# High-Fidelity Surrogate Based Multi-Objective Optimization Algorithm
## 1 Introduction  
Numerous competing objectives and constraint functions, as well as time-consuming and expensive simulations, are present in the majority of real-world optimization issues. High-fidelity models must frequently be expensively modelled in order to address these problems. Finding the Pareto optimum of multi-objective optimization problems (MOO) necessitates evaluating expensive fitness and constraint functions. However, only a few tests are allowed in practice due to the restricted computing resources available to address such problems, notably black box functions. Researchers [1, 2, 3] found that the development of surrogate models employing a few high-fidelity solution assessments to replace computationally expensive models is promising and fruitful. Expensive functions are commonly replaced by surrogate models such as the radial basis function, Kriging, or response surface method [4].  
In MOO problems demanding expensive computational analysis and simulation tools, for example FEA and CFD, surrogate models have grown in prominence and received more attention. Due to their capacity to imitate the real expensive model and their compliance with challenging computational requirements, surrogate models have been proved to be viable tools for MOO problems [5]. Numerous optimization applications demand labor- and resource-intensive fitness evaluations. The load considerably increases when dealingwith multiple-objective black box functions that need to be evaluated. The automated MOO algorithm (AMSP) proposed in this paper is based on surrogate approximations.  
The suggested algorithm automatically constructs an ensemble of surrogates from the three available surrogate models based on a methodology that will be introduced and explained in detail in this paper. The algorithm adaptively adjusts the effective surrogate model to determine the Pareto frontier for the MOO problem. The Response Surface Function (RSF), Radial Basis Function (RBF), and Kriging model are employed as surrogate approximations in this work [6; 7; 8; 9; 10; 11]. To fully make use of the potential design space, an efficient sampling technique must be used. Traditional sampling techniques are afflicted by the \"curse of dimensionality\", which causes an exponential increase in the number of sampling points needed to explore the design space as the number of design variables rises. The Latin Hypercube Designs (LHD) method [12] was consequently modified in this work. LHD is renowned for randomly and evenly covering the practicable portion of the design space in its sampling. These significantly reduce computation costs and increase the probability of finding the Pareto frontier for MOO problems. The suggested algorithm (AMSP) consistently and accurately locates the Pareto frontier for MOO problems. The computational cost is significantly reduced when AMSP is used to locate the Pareto frontier for expensive black-box functions. AMSP was put to the test using benchmark test problems and actual, realistic engineering challenges in order to show off its performance. The outcomes are seen as promising and encouraging.