Fuzzy Stochastic Dynamic Programming Research Articles

Fuzzy Set–Based System Performance Evaluation of an Irrigation Reservoir System

This paper presents the development of fuzzy set-based performance measures for an irrigation reservoir system to answer questions on how likely a system is to fail (fuzzy reliability), how quickly it is likely to recover from failure (fuzzy resiliency), and how severe the consequences of failure are likely to be (fuzzy vulnerability). The failure/success state of the system is defined as a fuzzy event. A fuzzy set with an appropriate membership function is defined to describe both the working and failed states, to account for the system being in partly working and partly failed state. Failure of the irrigation reservoir system is related to the evapotranspiration deficit of the crops in a period. Application of the performance measures is demonstrated with the case study of the Bhadra Reservoir system in Karnataka, India. The reservoir operation is simulated using three different reservoir operating policy models: steady-state policy obtained using a fuzzy stochastic dynamic programming (FSDP) model, steady-state policy obtained using a classical stochastic dynamic programming (SDP) model, and yearly operating policy using a conceptual operating policy (COP) model. All reservoir operating policy models consider the integration of the reservoir operation policy at 10-day time periods with water allocation decisions on a daily basis by maintaining the storage continuity and soil moisture balance. Inclusion of fuzziness in the performance measure gives realistic solutions by capturing uncertainties in the reservoir operating policy models. (C) 2017 American Society of Civil Engineers.

Reservoir Operation with Fuzzy State Variables for Irrigation of Multiple Crops

This paper presents the development and application of a stochastic dynamic programming model with fuzzy state variables for irrigation of multiple crops. A fuzzy stochastic dynamic programming (FSDP) model is developed in which the reservoir storage and soil moisture of the crops are considered as fuzzy numbers, and the reservoir inflow is considered as a stochastic variable. The model is formulated with an objective of minimizing crop yield deficits, resulting in optimal water allocations to the crops by maintaining storage continuity and soil moisture balance. The standard fuzzy arithmetic method is used to solve all arithmetic equations with fuzzy numbers, and the fuzzy ranking method is used to compare two or more fuzzy numbers. The reservoir operation model is integrated with a daily-based water allocation model, which results in daily temporal variations of allocated water, soil moisture, and crop deficits. A case study of an existing Bhadra reservoir in Karnataka, India, is chosen for the model application. The FSDP is a more realistic model because it considers the uncertainty in discretization of state variables. The results obtained using the FSDP model are found to be more acceptable for the case study than those of the classical stochastic dynamic model and the standard operating model, in terms of 10-day releases from the reservoir and evapotranspiration deficit. (C) 2015 American Society of Civil Engineers.

Operation of storage reservoir for water quality by using optimization and artificial intelligence techniques

Water quantity and quality are considered to be the main driving forces of the reservoir operation. Barra Bonita reservoir, located in the southeast region of Brazil, is chosen as the case study for the application of the proposed methodology. Herein, optimization and artificial intelligence (AI) techniques are applied in the simulation and operation of the reservoir. A fuzzy stochastic dynamic programming model (FSDP) is developed for calculating the optimal operation procedures. Optimization is applied to achieve multiple fuzzy objectives. Markov chain technique is applied to handle the stochastic characteristics of river flow. Water quality analysis is carried out using an artificial neural network model. Organic matter and nutrient loads are modeled as a function of river discharge through the application of a fuzzy regression model based on fuzzy performance functions. The obtained results show that the proposed methodology provides an effective and useful tool for reservoir operation.

A stochastic dynamic programming model with fuzzy storage states for reservoir operations

Application of stochastic dynamic programming (SDP) models to reservoir optimization calls for state variables discretization. Reservoir storage volume is an important variable whose discretization has a pronounced effect on the computational efforts. The error caused by storage volume discretization is examined by considering it as a fuzzy state variable. In this approach, the point-to-point transitions between storage volumes at the beginning and end of each period are replaced by transitions between storage intervals. This is achieved by using fuzzy arithmetic operations with fuzzy numbers. In this approach, instead of aggregating single-valued crisp numbers, the membership functions of fuzzy numbers are combined. Running a simulation model with optimal release policies derived from fuzzy and non-fuzzy SDP models shows that a fuzzy SDP with a coarse discretization scheme performs as well as a classical SDP having much finer discretized space. It is believed that this advantage in the fuzzy SDP model is due to the smooth transitions between storage intervals which benefit from soft boundaries.

UNCERTAINTY BASED OPERATION OF LARGE SCALE RESERVOIR SYSTEMS: DEZ AND KAROON EXPERIENCE1

ABSTRACT: Reservoir operation involves a complex set of human decisions depending upon hydrologic conditions in the supply network including watersheds, lakes, transfer tunnels, and rivers. Water releases from reservoirs are adjusted in an attempt to provide a balanced response to different demands. When a system involves more than one reservoir, computational burdens have been a major obstacle in incorporating uncertainties and variations in supply and demand. A new generation of stochastic dynamic programming was developed in the 1980s and 1990s to incorporate the forecast and demand uncertainties. The Bayesian Stochastic Dynamic Programming (BSDP) model and its extension, Demand Driven Stochastic Dynamic Programming (DDSP) model, are among those models. Recently, a Fuzzy Stochastic Dynamic Programming model (FSDP) also was developed for a single reservoir to model the errors associated with discretizing the variables using fuzzy set theory. In this study the DDSP and the FSDP models were extended and simplified for a complex system of Dez and Karoon reservoirs in the southwestern part of Iran. The simplified models are called Condensed Demand Driven Stochastic Programming (CDDSP) and Condensed Fuzzy Stochastic Dynamic Programming (CFSDP). The optimal operating policies developed by the CDDSP and the CFSDP models were simulated in a classical model and a fuzzy simulation model, respectively. The case study was used to demonstrate the advantages of implementing the proposed algorithm, and the results show the significant value of the proposed fuzzy based algorithm.

Comparison of Fuzzy and Nonfuzzy Optimal Reservoir Operating Policies

This paper compares reservoir operating policies obtained from fuzzy and nonfuzzy explicit stochastic dynamic programming. The reservoir operation problem for the Mansour Eddahbi dam in Morocco can be formulated as either a classical stochastic dynamic programming (SDP) problem, where the objective function stresses energy maximization with particular volumes being released for irrigation, or a fuzzy stochastic dynamic programming (FSDP) problem, in which both hydropower generation and irrigation are considered as fuzzy constraints and aggregated by the weighting method. System performance is estimated from simulation based on continuous reoptimization models using either the cost-to-go function generated by the SDP algorithm, or the membership function generated by the FSDP algorithm. Despite major differences in the mathematical representation of operating objectives and/or constraints, we show that both formulations yield similar measures of system performance.

Optimal operation of multipurpose reservoirs using flexible stochastic dynamic programming

This paper presents a fuzzy stochastic dynamic programming (FSDP) approach to derive steady-state multipurpose reservoir operating policies. The vagueness associated with some operating objectives as well as with the decision-making process is apprehended through fuzzy set theory. Operating objectives are considered as fuzzy sets and their membership functions represent decision maker’s preferences and satisfaction associated with particular states of the system. At each stage of the FSDP algorithm, current operating objectives are considered as flexible constraints while the fuzzy goal is obtained from the set of maximizing decisions calculated at the previous stage. The decision function results from the aggregation of the flexible constraints and the fuzzy goal. Continuous re-optimization models, with discrete FSDP-derived membership functions approximated by cubic splines, are used for implementing FSDP-derived results in real-time or simulated operation. The model can also employ different hydrologic state variables to describe the temporal persistence of the streamflow process. The proposed approach is implemented to derive operating policies for the Mansour Eddahbi reservoir (Morocco) with current inflow as the hydrologic state variable.

Reservoir operation using grey fuzzy stochastic dynamic programming

AbstractThis paper presents an optimal regulation programme, grey fuzzy stochastic dynamic programming (GFSDP), for reservoir operation. It is composed of a grey system, fuzzy theory and dynamic programming. The grey system represents data by covering the whole range without loss of generality, and the fuzzy arithmetic takes charge of the rules of reservoir operation. The GFSDP deals with the multipurpose decision‐making problem by fuzzy optimization theorem. The practicability and effectiveness of the proposed approach is tested on the operation of the Shiman reservoir in Taiwan. The current M5 operating rule curves of this reservoir also are evaluated. The simulation results demonstrate that this new approach, in comparison with the M5 rule curves, has superior performance with regard to the total water deficit and number of monthly deficits. Copyright © 2002 John Wiley & Sons, Ltd.

Fuzzy stochastic dynamic programming for marketing decision support

One of the most important goals in marketing is to realize the highest profit by applying appropriate means to optimize the process of acquiring customers. To assist the marketer in making marketing decisions, this paper introduces a stochastic dynamic programming model for the process of acquiring customers. It is actually a stochastic multistage decision process, whose state space consists of granularized information on customers and whose transitions are controlled by marketing actions. Then it shows how to control this process using fuzzy constraints and how to characterize the goal of maximizing profit by a fuzzy set. After an overview of approaches in dynamic programming under fuzziness given by Bellman and Zadeh, this paper further presents a new model of fuzzy stochastic dynamic programming to solve the decision problem for a stochastic system with implicitly defined termination time. It is argued that this study can facilitate research and development of both financial engineering and e-commerce. © 2000 John Wiley & Sons, Inc.