# High-Fidelity Surrogate Based Multi-Objective Optimization Algorithm
## 2 Literature Review  
MOO has emerged as a possible approach to overcoming obstacles with conflicting goals. The most effective trade-offs between a set of criteria are often determined by using a group of Pareto optima to solve MOO issues. Finding the final Pareto frontier for use in practice is challenging, especially when there are several competing objectives to take into account. In situations with two or three objective functions, it may be rather simple to describe the set of Pareto-optimal solutions in the objective function space. When we identify Pareto limits, we may completely understand the relationship between trade-offs between objectives. It has been demonstrated that surrogate models may accurately and efficiently identify Pareto-optimal solutions. Effective and durable search strategies are greatly needed to tackle such challenging multi-objective optimization problems. The majority of algorithms are evolutionary ones such as GA, PSO, and others. Black box functions have only been shown for a select few. These are the solutions provided for multi-objective optimization problems that demand pricey analysis and simulation methods, such as multi-physics modeling and simulation, FEA, and CFD analyses. The optimization of computationally expensive black box functions needs more focus and should be addressed due to the challenges these functions have presented to the optimization community. A promising method that might help with the resolution of these problems is the use of surrogate models. The expensive model (function) is simulated and predicted using surrogate models, which have a reduced computational cost. MOOP with expensive high fidelity computational models, such as sophisticated simulations and thorough analyses, the standard multi-objective optimization methods, are challenging to perform directly due to the high computational cost of objective and constraint function evaluations. As a response to these problems, surrogate models gain in popularity. There are typically two scenarios in which black box functions are used to address MOO problems. Numerous evolutionary algorithms (EAs) use the first scenario, which closely resembles the Pareto optimal [13; 14; 15]. Due to the costly evaluations of numerous non-Pareto set points required by these approaches, they are renowned for being computationally expensive. In the second scenario, surrogate models are used to assess each objective function. Naturally, the constructed surrogate models will determine how precise the Pareto-optimal border is. [PERSON] et al. [16] created a hyper-ellipse surrogate to approach the Pareto optimum frontier for bicriteria convex optimization problems. If the established approximation model is not sufficiently accurate, the Pareto-optimal frontier will not be considered a good approximation of the genuine Pareto-optimal frontier. In order to make use of the multi-objective design region and find the Pareto set using approximation models, [PERSON] et al. [17] used two surrogate approximations (response surface and Kriging models). Prior to applying the optimization strategy, they employ a technique that minimizes the loss of surrogate approximation accuracy. [PERSON] et al. [17] used the weighted and global criterion technique to construct an algorithm that incorporates several criterion optimizations into evolutionary structural optimization (ESO). [PERSON] et al. [15] developed a strategy for managing surrogate models for MOO. The framework includes a sequentially-updated surrogate model and a GA-based method. Instead of before, as in the preceding case, the surrogate model is altered during the optimization process [14]. The accuracy of the surrogate model is crucial for maintaining the integrity of the identified border sets in their proposed method. [PERSON]'s [15] research had a hard time locating frontier areas close to the extremes. The Pareto Set Pursuing (PSP) technique, proposed by [PERSON] and [PERSON] [18], entails creating sampling guidance functions based on surrogate models.