## 2 Materials and Methods
### Surrogate Models and Optimization Methods  
From the viewpoint of the optimizer, the system of geometry change, pre-processing, calculation, and evaluation is a black box. Surrogate models can predict the dependency of the constraints and objective functions on the input variables. Furthermore, different coupling methods of surrogates and optimization algorithms exist, classified as decoupled, surrogate-driven, and surrogate-assisted methods. Decoupled methods are the most straightforward approach as combining a surrogate and an optimization algorithm requires less effort. The surrogate models approximate the target functions, and the optimization algorithm searches the optima and predicts a good solution. The framework updates the surrogate model accordingly until it depletes the budget for expensive evaluations. The surrogate model is intrinsically built into the optimization procedure in surrogate-driven methods such as Bayesian optimization techniques, which use probabilistic surrogate models with sequential updates. A rather unpopular approach is surrogate-assisted methods, where surrogate models support the algorithm in a specific domain, e.g., local search [11]. An extensive range of optimization algorithms is applicable for this kind of problem. As the behavior response functions are typically highly multimodal and not present in their mathematical closed form, one needs to use heuristic or metaheuristic approaches for the optimization [9; 26]. Metaheuristics often adopt biological behavior for the optimization of the target function. Hence, a broad spectrum of different optimization approaches exists, which allow the optimization of black-box problems in varying disciplines. [PERSON] and [PERSON] [5] compare a Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) to an NSGA-II and apply both algorithms to a BIW-optimization task. The NSGA-II converged faster to the Pareto-frontier and covered a more significant part of the solution space. The benchmark results of different automotive crash optimizations are summarized in [7]. The comparison of an Evolutionary Algorithm (EA), Genetic Algorithms (GAs), and Simulated Annealing (SA) for Noise, Vibration, and Harshness (NVH) in BIW optimization showed that for the GA and EA, the mutation and population size play an outstanding role, and so do the number of parents and children. Elitism improves multi-objective optimizations, while non-elitist approaches work well for single-objective optimizations. Furthermore, the EA outperformed the other algorithms under high noise and non-linearity. Due to the diversification and good exploration, EAs tend to be very successful, as they consider the whole solution space in early conceptual design. Indeed, one should consider the more exploitive algorithm should. All of these metaheuristics differ in their intensification and diversification [27]. The Bacterial Foraging Algorithm (BFO) tends to be less performant than the GA, Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO) in the scenario of an aeroelastic wing shape optimization. Therefore, modified Cooperative Bacterial Foraging Optimization (CFBO) tends to perform like the mentioned algorithm regarding the optimization performance [28]. Single algorithms have characteristics of either good exploitation (intensification) or exploration (diversification). Thus, new approaches arise that combine the benefits of intensification and diversification by combining different metaheuristics, e.g., presented in [29]. Due to its simplicity and effectiveness, recent research implemented the NSGA-II into the IKOS framework. Furthermore, it was validated using two different generic b-pillar structures under a geometrical constraint [19; 30]. Due to the high computational demand of crash simulations, surrogate models should improve optimization speed [9; 12]. The following section reviews frameworks and Python libraries, which use optimization algorithms combined with surrogate models.