Next Article in Journal
Estimating Erodibility Parameters for Streambanks with Cohesive Soils Using the Mini Jet Test Device: A Comparison of Field and Computational Methods
Next Article in Special Issue
Reflection Phenomena in Underground Pumped Storage Reservoirs
Previous Article in Journal
Water Temperature, pH, and Road Salt Impacts on the Fluvial Erosion of Cohesive Streambanks
Previous Article in Special Issue
Parameter Estimation of Water Quality Models Using an Improved Multi-Objective Particle Swarm Optimization
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Water 2018, 10(3), 303;

NN-Based Implicit Stochastic Optimization of Multi-Reservoir Systems Management

Department of Electronics, Information, and Bioengineering, Politecnico di Milano, 20133 Milano, Italy
Author to whom correspondence should be addressed.
Received: 5 February 2018 / Revised: 27 February 2018 / Accepted: 9 March 2018 / Published: 10 March 2018
PDF [2591 KB, uploaded 12 March 2018]


Multi-reservoir systems management is complex because of the uncertainty on future events and the variety of purposes, usually conflicting, of the involved actors. An efficient management of these systems can help improving resource allocation, preventing political crisis and reducing the conflicts between the stakeholders. Bellman stochastic dynamic programming (SDP) is the most famous among the many proposed approaches to solve this optimal control problem. Unfortunately, SDP is affected by the curse of dimensionality: computational effort increases exponentially with the complexity of the considered system (i.e., number of reservoirs), and the problem rapidly becomes intractable. This paper proposes an implicit stochastic optimization approach for the solution of the reservoir management problem. The core idea is using extremely flexible functions, such as artificial neural networks (NN), for designing release rules which approximate the optimal policies obtained by an open-loop approach. These trained NNs can then be used to take decisions in real time. The approach thus requires a sufficiently long series of historical or synthetic inflows, and the definition of a compromise solution to be approximated. This work analyzes with particular emphasis the importance of the information which represents the input of the control laws, investigating the effects of different degrees of completeness. The methodology is applied to the Nile River basin considering the main management objectives (minimization of the irrigation water deficit and maximization of the hydropower production), but can be easily adopted also in other cases. View Full-Text
Keywords: reservoir operation; artificial neural networks; genetic algorithm; information completeness; Nile River basin; release rule reservoir operation; artificial neural networks; genetic algorithm; information completeness; Nile River basin; release rule

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Sangiorgio, M.; Guariso, G. NN-Based Implicit Stochastic Optimization of Multi-Reservoir Systems Management. Water 2018, 10, 303.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Water EISSN 2073-4441 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top