# Topology and Parametric Optimization-Based Design Processes for Lightweight Structures
## 5 Conclusions  
In this paper, a comparative study was conducted among ten design processes concerning TO and size/shape PO or possible combinations of them with a focus on mass reduction, optimization time, and maximum stress. In particular, three different case studies were used: A Hollow Plate, L-Bracket, and an MBB-Beam to apply the different processes presented here and compare their results. Three main design workflows were tested. In the first workflow, a TO of the structures was carried out at the first level, together with a possible redesign of the design solution, and a size PO at the second level. The second workflow was started with a size/shape PO at the first level, followed by a TO at the second one, and finished with a size PO at the third level. Finally, the third workflow constituted a simultaneous size/shape PO and TO of the structures at the first level, and a further size PO of the design result at the second. Furthermore, validation studies were executed for each of these processes concerning a FOS \(\geq\) 2. The results from all the case studies showed that following the processes from left to right, as they were presented in Figure 3, there is a continuous mass reduction of the structures while the process duration increased dramatically.  
There is no clear answer to the question about what the best process was. This depends on the designer's criteria. If the most crucial criterion is the mass reduction, regardless of the optimization time, the simultaneous size/shape PO and TO workflow (processes 8-10) gave the best results. On the other hand, if time is essential, the TO process gave the quickest design solutions. Concerning the maximum stress, it is not clear which process was better, and it is something that depends on the tested structure. Hence, the above conclusions are case dependent in a sense that starting from another initiation, the TO will result in a different local minimum of different performance. In this  
Figure 19: (**a**) The mass reduction in TO, PO, and PO + TO workflows, and (**b**) an illustration of the mass reduction in the three workflows vs. the size and design complexity, as well as typical examples in each workflow.  
work, the authors just consider the standard ANSYS implementation, which consists in starting with a full design domain initialization (no other alternative is provided), thus no trial and error were possible. However, the above conclusions are, in general, expected to apply true for the majority of test cases.  
There is a plethora of possible combinations between SO and PO. It is the designer who should choose the process that fits best with the specific design problem that he/she tries to confront. The parametrization of the structures' geometry and the choice of the factors in a PO is challenging and time demanding. The SA, together with the RSM, contributed to the identification of the most crucial design parameters. This reduced the optimization parameters and, thus, the optimization time. Furthermore, TO may lead to complex geometries that cannot be manufactured with conventional methods, or they are limited to the capabilities of 3D printing. Even though the redesign is a subjective, time-consuming procedure, and always dependent on the designer, it can increase the manufacturability of the topologically optimized design solutions. Finally, it can be concluded that both PO and TO have their advantages and disadvantages, but it is clear that their results are based on the designer choices before and after each optimization phase.