiang, T. Flood risk and its reduction in China. Adv. Water Resour. 2019, 130, 37-45. https://doi.org/10.1016/j.advwatres.2019.05.020.
  12. Rahimi, H.; Ardakani, M.K.; Ahmadian, M.; Tang, X. Multi-Reservoir Utilization Planning to Optimize Hydropower Energy and Flood Control Simultaneously. Environ. Process. 2020, 7, 41-52. https://doi.org/10.1007/s40710-019-00404-8.
  13. Zhu, F.; Zhong, P.-a.; Sun, Y.; Xu, B. Selection of criteria for multi-criteria decision making of reservoir flood control operation. J. Hydroinform. 2017, 19, 558-571. https://doi.org/10.2166/hydro.2017.059.
  14. Yakowitz, S. Dynamic programming applications in water resources. Water Resour. Res. 1982, 18, 673-696. https://doi.org/10.1029/WR018i004p00673.
  15. Barros Mario, T.L.; Tsai Frank, T.C.; Yang, S.-l.; Lopes Joao, E.G.; Yeh William, W.G. Optimization of Large-Scale Hydropower System Operations. J. Water Resour. Plan. Manag. 2003, 129, 178-188. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(178).
  16. Unver, O.I.; Mays, L.W. Model for real-time optimal flood control operation of a reservoir system. Water Resour. Manag. 1990, 4, 21-46. https://doi.org/10.1007/BF00429923.
  17. Bai, T.; Wu, L.; Chang, J.-x.; Huang, Q. Multi-Objective Optimal Operation Model of Cascade Reservoirs and Its Application on Water and Sediment Regulation. Water Resour. Manag. 2015, 29, 2751-2770. https://doi.org/10.1007/s11269-015-0968-0.
  18. Zhang, W.; Liu, P.; Chen, X.; Wang, L.; Ai, X.; Feng, M.; Liu, D.; Liu, Y. Optimal Operation of Multi-reservoir Systems Considering Time-lags of Flood Routing. Water Resour. Manag. 2016, 30, 523-540. https://doi.org/10.1007/s11269-015-1175-8.
  19. Li, J.; Zhong, P.A.; Yang, M.; Zhu, F.; Chen, J.; Xu, B.; Liu, W. Dynamic and Intelligent Modeling Methods for Joint Operation of a Flood Control System. J. Water Resour. Plan. Manag. 2019, 145, 04019044.
  20. Chen, H.-t.; Wang, W.-c.; Chen, X.-n.; Qiu, L. Multi-objective reservoir operation using particle swarm optimization with adaptive random inertia weights. Water Sci. Eng. 2020, 13, 136-144. https://doi.org/10.1016/j.wse.2020.06.005.
  21. SeethaRam, K.V. Three Level Rule Curve for Optimum Operation of a Multipurpose Reservoir using Genetic Algorithms. Water Resour. Manag. 2021, 35, 353-368. https://doi.org/10.1007/s11269-020-02738-7.
  22. Xu, Y.; Mei, Y. A modified water cycle algorithm for long-term multi-reservoir optimization. Appl. Soft Comput. 2018, 71, 317- 332. https://doi.org/10.1016/j.asoc.2018.06.031.
  23. Chen, H.-t.; Wang, W.-c.; Chau, K.-w.; Xu, L.; He, J. Flood Control Operation of Reservoir Group Using Yin-Yang Firefly Algorithm. Water Resour. Manag. 2021, 35, 5325-5345. https://doi.org/10.1007/s11269-021-03005-z.
  24. Chang, L.-C. Guiding rational reservoir flood operation using penalty-type genetic algorithm. J. Hydrol. 2008, 354, 65-74. https://doi.org/10.1016/j.jhydrol.2008.02.021.
  25. He, Y.; Xu, Q.; Yang, S.; Liao, L. Reservoir flood control operation based on chaotic particle swarm optimization algorithm. Appl. Math. Model. 2014, 38, 4480-4492. https://doi.org/10.1016/j.apm.2014.02.030.
  26. Kumar Jha, D.; Yorino, N.; Zoka, Y.; Sasaki, Y.; Hayashi, Y.; Iwata, K.; Oe, R. Incorporating Penalty Function to Reduce Spill in Stochastic Dynamic Programming Based Reservoir Operation of Hydropower Plants. IEEJ Trans. Electr. Electron. Eng. 2010, 5, 531-538. https://doi.org/10.1002/tee.20569.
  27. Moeini, R.; Soltani-nezhad, M.; Daei, M. Constrained gravitational search algorithm for large scale reservoir operation optimization problem. Eng. Appl. Artif. Intell. 2017, 62, 222-233. https://doi.org/10.1016/j.engappai.2017.04.012.
  28. Ngoc, T.A.; Hiramatsu, K.; Harada, M. Optimizing the rule curves of multi-use reservoir operation using a genetic algorithm with a penalty strategy. Paddy Water Environ. 2014, 12, 125-137. https://doi.org/10.1007/s10333-013-0366-2.
  29. Wang, W.; Jia, B.; Simonovic, S.P.; Wu, S.; Fan, Z.; Ren, L. Comparison of Representative Heuristic Algorithms for Multi- Objective Reservoir Optimal Operation. Water Resour. Manag. 2021, 35, 2741-2762. https://doi.org/10.1007/s11269-021-02864-w.
  30. Takahama, T.; Sakai, S. Constrained Optimization by ε Constrained Differential Evolution with Dynamic ε-Level Control. In Advances in Differential Evolution, Chakraborty, U.K., Ed.; Springer: Berlin/Heidelberg, Germany, 2008. https://doi.org/10.1007/978-3-540-68830-3\_5pp. 139-154.
  31. Chen, C.; Yuan, Y.; Yuan, X. An Improved NSGA-III Algorithm for Reservoir Flood Control Operation. Water Resour. Manag. 2017, 31, 4469-4483. https://doi.org/10.1007/s11269-017-1759-6.
  32. Stanovov, V.; Akhmedova, S.; Semenkin, E. Combined fitness-violation epsilon constraint handling for differential evolution. Soft Comput. 2020, 24, 7063-7079. https://doi.org/10.1007/s00500-020-04835-6.
  33. Zhou, J.; Zou, J.; Zheng, J.; Yang, S.; Gong, D.; Pei, T. An infeasible solutions diversity maintenance epsilon constraint handling method for evolutionary constrained multiobjective optimization. Soft Comput. 2021, 25, 8051-8062. https://doi.org/10.1007/s00500-021-05880-5.
  34. Alsattar, H.A.; Zaidan, A.A.; Zaidan, B.B. Novel meta-heuristic bald eagle search optimisation algorithm. Artif. Intell. Rev. 2020, 53, 2237-2264. https://doi.org/10.1007/s10462-019-09732-5.
  35. Alsaidan, I.; Shaheen, M.A.M.; Hasanien, H.M.; Alaraj, M.; Alnafisah, A.S. A PEMFC model optimization using the enhanced bald eagle algorithm. Ain Shams Eng. J. 2022, 13, 101749. https://doi.org/10.1016/j.asej.2022.101749.
  36. Angayarkanni, S.A.; Sivakumar, R.; Ramana Rao, Y.V. RETRACTED ARTICLE: Hybrid Grey Wolf: Bald Eagle search optimized support vector regression for traffic flow forecasting. J. Ambient Intell. Humaniz. Comput. 2021, 12, 1293-1304. https://doi.org/10.1007/s12652-020-02182-w.
  37. Eid, A.; Kamel, S.; Zawbaa, H.M.; Dardeer, M. Improvement of active distribution systems with high penetration capacities of shunt reactive compensators and distributed generators using Bald Eagle Search. Ain Shams Eng. J. 2022, 13, 101792. https://doi.org/10.1016/j.asej.2022.101792.
  38. Ferahtia, S.; Rezk, H.; Abdelkareem, M.A.; Olabi, A.G. Optimal techno-economic energy management strategy for building's microgrids based bald eagle search optimization algorithm. Appl. Energy 2022, 306, 118069. https://doi.org/10.1016/j.apenergy.2021.118069.
  39. Sayed, G.I.; Soliman, M.M.; Hassanien, A.E. A novel melanoma prediction model for imbalanced data using optimized SqueezeNet by bald eagle search optimization. Comput. Biol. Med. 2021, 136, 104712. https://doi.org/10.1016/j.compbiomed.2021.104712.
  40. Wang, W.-c.; Xu, L.; Chau, K.-w.; Xu, D.-m. Yin-Yang firefly algorithm based on dimensionally Cauchy mutation. Expert Syst. Appl. 2020, 150, 113216. https://doi.org/10.1016/j.eswa.2020.113216.
  41. Zhao, S.; Wang, P.; Heidari, A.A.; Zhao, X.; Ma, C.; Chen, H. An enhanced Cauchy mutation grasshopper optimization with trigonometric substitution: Engineering design and feature selection. Eng. Comput. 2021, 38, 4583-4616. https://doi.org/10.1007/s00366-021-01448-x.
  42. Miao, F.; Yao, L.; Zhao, X. Symbiotic organisms search algorithm using random walk and adaptive Cauchy mutation on the feature selection of sleep staging. Expert Syst. Appl. 2021, 176, 114887. https://doi.org/10.1016/j.eswa.2021.114887.
  43. Zhao, X.; Fang, Y.; Liu, L.; Xu, M.; Li, Q. A covariance-based Moth-flame optimization algorithm with Cauchy mutation for solving numerical optimization problems. Appl. Soft Comput. 2022, 119, 108538. https://doi.org/10.1016/j.asoc.2022.108538.
  44. Wu, Q. Hybrid forecasting model based on support vector machine and particle swarm optimization with adaptive and Cauchy mutation. Expert Syst. Appl. 2011, 38, 9070-9075. https://doi.org/10.1016/j.eswa.2010.11.093.
  45. Nickabadi, A.; Ebadzadeh, M.M.; Safabakhsh, R. A novel particle swarm optimization algorithm with adaptive inertia weight. Appl. Soft Comput. 2011, 11, 3658-3670. https://doi.org/10.1016/j.asoc.2011.01.037.
  46. Rauf, H.T.; Malik, S.; Shoaib, U.; Irfan, M.N.; Lali, M.I. Adaptive inertia weight Bat algorithm with Sugeno-Function fuzzy search. Appl. Soft Comput. 2020, 90, 106159. https://doi.org/10.1016/j.asoc.2020.106159.
  47. Shukla, A.K.; Singh, P.; Vardhan, M. An adaptive inertia weight teaching-learning-based optimization algorithm and its applications. Appl. Math. Model. 2020, 77, 309-326. https://doi.org/10.1016/j.apm.2019.07.046.
  48. Sun, Y.; Wang, X.; Chen, Y.; Liu, Z. A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst. Appl. 2018, 114, 563-577. https://doi.org/10.1016/j.eswa.2018.08.027.
  49. Khalilpourazari, S.; Khalilpourazary, S. An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Comput. 2019, 23, 1699-1722. https://doi.org/10.1007/s00500-017-2894-y.
  50. Wang, W.-C.; Xu, L.; Chau, K.-W.; Liu, C.-J.; Ma, Q.; Xu, D.-M. Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems. Expert Syst. Appl. 2023, 211, 118644. https://doi.org/10.1016/j.eswa.2022.118644.
  51. Seyyedabbasi, A. WOASCALF: A new hybrid whale optimization algorithm based on sine cosine algorithm and levy flight to solve global optimization problems. Adv. Eng. Softw. 2022, 173, 103272. https://doi.org/10.1016/j.advengsoft.2022.103272.
  52. He, Q.; Lin, J.; Xu, H. Hybrid Cauchy mutation and uniform distribution of grasshopper optimization algorithm. Control Decis. 2021, 36, 1558-1568. https://doi.org/10.13195/j.kzyjc.2019.1609.
  53. Wu, G.; Mallipeddi, R.; Suganthan, P. Problem Definitions and Evaluation Criteria for the CEC 2017 Competition and Special Session on Constrained Single Objective Real-Parameter Optimization; Technical Report; National University of Defense Technology, Changsha, Hunan, PR China and Kyungpook National University, Daegu, South Korea and Nanyang Technological University: Singapore, 2016.
  54. Zheng, Y.; Meng, Z.; Shen, R. An M-Objective Penalty Function Algorithm Under Big Penalty Parameters. J. Syst. Sci. Complex. 2016, 29, 455-471. https://doi.org/10.1007/s11424-015-3204-3.
  55. Tessema, B.; Yen, G.G. An Adaptive Penalty Formulation for Constrained Evolutionary Optimization. IEEE Trans. Syst. Man Cybern. -Part A: Syst. Hum. 2009, 39, 565-578. https://doi.org/10.1109/TSMCA.2009.2013333.
  56. Diao, Y.; Ma, H.; Wang, H.; Wang, J.; Li, S.; Li, X.; Pan, J.; Qiu, Q. Optimal Flood-Control Operation of Cascade Reservoirs Using an Improved Particle Swarm Optimization Algorithm. Water 2022, 14, 1239.
  57. Ferahtia, S.; Rezk, H.; Djerioui, A.; Houari, A.; Motahhir, S.; Zeghlache, S. Modified bald eagle search algorithm for lithium-ion battery model parameters extraction. ISA Trans. 2022; in press. https://doi.org/10.1016/j.isatra.2022.08.025.
  58. Ma, L.; Zhang, T.; Li, Q.; Wang, T. Spatial distribution, risk assessment, and source identification of the potentially toxic elements in the water-level fluctuation zone of the Dahuofang Reservoir, Northeast China. Environ. Monit. Assess. 2021, 193, 454. https://doi.org/10.1007/s10661-021-09237-1.
  59. Disclaimer/Publisher's Note: The statements, opinions and data contained in all publications are solely those of the individual au- thor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.