A tool for efficient, model-independent management optimization under uncertainty

doi:10.1016/j.envsoft.2017.11.019

Environmental Modelling & Software

Volume 100, February 2018, Pages 213-221

https://doi.org/10.1016/j.envsoft.2017.11.019 Get rights and content

Highlights

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PESTPP-OPT is a model-independent tool for management optimization.
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PESTPP-OPT uses sequential linear programming for high-dimensional problems.
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PESTPP-OPT implements parallel run management to reduce computational burden.
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PESTPP-OPT implements optimization under uncertainty with on-the-fly chance-constrained programming.

Abstract

To fill a need for risk-based environmental management optimization, we have developed PESTPP-OPT, a model-independent tool for resource management optimization under uncertainty. PESTPP-OPT solves a sequential linear programming (SLP) problem and also implements (optional) efficient, “on-the-fly” (without user intervention) first-order, second-moment (FOSM) uncertainty techniques to estimate model-derived constraint uncertainty. Combined with a user-specified risk value, the constraint uncertainty estimates are used to form chance-constraints for the SLP solution process, so that any optimal solution includes contributions from model input and observation uncertainty. In this way, a “single answer” that includes uncertainty is yielded from the modeling analysis. PESTPP-OPT uses the familiar PEST/PEST++ model interface protocols, which makes it widely applicable to many modeling analyses. The use of PESTPP-OPT is demonstrated with a synthetic, integrated surface-water/groundwater model. The function and implications of chance constraints for this synthetic model are discussed.

Section snippets

Software availability

The source code for PESTPP-OPT is available as part of the PEST++ software suite (Welter et al., 2015):

https://github.com/dwelter/pestpp.

In addition to the source code, the git repository includes statically-linked OSX and PC executables, as well as three example problems adapted from GWM (Ahlfeld et al., 2005) (e.g., the “dewater” problem, the “seawater” problem and the “supply2” problem), including the example problem presented herein.

Terminology

Parameter estimation and management optimization share many common elements, but, in some cases, employ different terminology, or worse, have similar terminology with differing definitions. Therefore, we now explicitly define how we use these terms in this paper.

In parameter estimation (PE) and uncertainty quantification (UQ) parlance, “parameters” are uncertain model inputs (any numeric quantity used both the simulator) that are nominated for adjustment during history matching and/or

Limitations

As with any modeling analysis tool, PESTPP-OPT is limited by the validity of the implicit and explicit assumptions used in its application. These include, but are not limited to:

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an approximately linear relation between decision variables and model-derived constraints is a valid representation of the relation
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an approximately linear relation between parameters and model-derived constraints is valid is a valid representation of the relation
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the second moment of the posterior parameter distribution

Implementation

PESTPP-OPT implements management optimization with FOSM-based chance constraints in a model-independent (non-intrusive) framework based on the model interface protocols from PEST (Doherty, 2010). Within the PESTPP-OPT tool, the open-source optimization library CLP (Forrest et al., 2016), part of the Computational Infrastructure for Operations Research (COIN-OR) Lougee-Heimer (2003) project, is used to solve linear programs using the simplex algorithm (Dantzig et al., 1955). The CLP solution

An example of linear programming with chance constraints

Here we present an example application of PESTPP-OPT based on the SUPPLY2 problem distributed with the GWM–2005 Groundwater Management software source code (Ahlfeld et al., 2005). The numerical model is a groundwater-flow model implemented in MODFLOW. The original SUPPLY groundwater management problem is described by Ahlfeld et al. (2005, p. 84–85):

This sample problem represents a transient water-supply problem in which total ground-water withdrawals over a 3-year period are limited by the

Conclusion

We have developed PESTPP-OPT, a model-independent tool for efficient optimization under uncertainty with minimal user intervention. PESTPP-OPT implements the proven simplex algorithm in an iterative fashion to solve the sequential linear programming problem. Using FOSM-based uncertainty estimation and a user-specified risk tolerance, PESTPP-OPT implements on-the-fly constraint uncertainty estimation, facilitating optimal solutions to resource management questions that include uncertainty.

Given

Acknowledgments

The authors thank Brian Wagner and two anonymous reviewers for the helpful suggestions.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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View full text

A tool for efficient, model-independent management optimization under uncertainty

Highlights

Abstract

Section snippets

Software availability

Terminology

Limitations

Implementation

An example of linear programming with chance constraints

Conclusion

Acknowledgments

Adv. Water Resour.

Environ. Model. Softw.

Environ. Model. Softw.

Adv. Water Resour.

Comput. Chem. Eng.

J. Hydrology

J. Hydrology

Environ. Model. Softw.

Environ. Model. Softw.

GWM-2005-A groundwater-management process for MODFLOW-2005 with local grid refinement (LGR) capability

U.S. Geol. Surv. Tech. Methods

GWM-a GroundWater Management Process for the U.S. Geological Survey Modular GroundWater Model (MODFLOW2000)

An Addendum to: GWM-a GroundWater Management Process for the U.S. Geological Survey Modular GroundWater Model (MODFLOW2000)

Applied Groundwater Modeling

Successive linear programming at exxon

Manag. Sci.

Streamflow depletion by wells–understanding and managing the effects of groundwater pumping on streamflow

U.S. Geol. Surv. Circ.

The method of probits

Science

Updated Numerical Model with Uncertainty Assessment of 1950-56 Drought Conditions on Brackish-water Movement within the Edwards Aquifer, San Antonio, Texas

Partial infeasibility method for chance-constrained aquifer management

J. Water Resour. Plan. Manag.

Chance-constrained programming

Manag. Sci.

The generalized simplex method for minimizing a linear form under linear inequality restraints

Pac. J. Math.

Quantifying data worth toward reducing predictive uncertainty

Ground Water