# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 5 Conclusions  
This paper proposes a novel sketch-constrained multi-solution topology optimization algorithm, designed for human-machine collaborative structural conceptual design exploration scenarios. It allows designers to express preliminary structural design features through hand-drawn sketches, which form constraints for the topology optimization algorithm. The algorithm divides the sketch content into open-line elements and closed-shape elements, and introduces line-based undirected structural boundary constraints and closed-shape-based regional material distribution constraints. The former imposes no material distribution restrictions on the areas on either side of the lines, enabling the exploration of many novel forms that integrate the sketch's line elements into the topology, creating unique visual effects. Additionally, compared to unconstrained topology optimization, it does not reduce the morphological diversity of the design solutions. The latter drives uniform material distribution within the shape regions, which, while somewhat reducing the design exploration space and diversity, enhances the visual prominence of the sketch's shape elements. Importantly, when line constraints are already in place, this approach does not reduce structural performance, allowing designers to gradually refine local structural designs while exploring other parts of the structure in a high-quality, divergent manner. Furthermore, the mutual suppression between the two sketch constraints can further enhance design diversity. In contrast, existing sketch constraint methods only directly use the overall sketch similarity constraint to control the topology optimization results. The experiments show that the proposed method provides designers with a finer and more flexible approach to controlling algorithm results through hand-drawn sketches, allowing for better balancing of structural performance, lightweight, visual effects, design exploration diversity, and novelty. Additionally, the design diversity offered by the proposed method is significantly stronger. This algorithm also integrates Fourier mapping-based feature size control, allowing designers to combine it with sketch constraints for flexible control over both the local features and overall complexity of the generated structure. By introducing randomness through perturbations in the Fourier sampling frequency and adopting a parallel optimization strategy based on adaptive scale adjustment, the algorithm generates diversified and innovative design solutions. The experiments show that the proposed Fourier sampling frequency perturbation method outperforms existing boundary condition parameter perturbation and design domain density perturbation methods both in terms of design solution quality and diversity. Based on the proposed parallel optimization strategy, the multi-solution topology optimization algorithm in this paper offers comprehensive advantages in manual controllability, design solution quality, diversity, and computational efficiency, providing an effective solution for current topology optimization algorithms that are unsuitable for structural innovation design exploration. The research and experimental process also identified several issues that need further resolution. First, the conflict between the sketch constraints reflecting human preferences and the algorithm's structural performance optimization objective has not been fully mitigated. Although the proposed algorithm uses sensitivity-based method to detect and remove unreasonable designs from the solution set, it is better to automatically generate solutions in which the material in each part of the structure not only satisfies the sketch constraints but also contributes to mechanical performance. Also, finite element calculations are the most time-consuming step in topology optimization algorithms, and exploring ways to avoid or accelerate the finite element computation process is also a valuable area for future research.