Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management

Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for...

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Published in:Water resources management Vol. 23; no. 4; pp. 661 - 695
Main Authors: Qin, X. S, Huang, G. H
Format: Journal Article
Language:English
Published: Dordrecht Dordrecht : Springer Netherlands 01.03.2009
Springer Netherlands
Springer
Springer Nature B.V
Subjects:
Atmospheric Sciences
Case studies
Chance-constrained programming
China
Civil Engineering
Computer simulation
cost effectiveness
Creeks & streams
Decision making
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Environment
Exact sciences and technology
Fuzzy sets
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology
Hydrology. Hydrogeology
Hydrology/Water Resources
Interval quadratic programming
Linear programming
Management
Mathematical analysis
Mathematical models
Monte Carlo method
Monte Carlo simulation
Nonlinearity
Optimization
Planning
Pollutants
Pollution
Pollution control
Pollution, environment geology
Probability
probability distribution
Quadratic programming
Quality management
Random variables
risk
rivers
simulation models
Stream water
streams
Studies
Uncertainty
waste reduction
Wastewater treatment
water management
Water quality
Water quality management
Water quality standards
Water resources
Water treatment
Far East
Asia
China
China, People's Rep
China, People's Rep., Xiangjiang R
China, People's Rep., Hunan Prov., Changsha
Chance-constrained programming
Uncertainty
Interval quadratic programming
Water quality management
rivers
models
cost
waste water
Monte Carlo analysis
probability
streams
digital simulation
pollution
point sources
water quality
optimization
water resource management
Water quality management . Uncertainty
strategy
ISSN:0920-4741, 1573-1650
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Abstract Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies.
AbstractList Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies.
Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies. [PUBLICATION ABSTRACT]
Author Huang, G. H
Qin, X. S
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IsPeerReviewed true
IsScholarly true
Issue 4
Keywords Chance-constrained programming
Uncertainty
Interval quadratic programming
Water quality management
rivers
models
cost
waste water
Monte Carlo analysis
probability
streams
digital simulation
pollution
point sources
water quality
optimization
water resource management
Water quality management . Uncertainty
strategy
Language English
License http://www.springer.com/tdm
CC BY 4.0
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PublicationSubtitle An International Journal - Published for the European Water Resources Association (EWRA)
PublicationTitle Water resources management
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Publisher Dordrecht : Springer Netherlands
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Snippet Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting...
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SubjectTerms Atmospheric Sciences
Case studies
Chance-constrained programming
China
Civil Engineering
Computer simulation
cost effectiveness
Creeks & streams
Decision making
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Environment
Exact sciences and technology
Fuzzy sets
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology
Hydrology. Hydrogeology
Hydrology/Water Resources
Interval quadratic programming
Linear programming
Management
Mathematical analysis
Mathematical models
Monte Carlo method
Monte Carlo simulation
Nonlinearity
Optimization
Planning
Pollutants
Pollution
Pollution control
Pollution, environment geology
Probability
probability distribution
Quadratic programming
Quality management
Random variables
risk
rivers
simulation models
Stream water
streams
Studies
Uncertainty
waste reduction
Wastewater treatment
water management
Water quality
Water quality management
Water quality standards
Water resources
Water treatment
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Title Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management
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