## 1 Introduction  
A common way to save weight in structural design is to use optimization approaches in the product development process (PDP) [1, 2], such as topology, shape, and size optimization. Certainly, engineers apply the mentioned optimization types in different stages of the PDP, for instance, the preliminary or conceptual design. Engineers mostly use shape optimization in all design-relevant stages of the PDP. Primarily, Computer-aided Design (CAD) and Non-Uniform Rational B-Splines (NURBS)-based approaches vary the geometry of parts before the geometry is meshed and calculated [3, 4]. Especially in automotive design, complex structures with multiple requirements exist, with crash safety being the most challenging. Due to decreasing computational cost, crash calculations are state of the art in the automotive design process regarding the dimensioning of structural components. Notably, optimizing the Body-in-White (BIW) structures with shape optimization typically results in costly numerical evaluations. Each evaluated data point represents a linear and, often, also a non-linear calculation. Hence, the potential of automotive BIW crash optimization strongly depends on optimization algorithms that precisely find a good design by using a minimum of the expensive function evaluations. For instance, good designs in a crash are lightweight and fulfill all requirements towards crash safety, package, and structural stiffness [5; 6; 7]. There are different optimization algorithms that assist in minimizing the objective and constraint functions. [PERSON] and [PERSON] [8] optimized the mass, energy absorbed, maximum section force, deflection, and intrusion of a bumper structure under crash load. Common engineering optimization problems such as crash optimization are black-box functions. They usually exhibit numerical noise, multimodal behavior, and uncertainties. In this case, deterministic search strategies cannot be used, as deterministic methods require the problem to exhibit specific mathematical characteristics. These characteristics are not given in crash optimization [9; 10]. The most common algorithm type, which operates this optimization problem sufficiently and effectively, are heuristic and metaheuristic optimization approaches. Problems with these approaches arise when black-box evaluations are costly. In this case, surrogate models can significantly improve the amount of high-fidelity computer simulations. In particular, this is even more critical for multi-objective optimization tasks [9]. Indeed, a surrogate model is a mathematical model that provides cheaper responses to the input-output relationship for computationally expensive jobs [11]. Optimizing BIW components in automotive crashes combines multiple challenges, such as multimodality, costly functional evaluations for numerical analysis, numerical noise, and multi-objective target functions. For instance, suitable surrogates and optimization algorithms play an outstanding role in these optimization tasks [12; 13; 14]. Such processes use different optimization strategies such as Single-Objective Optimizations (SOOs) to handle one and Multi-Objective Optimizations (MOOs) to handle multiple objective functions [15]. In SOOs, all objectives and constraints are summed to a single objective function using approaches such as the weighted-sum-method. The algorithm optimizes only one objective function [16]. At the same time, MOO algorithms offer a more extensive solution space but lead to a higher dimensionality of the optimization problem by creating Pareto-efficient designs [15]. During the development process, the main obstacles in BIW design are the strict geometry and design requirements, which need to be considered [17]. Engineering optimization typically fails to handle these geometry-based constraints during optimization. For this reason, a new approach for the handling of geometrical constraints in package and design optimization was implemented in a Python-based framework called IKOS [18] by the authors.