Multilayer feedforward networks are universal approximators
Neural Networks
Neural Computation
Screening, predicting, and computer experiments
Technometrics
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
A Note on the Griewank Test Function
Journal of Global Optimization
A comprehensive survey of fitness approximation in evolutionary computation
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On the Design of Optimization Strategies Based on Global Response Surface Approximation Models
Journal of Global Optimization
Metamodeling using extended radial basis functions: a comparative approach
Engineering with Computers
Improved Strategies for Radial basis Function Methods for Global Optimization
Journal of Global Optimization
Comparison of Stochastic Global Optimization Methods to Estimate Neural Network Weights
Neural Processing Letters
Environmental Modelling & Software
Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks
Environmental Modelling & Software
A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions
INFORMS Journal on Computing
Parallel Stochastic Global Optimization Using Radial Basis Functions
INFORMS Journal on Computing
Self-adaptive multimethod search for global optimization in real-parameter spaces
IEEE Transactions on Evolutionary Computation
A framework for evolutionary optimization with approximate fitnessfunctions
IEEE Transactions on Evolutionary Computation
Local function approximation in evolutionary algorithms for the optimization of costly functions
IEEE Transactions on Evolutionary Computation
Geometrical interpretation and architecture selection of MLP
IEEE Transactions on Neural Networks
Training feedforward networks with the Marquardt algorithm
IEEE Transactions on Neural Networks
A New Formulation for Feedforward Neural Networks
IEEE Transactions on Neural Networks
Environmental Modelling & Software
Model reduction in model predictive control of combined water quantity and quality in open channels
Environmental Modelling & Software
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Metamodelling is an increasingly more popular approach for alleviating the computational burden associated with computationally intensive optimization/management problems in environmental and water resources systems. Some studies refer to the metamodelling approach as function approximation, surrogate modelling, response surface methodology or model emulation. A metamodel-enabled optimizer approximates the objective (or constraint) function in a way that eliminates the need to always evaluate this function via a computationally expensive simulation model. There is a sizeable body of literature developing and applying a variety of metamodelling strategies to various environmental and water resources related problems including environmental model calibration, water resources systems analysis and management, and water distribution network design and optimization. Overall, this literature generally implies metamodelling yields enhanced solution efficiency and (almost always) effectiveness of computationally intensive optimization problems. This paper initially develops a comparative assessment framework which presents a clear computational budget dependent definition for the success/failure of the metamodelling strategies, and then critically evaluates metamodelling strategies, through numerical experiments, against other common optimization strategies not involving metamodels. Three different metamodel-enabled optimizers involving radial basis functions, kriging, and neural networks are employed. A robust numerical assessment within different computational budget availability scenarios is conducted over four test functions commonly used in optimization as well as two real-world computationally intensive optimization problems in environmental and water resources systems. Numerical results show that metamodelling is not always an efficient and reliable approach to optimizing computationally intensive problems. For simpler response surfaces, metamodelling can be very efficient and effective. However, in some cases, and in particular for complex response surfaces when computational budget is not very limited, metamodelling can be misleading and a hindrance, and better solutions are achieved with optimizers not involving metamodels. Results also demonstrate that neural networks are not appropriate metamodelling tools for limited computational budgets while metamodels employing kriging and radial basis functions show comparable overall performance when the available computational budget is very limited.