Surrogate-based pumping optimization of coastal aquifers under limited computational budgets

Abstract

The computationally expensive variable density and salt transport numerical models hinder the implementation of simulation-optimization routines for coastal aquifer management. To reduce the computational cost, surrogate models have been utilized in pumping optimization of coastal aquifers. However, it has not been previously addressed whether surrogate modelling is effective given a limited number of numerical simulations with the seawater intrusion model. To that end, two surrogate-based optimization (SBO) frameworks are employed and compared against the direct optimization approach, under restricted computational budgets. The first, a surrogate-assisted algorithm, employs a strategy which aims at a fast local improvement of the surrogate model around optimal values. The other, balances global and local improvement of the surrogate model and is applied for the first time in coastal aquifer management. The performance of the algorithms is investigated for optimization problems of moderate and large dimensionalities. The statistical analysis indicates that for the specified computational budgets, the sample means of the SBO methods are statistically significantly better than those of the direct optimization. Additionally, the selection of cubic radial basis functions as surrogate models, enables the construction of very fast approximations for problems with up to 40 decision variables and 40 constraint functions.

GOPS: efficient RBF surrogate global optimization algorithm with high dimensions and many parallel processors including application to multimodal water quality PDE model calibration

“…RBF was first introduced in global optimization by Gutmann (2001), and there are various RBF-based serial methods proposed (Jakobsson et al 2010;Regis and Shoemaker 2005, 2007b, 2013. RBF-based methods are proven to be effective for solving real-word computationally expensive problems, e.g., designing the specifics of trains (Björkman and Holmström 2000), groundwater problem (Christelis et al 2018;Mugunthan et al 2005), watershed problem Shoemaker 2007b, 2013), methane emission problem (Müller et al 2015), and aerodynamic regional airliner wing design (Sóbester et al 2014). Jakobsson et al (2010) applied an RBF-based global optimization method to the combustion engine design problem, which is a noisy function and computationally expensive with one simulation taking 42 h. There are also efforts made on using RBF-based methods to solve high dimensional problems.…”

Gaussian Process Regression Tuned by Bayesian Optimization for Seawater Intrusion Prediction

“…The latter proved to be computationally more efficient, providing solutions near the global optimum. Christelis et al [25] employed two surrogate-based optimization (SBO) frameworks, under restricted computational budgets to improve the efficiency of optimization algorithms in problems of moderate and large dimensionalities. In a more recent study, Christelis and Mantoglou employed variable-fidelity surrogate models and evolutionary algorithms to calculate the maximum allowed pumping rates in coastal aquifers.…”

Metamodel-assisted analysis of an integrated model composition: An example using linked surface water – groundwater models

“…Kriging and RBF metamodels have been mainly preferred in water resources optimization problems (e.g. Bau and Mayer, 2006;Shoemaker et al, 2007;Castelleti et al, 2010;Razavi et al, 2012b;Tsoukalas and Makropoulos, 2015a;Tsoukalas and Makropoulos, 2015b;Christelis and Mantoglou, 2016;Tsoukalas et al, 2016;Christelis et al, 2018). They can operate as interpolating metamodels, that is, they pass through all the previously evaluated points with the original model and thus can get more accurate on predicting the response of the original model as new input-output data become available (Forrester et al, 2008).…”