# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 2 Related Works  
### Human Control in Topology Optimization  
The main advantage of TO is that designers only need to specify the design objectives, constraints, and load conditions within the design domain, without the need to provide prior knowledge for structural design parameterization. Most existing TO algorithms, particularly the earlier developed ones [29; 30; 31], provide an optimal solution of structural topology for a TO problem according to the design factor of mechanical performance. However, as numerous factors need to be considered in engineering practice, the TO algorithms fail to produce satisfactory solutions directly, leading to laborious iterations between human designers and the algorithms [32; 33]. This problem became more pronounced due to the immature post-processing techniques of TO solutions. Effective human control over TO solutions is the key to this problem, which is becoming a highlight topic in this research field. Recent studies on this problem have focused on controlling the length scale of geometric features [14; 15; 16; 17; 18], as the length scale is very important not only for mechanical performance but also other factors like manufacturability. Traditional TO algorithms tend to generate excessively fine-grained structures, which can incur problems in addictive manufacturing process such as local collapse or difficulty in support material removal. [PERSON] et al. [15] and [PERSON] et al. [16] achieved interactive control of the feature sizes within a region of interest through a proximity-based weighting function and three-phase projection scheme, respectively. The latter further enabled control of multi-phase maximum and minimum solid feature sizes and/or void feature sizes. [PERSON] et al. [34] explicitly derived the numerical formulation of minimum structural feature size constraints for density-based TO algorithms, offering broad applicability and low sensitivity to algorithm parameters. [PERSON] et al. [35] introduced a hole-filling strategy in the bidirectional evolutionary structural optimization (BESO) framework to control structural complexity by filling internal cavities and tunnels, respectively, with preset structures whose size parameters were adjustable. [PERSON] et al. [14] introduced a Fourier mapping layer in a density-based neural implicit TO framework to control the maximal and minimal geometric feature size. [PERSON] et al. [36] provided a detailed review and comparative analysis of studies on length-scale control for density-based TO algorithms. Research on human controllability also includes using specific geometric patterns [19; 20; 21; 22]. [PERSON] et al. [19] used predefined texture patterns to guide the optimization, dividing the design domain into multiple groups, where the repetition of the control pattern within each group was managed independently. [PERSON] et al. [20] achieved similar controllability by arranging predefined patterns to determine the design domain. [PERSON] et al. [21] derived specific geometric constraints for the internal regions of shell structures to make the generated structures match the predefined patterns. [PERSON] et al. [25] proposed using free-hand sketches for TO guidance by extracting multi-level morphological features from design images using convolutional neural networks and introducing a similarity constraint between the extracted morphological features of TO solutions and the sketch. Their proposed method generates structural designs that embody the high-level morphological semantics of the sketch. [PERSON] et al. [23] used aesthetic images as guidance, employing independent feature extraction neural modules for the aesthetic style and form content of the images, respectively, which were then used to apply separate constraints. [PERSON] et al. [37] proposed exploiting the text-image priors embedded in the CLIP model [38] to enable text-based control over the aesthetic styling of the generated structures. [PERSON] et al. [12] proposed combining drawing guidance with manual scoring to modify TO solutions interactively.