# Topology and Parametric Optimization-Based Design Processes for Lightweight Structures
## 1 Introduction  
Two notable categories in Structural Optimization (SO) are the Parametric Optimization (PO) and Topology Optimization (TO). These optimization approaches have been increasingly applied as material reduction methods in the industry over the last decades. The gains from these optimization methods are notable and have thoroughly been presented in the literature [1; 2]. On the one hand, PO allows a selective optimization of the model based on the given parameters and their value range. It can easily guide to global shape and size optimum solutions for linear and convex problems, but it cannot optimize the topology of the structure [3]. Furthermore, both the Design of Experiments (DOE) and Sensitivity Analysis (SA) were developed simultaneously with the PO to support the implementation and the choice of the most crucial parameters in optimization, respectively [4]. On the other hand, TO reduces the material usage while enhancing both the quality and the robustness of the structures. In addition, it increases the design flexibility, as well as shortens the design process and thus the time to market [5]. However, it is a hard and time-demanding procedure, which can result in complex shapes that are difficult and expensive to be manufactured. For this reason, TO can be categorized as TO for Additive Manufacturing (AM) and TO for Conventional Manufacturing Processes (CMP). The traditional TO is mainly oriented to AM. In general, the topologically optimized design solutions are characterized by their organic shapes. AM enables the direct use of these shapes and decreases the number of geometric restrictions. However, it is possible to prefer CMP to AM. In this case, the designer adds the corresponding geometric restrictions due to manufacturing constraints, suchas design for extrusion or size minimums [6]. The choice between these two different TO orientations depends on the optimized design, the cost, and the production time. A plethora of research papers focused on either development of new approaches or improvement of the existing optimization methods [7; 8]. However, there is limited literature that compares the aforementioned optimization methods or possible combinations of them with respect to their results and optimization time [9; 10]. The identification of the ideal design process is challenging. Furthermore, the geometric and boundary uncertainties in a fuzzy design environment make this decision harder. In this paper, the authors answer critical questions about practical issues in both TO and PO. Concerning the post-processing of the topology optimized results, it is not clear if a designer will use them as a starting point of his/her initial designs or if they will constitute the final designs of a structure. In the second case, AM, with 3D printing, is inevitable as a manufacturing method while the CMP can mainly be used in the first case. Furthermore, possible combinations between topology and parametric optimization were explored in the pursuit of the ideal design process with respect to mass reduction and maximum stress as measuring parameters. In addition to them, an approximation of the optimization time was calculated. The optimization time encompasses the used time for the individual phases of TO, PO, Validation (V), and Redesign (R) and was calculated based on the software's outputs and the designer's measurements. Different combinations of topology and parametric optimization were developed. In particular, ten design processes were created in this comparative study. The main goal was to identify the ideal methodology based on the aforementioned parameters. For this reason, three benchmarking examples, a Hollow Plate, an L-Bracket, and a Messerschmitt-Bolkow-Blohm Beam (MBB-Beam), were used as case studies. The designer looking for lightweight structures could use the findings of this paper to choose the design process that fits his/her design case and optimization goals.