# A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System
### Overview of Optical Imaging System Design
[PERSON]'s adaptive optimization method, described by [PERSON] and [PERSON] [43] and [PERSON] [44], is the first optimization method where the number of aberrations is smaller than that of variable constructional parameters. Modern evolutionary optimization algorithms primarily comprise genetic algorithms (GAs) and evolution strategies (ESs). GAs can be applied to solve complicated search and optimization problems with the implementation of adaptive methods, which are mainly based on a simplified genetic processes simulation [45; 46; 47]. The simple genetic algorithm (SGA) proposed by [PERSON] [48] only consists of the most fundamental elements that every genetic algorithm must have. These elements include the individual population, the individual's merit function selection, the crossover to create a new progeny, and the arbitrary mutation of a new progeny. The adaptive steady-state genetic algorithm used for the construction of the genetic algorithm for the optimization of optical systems was defined by [PERSON] [49], and each genetic algorithm consists of three modules: the evaluation module, the population module, and the reproduction module. Evolution strategies (ESs) were developed by [PERSON] [50] with the target of solving parameter optimization problems and mainly consist of the two-membered evolution strategy and the multimembered evolution strategy algorithms that mimic the natural selection principle. One of the most essential differences between classical and modern optimization algorithms is the optimum searched by these approaches; the classical optimization algorithms can only search for local optimal results, while the modern algorithms attempt to search for the global optimum. The theory behind the optimum difference is that the classical optimization algorithms do not allow for the deterioration of the merit function, so they cannot escape the first local optimum they find. As for the evolutionary algorithms, even though they cannot find the global optimum all the time, they can find adequately good results close to the global optimum [51]. In addition to the above-mentioned approaches, the study of applying machine learning based on deep neural networks (DNNs) [4; 52; 53; 54; 55] in optical system design became prominent in recent years. [PERSON] et al. [52] demonstrated that the approach of neural network-based deep learning can immediately generate a good starting point in freeform reflective imaging systems. [PERSON] [4] has proven that the combination of applying DNN as a surrogate model and optical optimization can improve the efficiency of optimization, with a 90% decrease in evaluated function budget compared with optimization without a surrogate model. After that, [PERSON] [53] extended his work into the field of deep convolutional neural networks (CNNs) and proved that the trained networks can reach a much faster convergence in solving inverse scattering global optimization problems. In this paper, a Cooke triplet lens is implemented for the optimization problem. Even with only three lenses, the optimization problem related to the curvature of surfaces,thickness of element and airspace, and selection of element glass is not trivial. Moreover, optimization of the triplet offers constructive insight concerning the characteristics of appropriate optimization algorithms.