## 1 Introduction  
Topology optimization (TO) naturally gives a wider set of possibilities and a larger degree of freedom with regard to the design space availability, as compared to size and shape optimization. Due to this, TO has been the most widely accepted and well-established structural optimization tool [1]. To improve the performance of TO, passing through a natural process of scientific progress, several approaches have been established, such as the homogenization method [2, 3], the SIMP method [4, 5], the level set method [6, 7], the MMC/MMV method [8, 9], and some evolutionary and heuristic methods [10, 11, 12]. For the last few decades, TO has been implemented effectively as a conceptual design tool to achieve the desired mechanical performance with feasible manufacturing [1, 13, 14]. The desired mechanical performance is achieved with the help of a specific objective function (e.g., compliance minimization, maximization of fundamental frequency, mass reduction, etc.) and suitable design constraints (e.g., displacement, fatigue, stress, etc.). Similarly, the feasible manufacturing is obtained through several manufacturing constraints (e.g., draw, extrusion, member size, overhang size, symmetry, etc.). Before the advent of additive manufacturing (AM), manufacturing of the topologically optimized designs was challenging task, sometimes not totally achievable,due to complex geometrical features and hidden cavities. Though several manufacturing constraints could have been considered in order to facilitate conventional manufacturing, a process of remodeling of the optimized design was required for achieving a feasible manufacturing. This procedure resulted not only in an increase of the final mass of the piece, but also in an increase of the design processing time. Therefore, the advent of additive manufacturing and its subsequent advancements further increased the applications of topology optimization with regard to a feasible manufacturing of complex geometries without any remodeling (or, in a few cases, with little remodeling operations connected to specific AM constraints). TO presents numerous remarkable practical applications such as the design of structures with multi-objectives [15], multi-scale [16; 17; 18] and multi-material [19; 20], design of functionally graded structures [21; 22], design of energy absorption structures to improve resistance against crash failures [23; 24], design of periodic structures to improve stability against buckling failure [25], design of architectural structures [26; 27], production of sustainable design [28], etc. Similarly, TO provides several other worthwhile applications in conjunction with other optimization tools such as TO with lattice structures to improve resistance against buckling failure [29; 30], and designing efficient heat dissipation structures [31], TO with shape optimization [32; 33] for better shape and maximum weight reduction, TO with generative design [34; 35] to achieve better structural performance, or with tools able to select design variants for optimizing both product and process features [36], etc. Furthermore, researchers are currently working on TO in order to produce some state-of-the-art designs regarding structures with negative Poisson ratio [37], structures with negative thermal expansion [38], structures with natural convection [39], load-supporting structures for civil engineering [40; 41], etc. On the other hand, there are still some open issues evolving around TO. These issues are mainly concerned with the aesthetic problem [42]; additive manufacturing problems related to large overhanging members [43; 44; 45; 46], the remodeling of the optimized structure due to poor shape geometry [47]; stress-related problems [48; 49; 50]; the application of manufacturing constraints [14]; the optimization of multi-scale and multi-material structures [16; 17; 18; 19; 20], etc.