A Probabilistic Approach to Surrogate‐Assisted Multi‐Objective Optimization of Complex Groundwater Problems

Groundwater management involves a complex decision‐making process, often with the need to balance the trade‐off between meeting society's demand for water and environmental protection. Therefore effective management of groundwater resources often involves some form of multi‐objective optimizati...

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Published in:Water resources research Vol. 61; no. 5
Main Authors: Macasieb, Reygie Q., White, Jeremy T., Pasetto, Damiano, Siade, Adam J.
Format: Journal Article
Language:English
Published: Washington John Wiley & Sons, Inc 01.05.2025
Wiley
Subjects:
Algorithms
Coastal management
Computer applications
computer software
Decision making
decision‐support
Environmental management
Environmental protection
Evolutionary algorithms
Gaussian process
Groundwater
Groundwater management
Groundwater resources
machine learning
multi‐objective optimization
Nonlinear systems
Nonlinearity
normal distribution
Optimization
Probability theory
Redevelopment
Simulation models
Software
Statistical analysis
surrogate modeling
Uncertainty
Water demand
water management
Water resources
water resources management
ISSN:0043-1397, 1944-7973
Online Access:Get full text
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Summary:Groundwater management involves a complex decision‐making process, often with the need to balance the trade‐off between meeting society's demand for water and environmental protection. Therefore effective management of groundwater resources often involves some form of multi‐objective optimization (MOO). Many existing software tools offer simulation model‐enabled optimization, including evolutionary algorithms, for solving MOO problems. However, such analyses involve a huge amount of numerical process‐based model runs, which require significant computational effort, depending on the nonlinearity and dimensionality of the problem, in order to seek the optimal trade‐off function known as the Pareto front. Surrogate modeling, through techniques such as Gaussian Process Regression (GPR), is an emerging approach to significantly reduce the number of these model evaluations thereby speeding up the optimization process. Yet, surrogate model predictive uncertainty remains a profound challenge for MOO, as it could mislead surrogate‐assisted optimization, which may result in either little computational savings from excessive retraining, or lead to suboptimal and/or infeasible solutions. In this work, we present probabilistic Pareto dominance criteria that considers the uncertainty of GPR emulation during MOO, producing a “cloudy” Pareto front which provides an efficient decision space sampling mechanism for retraining the GPR. We then developed a novel acquisition strategy to manage the solution repository from this cloud and generate an ensemble of infill points for retraining. We demonstrate the capabilities of the algorithm through benchmark test functions and a typical density‐dependent coastal groundwater management problem. Key Points We present an effective algorithm for solving constrained nonlinear multi‐objective optimization problems with less computational effort The method applies a new acquisition strategy to efficiently aid sequential retraining of the surrogate model thereby improving its accuracy Probabilistic Pareto dominance is used to incorporate uncertainty in evaluating the dominance relationship between emulated positions
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ISSN:0043-1397
1944-7973
DOI:10.1029/2024WR038554