Managing computational complexity using surrogate models: a critical review

In simulation-based realization of complex systems, we are forced to address the issue of computational complexity. One critical issue that must be addressed is the approximation of reality using surrogate models to replace expensive simulation models of engineering problems. In this paper, we critically review over 200 papers. We find that a framework for selecting appropriate surrogate modeling methods for a given function with specific requirements has been lacking. Having such a framework for surrogate model users, specifically practitioners in industry, is very important because there is very limited information about the performance of different models before applying them on the problem. Our contribution in this paper is to address this gap by creating practical guidance based on a trade-off among three main drivers, namely, size (how much information is necessary to compute the surrogate model), accuracy (how accurate the surrogate model must be) and computational time (how much time is required for the surrogate modeling process). Using the proposed guidance a huge amount of time is saved by avoiding time-consuming comparisons before selecting the appropriate surrogate model. To make this contribution, we review the state-of-the-art surrogate modeling literature to answer the following three questions: (1) What are the main classes of the design of experiment (DOE) methods, surrogate modeling methods and model-fitting methods based on the requirements of size, computational time, and accuracy? (2) Which surrogate modeling method is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? (3) Which DOE is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? Based on these three characteristics, we find six different qualitative categories for the surrogate models through a critical evaluation of the literature. These categories provide a framework for selecting an efficient surrogate modeling process to assist those who wish to select more appropriate surrogate modeling techniques for a given function. It is also summarized in Table 4 and Figs. 2, 3. MARS, response surface models, and kriging are more appropriate for large problems, acquiring less computation time and high accuracy, respectively. Also, Latin Hypercube, fractional factorial designs and D-Optimal designs are appropriate experimental designs. Our contribution is to propose a qualitative evaluation and a mental model which is based on quantitative results and findings of authors in the published literature. The value of such a framework is in providing practical guide for researchers and practitioners in industry to choose the most appropriate surrogate model based on incomplete information about an engineering design problem. Another contribution is to use three drivers, namely, computational time, accuracy, and problem size instead of using a single measure that authors generally use in the published literature.