Optimizing Multiple Linear Rules for Multi-Reservoir Hydropower Systems Using an Optimization Method with an Adaptation Strategy

  • Iman AhmadianfarEmail author
  • Omid Bozorg-Haddad
  • Xuefeng Chu


Water resources crisis has a significant impact on hydropower energy production, which highlights the importance of water resources management. Reservoirs are effective and powerful systems to manage water resources. Due to the growing water demands and the limited water resources, optimizing these systems to maximize the production of hydropower energy is an essential task. In this study, an effective differential evolution (DE) algorithm with mutation strategy adaptation (MSA-DE) is developed to promote the local and global search capabilities in a feasible domain. In addition, an elitist strategy is applied to escape local optimum trap. In the present study, the MSA-DE algorithm was applied to optimize the multiple linear rules for two multi-reservoir operation systems (3- and 4-reservoir systems) in Iran. In the 3-reservoir system, the best objective function value in 10 runs was 123.57 for the MSA-DE, while the corresponding values for the DE, artificial bee colony (ABC), and genetic algorithm (GA) were 126.42, 147.38, and 126.68, respectively. For the 4-reservoir system, the best objective function values for the MSA-DE, DE, ABC, and GA were 130.50, 159.75, 174.41, and 140.63, respectively. The results demonstrated that the MSA-DE algorithm can be used to derive optimal operating rules for multi-reservoir systems by enhancing appropriate solutions, while it still preserves the accuracy and efficiency of the solutions.


Multi-reservoir hydropower system Multiple linear rule Differential evolution Adaptation strategy Optimization 


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Conflict of Interest



  1. Afshar A, Emami Skardi MJ, Masoumi F (2015) Optimizing water supply and hydropower reservoir operation rule curves: an imperialist competitive algorithm approach. Eng Optim 47:1208–1225CrossRefGoogle Scholar
  2. Ahmadi Najl A, Haghighi A, Mohammadvali-Samani H (2016) Simultaneous optimization of operating rules and rule curves for multireservoir systems using a self-adaptive simulation-GA model. J Water Resour Plan Manag 142:04016041CrossRefGoogle Scholar
  3. Ahmadianfar I, Adib A, Salarijazi M (2015) Optimizing multireservoir operation: Hybrid of bat algorithm and differential evolution. J Water Resour Plan Manag 142:05015010CrossRefGoogle Scholar
  4. Barros MT, Tsai FT, Yang S-L, Lopes JE, Yeh WW (2003) Optimization of large-scale hydropower system operations. J Water Resour Plan Manag 129:178–188CrossRefGoogle Scholar
  5. Bellman R (1954) The theory of dynamic programming. RAND Corp, Santa MonicaCrossRefGoogle Scholar
  6. Bozorg-Haddad O, Afshar A, Mariño MA (2008) Design-operation of multi-hydropower reservoirs: HBMO approach. Water Resour Manag 22:1709–1722CrossRefGoogle Scholar
  7. Bozorg-Haddad O, Hosseini-Moghari S-M, Loáiciga HA (2015) Biogeography-based optimization algorithm for optimal operation of reservoir systems. J Water Resour Plan Manag 142:04015034CrossRefGoogle Scholar
  8. Bozorg-Haddad O, Janbaz M, Loáiciga HA (2016) Application of the gravity search algorithm to multi-reservoir operation optimization. Adv Water Resour 98:173–185CrossRefGoogle Scholar
  9. Cervellera C, Chen VC, Wen A (2006) Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization. Eur J Oper Res 171:1139–1151CrossRefGoogle Scholar
  10. Dai C, Cai Y, Lu W, Liu H, Guo H (2016) Conjunctive water use optimization for watershed-Lake water distribution system under uncertainty: a case study. Water Resour Manag 30:4429–4449CrossRefGoogle Scholar
  11. Ehteram M, Karami H, Mousavi SF, Farzin S, Celeste AB, Shafie A-E (2018) Reservoir operation by a new evolutionary algorithm: Kidney algorithm. Water Resour Manag 32:4681–4706CrossRefGoogle Scholar
  12. Fan H-Y, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129CrossRefGoogle Scholar
  13. Hakimi-Asiabar M, Seyyed HG, Reza K (2010) Deriving operating policies for multi-objective reservoir systems: application of self-learning genetic algorithm. Applied Soft Computing 10.4(2010):1151–1163CrossRefGoogle Scholar
  14. He D, Wang F, Mao Z (2008) A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect. Int J Electr Power Energy Syst 30:31–38CrossRefGoogle Scholar
  15. Hınçal O, Altan-Sakarya AB, Ger AM (2011) Optimization of multireservoir systems by genetic algorithm. Water Resour Manag 25:1465–1487CrossRefGoogle Scholar
  16. Holland JH (1992) Genetic algorithms. Sci Am 267:66–73CrossRefGoogle Scholar
  17. Hossain MS, El-Shafie A (2013) Intelligent systems in optimizing reservoir operation policy: a review. Water Resour Manag 27:3387–3407CrossRefGoogle Scholar
  18. Jabr RA, Coonick AH, Cory BJ (2000) A homogeneous linear programming algorithm for the security constrained economic dispatch problem. IEEE Trans Power Syst 15:930–936CrossRefGoogle Scholar
  19. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471CrossRefGoogle Scholar
  20. Karamouz M, Houck MH, Delleur JW (1992) Optimization and simulation of multiple reservoir systems. J Water Resour Plan Manag 118:71–81CrossRefGoogle Scholar
  21. Lin C, Qing A, Feng Q (2011) A comparative study of crossover in differential evolution. J Heuristics 17:675–703CrossRefGoogle Scholar
  22. Moravej M, Hosseini-Moghari S-M (2016) Large scale reservoirs system operation optimization: the interior search algorithm (ISA) approach. Water Resour Manag 30:3389–3407CrossRefGoogle Scholar
  23. Pandit M, Srivastava L, Pal K (2013) Static/dynamic optimal dispatch of energy and reserve using recurrent differential evolution. IET Gener Transm Distrib 7:1401–1414CrossRefGoogle Scholar
  24. Puterman ML (1994) Markov Decision Processes. J. Wiley and Sons, HobokenCrossRefGoogle Scholar
  25. Samadi-koucheksaraee, A., Ahmadianfar, I., Bozorg-Haddad, O., & Asghari-pari, S. A. (2019). Gradient Evolution Optimization Algorithm to Optimize Reservoir Operation Systems. Water resources management, 33, 603-625Google Scholar
  26. Sayah S, Zehar K (2008) Modified differential evolution algorithm for optimal power flow with non-smooth cost functions. Energy Convers Manag 49:3036–3042CrossRefGoogle Scholar
  27. Sharif M, Wardlaw R (2000) Multireservoir systems optimization using genetic algorithms: case study. J Comput Civ EngGoogle Scholar
  28. Storn R, Price K (1995) Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. ICSI Berkeley, BerkeleyGoogle Scholar
  29. Taghian M, Ahmadianfar I (2018) Maximizing the Firm Energy Yield Preserving Total Energy Generation Via an Optimal Reservoir Operation. Water Resour Manag 32:141–154CrossRefGoogle Scholar
  30. Takriti S, Krasenbrink B (1999) A decomposition approach for the fuel-constrained economic power-dispatch problem. Eur J Oper Res 112:460–466CrossRefGoogle Scholar
  31. Xin B, Chen J, Zhang J, Fang H, Peng Z-H (2012) Hybridizing differential evolution and particle swarm optimization to design powerful optimizers: a review and taxonomy. IEEE Transactions on Systems, Man, and Cybernetics. Part C (Applications and Reviews) 42:744–767Google Scholar
  32. Yang Z, Liu P, Cheng L, Wang H, Ming B, Gong W (2018) Deriving operating rules for a large-scale hydro-photovoltaic power system using implicit stochastic optimization. J Clean ProdGoogle Scholar
  33. Yazdi J, Moridi A (2018) Multi-Objective Differential Evolution for Design of Cascade Hydropower Reservoir Systems. Water Resour Manag 32:4779–4791CrossRefGoogle Scholar
  34. Yeh WWG (1985) Reservoir management and operations models: A state-of-the-art review. Water Resour Res 21:1797–1818CrossRefGoogle Scholar
  35. Zhang R, Zhou J, Ouyang S, Wang X, Zhang H (2013) Optimal operation of multi-reservoir system by multi-elite guide particle swarm optimization. Int J Electr Power Energy Syst 48:58–68CrossRefGoogle Scholar
  36. Zhao T, Zhao J, Yang D (2012) Improved dynamic programming for hydropower reservoir operation. J Water Resour Plan Manag 140:365–374CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringBehbahan Khatam Alanbia University of TechnologyBehbahanIran
  2. 2.Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural ResourcesUniversity of TehranTehranIran
  3. 3.Department of Civil & Environmental EngineeringNorth Dakota State UniversityFargoUSA

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