Water Resources Management

, Volume 24, Issue 11, pp 2527–2552 | Cite as

Robust Methods for Identifying Optimal Reservoir Operation Strategies Using Deterministic and Stochastic Formulations



Water allocation in a competing environment is a major social and economic challenge especially in water stressed semi-arid regions. In developing countries the end users are represented by the water sectors in most parts and conflict over water is resolved at the agency level. In this paper, two reservoir operation optimization models for water allocation to different users are presented. The objective functions of both models are based on the Nash Bargaining Theory which can incorporate the utility functions of the water users and the stakeholders as well as their relative authorities on the water allocation process. The first model is called GA–KNN (Genetic Algorithm–K Nearest Neighborhood) optimization model. In this model, in order to expedite the convergence process of GA, a KNN scheme for estimating initial solutions is used. Also KNN is utilized to develop the operating rules in each month based on the derived optimization results. The second model is called the Bayesian Stochastic GA (BSGA) optimization model. This model considers the joint probability distribution of inflow and its forecast to the reservoir. In this way, the intrinsic and forecast uncertainties of inflow to the reservoir are incorporated. In order to test the proposed models, they are applied to the Satarkhan reservoir system in the north-western part of Iran. The models have unique features in incorporating uncertainties, facilitating the convergence process of GA, and handling finer state variable discretization and utilizing reliability based utility functions for water user sectors. They are compared with the alternative models. Comparisons show the significant value of the proposed models in reservoir operation and supplying the demands of different water users.


Reservoir operation Optimization model Genetic Algorithm Bayesian Decision Theory Inflow uncertainty Water allocation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Araghinejad S, Burn DH, Karamouz M (2006) Long-lead probabilistic forecasting of streamflow using ocean-atmospheric and hydrological predictors. Water Resour Res 42:1–11. doi: 10.1029/2004WR003853 CrossRefGoogle Scholar
  2. Bannayan M, Hoogenboom G (2008) Predicting realization of daily weather data for climate forecasts using the non-parametric nearest-neighbor re-sampling technique. Int J Climatol 28(10):1357–1368. doi: 10.1002/joc.1637 CrossRefGoogle Scholar
  3. Burn DH, Yulianti S (2001) Waste-load allocation using genetic algorithms. J Water Res Plan Manage 127(2):121–129. doi: 10.1061/(ASCE)0733-9496(2001)127:2(121) CrossRefGoogle Scholar
  4. Celeste AB, Suzuki K, Kadota A (2008) Integrating long- and short-term reservoir operation models via stochastic and deterministic optimization: case study in Japan. J Water Res Plan Manage 134(5):440–448CrossRefGoogle Scholar
  5. Chang F, Hui S, Chen Y (2002) Reservoir operation using grey fuzzy stochastic dynamic programming. Hydrol Processes 16(12):2395–2408CrossRefGoogle Scholar
  6. East V, Hall MJ (1994) Water resources system optimization using genetic algorithms. In: 1st int. conf. on hydroinformatics, Balkema, Rotterdam, The Netherlands, pp 225–231Google Scholar
  7. Eiger G, Shamir U (1991) Optimal operation f reservoirs by stochastic programming. Eng Opt 17:293–312CrossRefGoogle Scholar
  8. Galeati G (1990) A comparison of parametric and non-parametric methods for runoff forecasting. Hydrol Sci J 35(1):79–94CrossRefGoogle Scholar
  9. Ganji A, Khalili D, Karamouz M, Ponnambalam K, Javan M (2007) A fuzzy stochastic dynamic nash game analysis of policies for managing water allocation in a reservoir system. Water Resour Manage 22:51–66CrossRefGoogle Scholar
  10. Gen MR, Chang L (2000) Genetic algorithm and engineering optimization. Chichester: WileyGoogle Scholar
  11. Harsanyi JC, Selten R (1972) A generalized Nash solution for two-person bargaining games with incomplete information. Manage Sci 18:80–106CrossRefGoogle Scholar
  12. Hashimoto TJ, Stedinger R, Loucks DP (1982) Reliability, resiliency, and vulnerability criteria for water resources performance evaluation. Water Resour Res 18(1):14–20CrossRefGoogle Scholar
  13. Herrera F, Lozano M (2003) Fuzzy adaptive genetic algorithms: design, taxonomy, and future directions. Soft Comput 7(8):545–562. doi: 10.1007/s00500-002-0238-y Google Scholar
  14. Karamouz M, Houck M (1987) Comparison of stochastic and deterministic dynamic programming for reservoir operating rule generation. Water Resour Bull 23(1):1–9Google Scholar
  15. Karamouz M, Mousavi SJ (2003) Uncertainty based operation of large scale reservoir systems: Dez and Karoon experience. J Am Water Resour Assoc 39(4):961–975CrossRefGoogle Scholar
  16. Karamouz M, Vasiliadis HV (1992) Bayesian stochastic optimization of reservoir operation using uncertain forecasts. Water Resour Res 28(5):1221–1232CrossRefGoogle Scholar
  17. Karamouz M, Szidarovszky F, Zahraie B (2003) Water resources systems analysis. Lewis, Boca RatonGoogle Scholar
  18. Karamouz M, Ahmadi A, Moridi A (2009) Probabilistic reservoir operation using Bayesian stochastic model and support vector machine. Adv Water Res 32:1588–1600. doi: 10.1016/j.advwatres.2009.08.003 CrossRefGoogle Scholar
  19. Karlsson M, Yakowitz S (1987) Nearest-neighbor methods for nonparametric rainfall-runoff forecasting. Water Resour Res 23(7):1300–1308CrossRefGoogle Scholar
  20. Kelman J, Stedinger JR, Cooper LA, Hsu E, Yuan SQ (1990) Sampling stochastic dynamic programming applied to reservoir operation. Water Resour Res 26(3):447–454CrossRefGoogle Scholar
  21. Kember G, Flower AC (1993) Forecasting river flow using nonlinear dynamics, stochastic. Stoch Hydrol Hydraul 7:205–212CrossRefGoogle Scholar
  22. Kerachian R, Karamouz M (2006) Optimal reservoir operation considering the water quality issues: a stochastic conflict resolution approach. Water Resour Res 42:1–17. doi: 10.1029/2005WR004575 CrossRefGoogle Scholar
  23. Lall U, Sharma A (1996) A nearest neighbor bootstrap for resampling hydrologic time series. Water Resour Res 32(3):679–693CrossRefGoogle Scholar
  24. Mei-yi L, Zi-xing C, Guo-yun S (2004) An adaptive genetic algorithm with diversity-guided mutation and its global convergence property. J Cent South Univ Technol 11(3):323–327. doi: 10.1007/s11771-004-0066-6 CrossRefGoogle Scholar
  25. Michalewicz Z (1992) Genetic algorithms data structures evolutionary programs. Springer, New YorkGoogle Scholar
  26. Nash JF (1950) The bargaining problem. Econometrica 18:155–162CrossRefGoogle Scholar
  27. Ostfeld A, Salomons S (2005) Hybrid genetic-instance based learning algorithm for CE-QUAL-W2 calibration. J Hydrol 310:122–142. doi: 10.1016/j.jhydrol.2004.12.004 CrossRefGoogle Scholar
  28. Pelikan M, Goldberg DE, Cantu-Paz E (2000) Linkage problem, distribution estimation, and Bayesian networks. Evol Comput 8(3):311–340CrossRefGoogle Scholar
  29. Richards A, Singh N (1997) Two level negotiations in bargaining over water, Game Theoretical Applications to Economics and Operations Research. Kluwer, BostonGoogle Scholar
  30. Seifi A, Hipel KW (2001) Interior-point method for reservoir operation with stochastic inflows. J Water Res Plan Manage 127(1):48–57. doi: 10.1061/(ASCE)0733–9496(2001)127:1(48) CrossRefGoogle Scholar
  31. Srinivas M, Patnaik LM (1994) Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans Syst Man Cybern 24(4):656–667CrossRefGoogle Scholar
  32. Stedinger JR, Sule BF, Loucks DP (1984) Stochastic dynamic programming models for reservoir operation optimization. Water Resour Res 20(11):1499–1505CrossRefGoogle Scholar
  33. Teegavarapu RSV, Simonovic SP (2001) Optimal operation of water resource systems: trade-offs between modeling and practical solutions. Integr Water Resour Manage, IAHS Red Book, 272, IAHS, pp 257–263Google Scholar
  34. Todini E (2000) Real-time flood forecasting: operational experience and recent advanced. In: Marsalek J et al (eds) Flood issues in contemporary water management. Kluwer, Dordrecht, pp 261–270Google Scholar
  35. Trezos T, Yeh WW-G (1987) Use of stochastic dynamic programming for reservoir management. Water Resour Res 23(6):983–996CrossRefGoogle Scholar
  36. Varian HR (1995) Coase, competition, and compensation. Japan World Econ 7(1):13–27CrossRefGoogle Scholar
  37. Wardlaw R, Sharif M (1999) Evaluation of genetic algorithms for optimal reservoir system operation. J Water Res Plan Manage 125(1):25–33CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Civil EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.School of Civil EngineeringUniversity of TehranTehranIran
  3. 3.Polytechnic Institute of NYUBrooklynUSA
  4. 4.Water Engineering Research CenterTarbiat Modares UniversityTehranIran

Personalised recommendations