## 2 Materials and Methods
### Surrogate Models and Optimization Methods
[PERSON] and [PERSON] combine the PSO with a BFO to form the PSO-BFO algorithm [31]. The algorithm uses a Radial Basis Function (RBF) surrogate model to optimize the behavior of a full-frontal impact and side impact of an SFE CONCEPT BIW model. While the PSO tends to have excellent explorative behavior, the BFO is better for exploitation. Hence, combining both algorithms with a surrogate improves the structural performance in both crash scenarios. The combined algorithm outperformed the PSO-GA and the simple PSO and BFO. Besides the structural applications, different black-box optimization approaches exist. The following paragraph mentions notable exemplary implementations. Based on the MOCE+ algorithm, [PERSON] and [PERSON] propose the Simple Multi-Objective Cross-Entropy (SMOCE) algorithm [32]. The algorithm uses elitism clustering by histograms of the objective functions. One of the main benefits of this algorithm is its robustness and the low amount of algorithm parameters that makes the algorithm very consistent. The authors performed a comparative study for commonly used test problems with two objective functions. The study found that the SMOCE outperforms the MOCE+, NSGA-II, MOEA/D, MOPSO, SPEA-II, and PESA-II for hyper area exploration. The other algorithm may benefit from a smaller sampling size and generations (epochs); the SMOCE appears suitable for inexpensive function calls, e.g., analytical functions, as demonstrated in the article. [PERSON] and [PERSON] describe the Max-value Entropy Search for Multi-Objective Optimization (MESMO) with Bayesian Optimization for Network on Chip optimizations in [33]. The MESMO uses an output-space, entropy-based acquisition function to detect evaluation points, which leads to the efficient detection of the Pareto-frontier points. The authors compare MESMO to different [PERSON] approaches, which are Pareto-efficient global optimization (ParEGO), the Predictive entropy search for Multi-objective Bayesian Optimization (PESMO), S-Metric-Selection-based Efficient Global Optimization (SMSego) expected improvement in Pareto hypervolume (EHI), and the probability of improvement in stepwise uncertainty reduction (SUR). The paper compares all algorithms for the same two synthetic benchmark problems, which combine classical, single-objective benchmark problems. MESMO outperforms the other algorithms in terms of robustness and convergence. Another approach is the GOMORS framework, a multi-objective EA that uses RBF-surrogate models [21]. The EA predicts new function points based on the surrogate model and generates possible candidates. A few points are selected based on rules, which balance exploration, exploitation, and frontier diversification. The selected candidates are then evaluated based on the costly function evaluation. The expensive black-box evaluations then update the RBF-surrogates, which serve as the foundation for further optimizations with the EA. Indeed, different embedded EAs have been evaluated, such as the NSGA-II, MOEA/D, and AMALGAM. The AMALGAM outperformed the other algorithms slightly. The GOMORS was then directly compared to the ParEGO and NSGA-II on a groundwater remediation problem and synthetic test functions. The GOMORS topped the ParEGO [34] and the NSGA-II regarding the effectivity. The authors state GOMORS to find suitable solutions under a low amount of costly function evaluations.