# A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System
### Overview of Surrogate-Based Modelling  
A surrogate model is also referred to as a \"metamodel\", \"response surface model\", \"approximation model\", or \"emulator\" in different research fields. In complex computer simulations, finding more data requires additional experiments, which would result in extensive material or economic cost as well as computational expense. Consequently, obtaining an analytical form of derivatives or the objective function is relatively challenging. However, the derivation of the information from a surrogate model is comparatively easier, as the analytical form is known and, hence, is cheaper to evaluate. Building through the sampled data that are obtained by evaluating a set of sample points in the target space via expensive analysis code, a surrogate model can be used to efficiently predict the output of the code at any unknown point [56].  
The representative surrogate models include the polynomial response surface model (PRSM) [57; 58], Kriging [59; 60], radial basis functions (RBFs) [61; 62], artificial neural network (ANN) [63; 64], support vector regression (SVR) [65; 66], etc.  
According to [PERSON] et al. [67] and [PERSON] [68], PRSM can be applied in aircraft design. Kriging is based on the idea that a surrogate can be represented as a realization of a stochastic process. This idea was first proposed in the field of geostatistics by [PERSON] [69] and [PERSON] [70]. It gained popularity after being used for the design and analysis of computer experiments by [PERSON], [PERSON], [PERSON], and [PERSON] [60]. Kriging is also known as a Gaussian process regression in the field of machine learning [71; 72]. Kriging is used for process flowsheet simulations [73], design simulations [74], pharmaceutical process simulations [75], and feasibility analysis [76]. Radial basis functions have been developed for the interpolation of scattered multivariate data. RBFs are used for feasibility analysis [77] and parameter estimation [78]. ANN is used for process modelling [79], process control [80], and optimization [81; 82]. SVR is shown to achieve comparable accuracy with that of other surrogates [83]. SVR models are accurate as well as fast in prediction; however, the time required to build this model is high because finding the unknown parameters requires solving a quadratic programming problem. This added complexity hinders the popularity of SVR [6].  
Among them, Kriging has earned popularity in the fields of aerodynamic design optimization [84; 85; 86; 87; 88] and structural and multidisciplinary optimization [89; 90]. Generally, geostatistical interpolation methods that calculate the spatial autocorrelation between measurements and utilize the spatial structure of measurements around the prediction location comprise universal Kriging, ordinary Kriging, and co-Kriging [91]. Isotropy (uniform values in all directions) is assumed during the Kriging process unless anisotropy is specified. Consequently, comparisons between isotropic and anisotropic semi-variogram-derived surfaces are not often made. Thus far, the application of anisotropy within Kriging has been shown to be superfluous for local- and regional-scale modelling, although [PERSON] et al. [90] hypothesized that it may be more useful for meso- and macro-scale modelling.  
According to the properties of surrogate-based models, Kriging is quite suitable for the multi-objective optimization of optical systems with high dimensions; hence, in this paper, the surrogate-based model applied to the triplet is Kriging.