Fuzzy-State Stochastic Dynamic Programming for Reservoir Operation
Publication: Journal of Water Resources Planning and Management
Volume 130, Issue 6
Abstract
A new way of incorporating fuzzy logic concepts is introduced in order to better capture and manage some uncertainties in applying stochastic dynamic programming (SDP) formulations for reservoir operation. A model called fuzzy-state stochastic dynamic programming (FSDP), which takes into account both uncertainties due to random nature of hydrological variables and imprecision due to variable discretization is introduced in this study. In this model, fuzzy transition probabilities for stochastic hydrologic state variables are calculated by defining a fuzzy Markov chain. These fuzzy probabilities are derived based on fuzzy frequency concept considering different frequencies for different points of a class interval. In order to show how effective the proposed method is, FSDP was applied to the Zayandeh–Rud river–reservoir system in Isfahan, in the central part of Iran, and was compared with a demand driven stochastic dynamic programming model. The results show the robustness of the FSDP solutions with respect to the type of discretization scheme used in calculating the transition probabilities.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bellman, R. E., and Zadeh, L. A. (1970) “Decision making in a fuzzy environment.” Manage. Sci.,17(4), 141–164.
27.
Chang, F.-J., Hui, S.-C., and Chen, Y.-C. (2002). “Reservoir operation using grey fuzzy stochastic dynamic programming.” Hydrolog. Process., 16(12), 2395–2408.
2.
Dubrovin, T., Jolma, A., and Turunen, E. (2002). “Fuzzy model for real-time reservoir operation.” J. Water Resour. Plan. Manage., 128(1), 66–73.
3.
Esogbue, A. O., Theologidu, M., and Kejiao, G. (1992). “On the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems.” Fuzzy Sets Syst., 49(1), 155–172.
4.
Fontane, D. G., Gates, T. K., and Moncade, E. (1997). “Planning reservoir operations with imprecise objectives.” J. Water Resour. Plan. Manage., 123(3), 154–162
5.
Goulter, I. C., and Tai, F. K. (1985). “Practical implications in the use of stochastic dynamic programming for reservoir operation.” Water Resour. Bull., 21(1), 65–74.
6.
Johnson, S. A., Stedinger, J., Shoemaker, Li Y., and Tejada-Guibert, J. A. (1993). “Numerical solution of continuous-state dynamic programming using linear and spline interpolation.” Oper. Res., 41(13), 484–500.
28.
Karamouz, M. and Mousavi, S. J. (2003). “Uncertainty–based operation of large scale reservoir systems: Dez and Karoun Experience.” J. Am. Water Resour. Assoc., 39(4), 961–975.
7.
Karamouz, M., and Vasiliadis, H. V. (1992). “Bayesian stochastic optimization of reservoir operation using uncertain forecasts.” Water Resour. Res., 28(5), 1221–1232.
8.
Klemes, V. (1977). “Discrete representation of storage for stochastic reservoir optimization.” Water Resour. Res., 13, 149–158.
9.
Liu, B. and Esogbue, A. O. (1996). “Fuzzy criterion set and fuzzy criterion dynamic programming.” J. Math. Anal. Appl., 199(1), 293–311.
10.
Loganathan, G.V., and Bhattacharya, D. (1990). “Reservoir operations by fuzzy goal programming.” Proc. 17th ASCE WRPM Annual National Conf. on Optimizing the Resources for Water Management, Forth Worth, Texas, 456–461.
11.
Loucks, D.P., Stedinger, J.R., and Haith, D.A. H. (1981). Water resources systems planning and analysis, Prentice–Hall, Engelwood Cliffs, N. J.
12.
Panigrahi, D. P., and Mujumdar, P. P. (2000). “Reservoir operation modeling with fuzzy logic.” Water Resour. Manage., 14, 89–109
13.
Ponnambalam, K., Karray, F., and Mousavi, S. J. (2003). “Minimizing variance of reservoir systems operations benefits using soft computing tools.” Fuzzy Sets Syst., 139(2), 451–461.
14.
Ponnambalam, K., Mousavi, S. J., and Karray, F. (2001). “Regulation of Great Lakes reservoirs system by a nero-fuzzy optimization model.” Int. J. Comput. Anticipatory Syst., 9, 272–285.
15.
Russell, S. O., and Campbell, P. E. (1996). “Reservoir operating rules with fuzzy programming.” J. Water Resour. Plan. Manage., 122(3), 165–170.
16.
Shrestha, B. P., Duckstein, L. E., and Stakhiv, E. (1996). “Fuzzy rule-based modeling of reservoir operation.” J. Water Resour. Plan. Manage., 122(4), 262–269.
17.
Suharyanto, and Goulter, I.C. (1996). “Use of fuzzy set theory for consideration of storage non-specificity in stochastic dynamic programming for reservoir operation.” Proc. 7th IAHR Int. Symp. on Stochastic Hydraulics, K. S. Tickle, et al., eds., Mackay, Queensland, Australia, 129–136.
18.
Suharyanto, and Wasimi, S.A. (1996). “Effects of fuzzy constraints in Reservoir Operation strategy.” Proc. 7th IAHR Int. Symp. on Stochastic Hydraulics K. S. Tickle et al., eds., Mackay, Queensland, Australia, 111–118.
19.
Teegavarapu, R. S. V., and Siminovic, S. P. (1999). “Modeling uncertainty in reservoir loss functions using fuzzy sets.” Water Resour. Res., 35(9), 2815–2823.
20.
Tejada-Guibert, J. A., Johnson, S. A., and Stedinger, J. R. (1993). “Comparison of two approaches for implementing multi-reservoir operating policies derived using dynamic programming.” Water Resour. Res., 29(12), 3969–3980.
21.
Tejada-Guibert, J. A., Johnson, S. A, and Stedinger, J. R. (1995). “The value of hydrologic information in stochastic dynamic programming models of a multireservoir system.” Water Resour. Res., 31(10), 2571–2579.
22.
Tilmant, A., Fortemps, P., and Vanclooster, M. (2002a). “Effect of averaging operators in fuzzy optimization of reservoir operation.” Water Resour. Manage., 16(1), 1–22.
23.
Tilmant, A., Vanclooster, M., Ducketein, L., and Persoons, E. (2002b). “Comparison of fuzzy and nonfuzzy optimal reservoir operating policies.” J. Water Resour. Plan. Manage., 128(6), 390–398.
24.
Vasiliadis, H. V., and Karamouz, M. (1994). “Demand-driven operation of reservoirs using uncertainty-based optimal operating policies.” J. Water Resour. Plan. Manage., 120(1), 101–114.
25.
Yakowitz, S. (1982). “Dynamic programming applications in water resources.” Water Resour. Res., 18(4), 673–696.
26.
Yeh, W. W-G. (1985). “Reservoir management and operations models: a state-of-the-art review.” Water Resour. Res., 21(12), 1797–1818.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 130 • Issue 6 • November 2004
Pages: 460 - 470
Copyright
Copyright © 2004 ASCE.
History
Published online: Oct 15, 2004
Published in print: Nov 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.