# Topology and Parametric Optimization-Based Design Processes for Lightweight Structures
## 2 Types of Structural Optimization  
Structural Optimization (SO) is a mathematical optimization of the structure's material with respect to given boundary conditions and constraints [11]. [PERSON] [12] categorized the different SO approaches, based on the mathematical form of their objective function, to Gradient-Based Topology Optimization Techniques (GTO) and Non-Gradient Topology Optimization Techniques (NGTO). On the one hand, the former category encompasses several approaches, such as the Homogenization Approach, the Density Approach (SIMP), and the gradient-based forms of the Level Set Method (LSM), the Evolutionary Structural Optimization (ESO), the Phase-Field Methods, and the Topological Derivatives. In general, the GTO techniques utilize algorithms that are characterized by a single-point search and, thus, suffer from multimodal problems. For this reason, NGTO techniques have also developed [13]. The NGTO techniques are stochastic approaches that were created to overcome the multimodal optimization problem as well as the derivation complexities created by the GTO, especially in commercial software tools. These methods allow multiple-point searches and utilize different evolution strategies such as Genetic Algorithms, Artificial Immune Algorithms, Ant Colonies, Particle Swarms, Simulated Annealing, Harmony Search, and Differential Evolution Schemes [12]. However, some of these strategies use gradient or gradient-like information in order to improve their evolutionary search for optimal solutions. A notable example of the latter category is the Covariance matrix adaptation evolution strategy (CMA-ES) based topology optimization, using a level set expression to solve multimodal optimal design problems [13]. In this paper, the LSM in ANSYS software (2019 R2 version, ANSYS, Inc., Canonsburg, PA, USA) was used to conduct the TO simulations. The theoretical background of this method is described in Section 2.1. The SO, as presented by [PERSON] and [PERSON] [14], consists of three different types of optimization: Size, shape, and topology. According to [PERSON] and [PERSON] [15], size optimization refers to the physical size of the members within the structure, such as thickness, while shape optimization refers to the geometric layout (the boundary of the state equation). There is either nonparametric (free form) or parametric shape optimization. In the case of nonparametric shape optimization, the design space consists of the surface nodes (design nodes) of the finite element model. On each of the design points, a displacement vector is placed. The scalar optimization displacements along these vectors constitute the implicit parameters in this type of free form optimization. On the other hand, the parametric shape optimization is linked to the Computer-aided design (CAD) geometry of the structure [9]. Finally, TO generates material layout concepts by changing the number and the configuration of the structure members, i.e., the number of the holes in a structure. In these three categories, we can add the topography, topometry, and lattice optimization. Topography optimization is a particular case of shape optimization where the nodes in a structure can be moved either transverse or to a given direction related to the original points using perturbation vectors [16]. Topometry optimization is a more general type of size optimization where each element can be optimized independently [16]. Finally, lattice optimization generates a lattice-optimized structure within a region of interest by including repeating cellular structures with varying thickness [17]. Figure 1 illustrates the aforementioned types of SO by presenting an example of a Hollow Plate. In this example, the size optimization of the plate could be the optimization of its thickness or/and its section size (length and height). In the case of nonparametric shape optimization, both the external shape of the Hollow Plate and the shape of its internal members (in this case, the hole's shape) could be optimized.