# Multi-Objective Optimization of Production Objectives Based on Surrogate Model
## 2 Background of Multi-Objective Optimization Based on a Surrogate Model
### Modeling of Surrogates and Their Application in a Multi-Objective Optimization  
Metamodeling or surrogate modeling (through the following text) is a technique for the construction of \"a model of the model\" or \"surrogates\" to cover the essential features of the input-output system behavior [16]. It approximates the black-box function analytically or generates a new model with better properties for further computation. We can find plenty of works related to this field, focusing on optimization via metamodeling, [PERSON] and [PERSON] [16] give an extensive survey of different types of surrogate models used for implementation in the objective function. Geometric models such as Response Surface Models generated by Response Surface Methodology (RSM) within the Design of Experiments technique, Radial Basis Function (RBF) models, statistical models such as Kriging or Gauss regression, and models based on Machine Learning methods--Artificial Neural Networks (ANN) or Support Vector Machines (SVM)--are among the most widespread. The authors also provide an overview of works when multi-objective optimization (MOO) and metamodeling are combined. [PERSON] et al. [11] discuss the most popular surrogate models being used in engineering designs suitable also for black-box optimization and the difficulties related to their application. They mention that polynomial models that are well-studied and employed in trust-region methods to provide approximation of the true function in local areas are unsuitable as global models for highly nonlinear multidimensional functions. The authors introduce models that are better performed in that sense, such as RBF and Kriging. [PERSON] and [PERSON] [21] and [PERSON] and [PERSON] [22] particularly focus on metamodeling in multi-objective optimization. [PERSON] et al. [23] pay attention to Kriging metamodeling in multi-objective simulation optimization. In a survey of [PERSON] and [PERSON] [12], the authors introduce non-nature inspired methods for handling computationally expensive multi-objective optimization problems using surrogates. As for polynomial modeling, [PERSON] et al. [24] analyze the quality of fits in case of applying first- and second-order polynomials and other classes of metamodels in metamodel-based simulation optimization from the local and global fit point of view. Regarding utilizing the surrogate-based optimization methods in engineering applications of real-world problems, one can find them mainly in the field of design of systems or product properties. [PERSON] et al. [25] suggest a multi-objective optimization framework for offshore renewable energy mooring systems applying a random forest-based surrogate model coupled to a genetic algorithm. [PERSON] et al. [26] compare the predictive cyclone models generated by response surface methodology, back propagation neural network, and group method of data-handling networks and apply them in multi-objective optimization of the cyclone separation performance via genetic algorithm, too. [PERSON] et al. [27] compare the multi-objective optimization of an air intake ventilation system utilizing an evolutionary algorithm with and without a surrogate. In particular, in the domain of designing manufacturing processes, the multi-objective optimization via metamodels coupled to simulation for machining and turning processes, respectively, is applied e.g., in [PERSON] et al. [28] or [PERSON] et al. [29]. For the optimization of a friction-drilling process, [PERSON] et al. [30] describe a novel strategy for real industrial conditions based on Adaboost ensembles. Regarding the results, this prediction model provided the highest accuracy and was more easily optimized than models that resulted from other machine learning techniques. In relation to the manufacturing systems control, when the optimization of production objectives had been solved, we can observe a predominance of applying heuristic approaches, mainly evolutionary algorithms in the recent works. [PERSON] et al.