Numerical assessment of metamodelling strategies in computationally intensive optimization

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. 2011 Elsevier Ltd. All rights reserved.