Optimal control of nonlinear groundwater hydraulics using differential dynamic programming

Jones, LaDon; Willis, Robert; Yeh, William W.‐G.

doi:10.1029/wr023i011p02097

Cited by 94 publications

(53 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This example problem is obtained from Jones et al (1987) and Wang & Zheng(1998). The problem is to find optimal pumping rates that would yield the minimum cost from an GA, SA, PSO and ACO are presented in Table 3.…”

Section: Example 2: Hydraulic Capture Zone Designmentioning

confidence: 99%

Swarm intelligence for groundwater management optimization

Sedki

Ouazar

2010

Journal of Hydroinformatics

View full text Add to dashboard Cite

This paper presents some simulation-optimization models for groundwater resources management. These models couple two of the most successful global optimization techniques inspired by swarm intelligence, namely particle swarm optimization (PSO) and ant colony optimization (ACO), with one of the most commonly used groundwater flow simulation code, MODFLOW. The coupled simulation-optimization models are formulated and applied to three different groundwater management problems: (i) maximization of total pumping problem,(ii) minimization of total pumping to contain contaminated water within a capture zone and (iii) minimization of the pumping cost to satisfy the given demand for multiple management periods. The results of PSO-and ACO-based models are compared with those produced by other methods previously presented in the literature for the three case studies considered. It is found that PSO and ACO are promising methods for solving groundwater management problems, as is their ability to find optimal or near-optimal solutions.

show abstract

Section: Example 2: Hydraulic Capture Zone Designmentioning

confidence: 99%

Swarm intelligence for groundwater management optimization

Sedki

Ouazar

2010

Journal of Hydroinformatics

View full text Add to dashboard Cite

show abstract

“…These studies considered physical system as lumped. Jones et al (1987) used a DDP algorithm to reduce computational burden for unsteady, nonlinear (unconfined), ground water system management problems.…”

Section: Conjunctive Use Modelsmentioning

confidence: 99%

Conjunctive use modeling for multicrop irrigation

Vedula

Mujumdar

Sekhar

2005

Agricultural Water Management

View full text Add to dashboard Cite

A mathematical model is developed to arrive at an optimal conjunctive use policy for irrigation of multiple crops in a reservoir-canal-aquifer system. The integration of the reservoir operation for canal release, ground water pumping and crop water allocations during different periods of crop season (intraseasonal periods) is achieved through the objective of maximizing the sum of relative yields of crops over a year considering three sets of constraints: mass balance at the reservoir, soil moisture balance for individual crops, and governing equations for ground water flow. The conjunctive use model is formulated with these constraints linked together by appropriate additional constraints as a deterministic linear programming model. A two-dimensional isotropic, homogeneous unconfined aquifer is considered for modeling. The aquifer response is modeled through the use of a finite element ground water model. A conjunctive use policy is defined by specifying the ratio of the annual allocation of surface water to that of ground water pumping at the crop level for the entire irrigated area. A conjunctive use policy is termed stable when the policy results in a negligible change in the ground water storage over a normal year. The applicability of the model is demonstrated through a case study of an existing reservoir command area in Chitradurga district, Karnataka State, India.

show abstract

“…Derivative-based optimization has been previously applied to management of groundwater flow, but the method has not been previously used for problems incorporating contaminant transport in unconfined aquifers. The SALQR algorithm was applied to the problem of optimizing water quantity management in unconfined aquifers by Jones et al [1987] (the algorithm was referred to by Jones et al as differential dynamic programing, or DDP). Jones et al did not consider contaminant transport or remediation.…”

mentioning

confidence: 99%

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

Mansfield¹,

Shoemaker²

1999

Water Resources Research

View full text Add to dashboard Cite

Abstract. This paper extends earlier work on derivative-based optimization for costeffective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined-and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined-and confined-aquifer models to estimate which aquifers require unconfinedaquifer optimization and which can be adequately approximated by the simpler confinedaquifer analysis.

show abstract

Optimal control of nonlinear groundwater hydraulics using differential dynamic programming

Cited by 94 publications

References 17 publications

Swarm intelligence for groundwater management optimization

Swarm intelligence for groundwater management optimization

Conjunctive use modeling for multicrop irrigation

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

Contact Info

Product

Resources

About