Gradient-free black-box optimization (BBO) is widely used in engineering design and provides a flexible framework for topology optimization (TO), enabling the discovery of high-performing structural designs without requiring gradient information from simulations. Yet, its success depends on two key choices: the geometric parameterization defining the search space and the optimizer exploring it. This study investigates this interplay through a compliance minimization problem for a cantilever beam subject to a connectivity constraint. We benchmark three geometric parameterizations, each combined with three representative BBO algorithms: differential evolution, covariance matrix adaptation evolution strategy, and heteroscedastic evolutionary Bayesian optimization, across 10D, 20D, and 50D design spaces. Results reveal that parameterization quality has a stronger influence on optimization performance than optimizer choice: a well-structured parameterization enables robust and competitive performance across algorithms, whereas weaker representations increase optimizer dependency. Overall, this study highlights the dominant role of geometric parameterization in practical BBO-based TO and shows that algorithm performance and selection cannot be fairly assessed without accounting for the induced design space.

翻译：无梯度黑盒优化在工程设计中广泛应用，并为拓扑优化提供了一个灵活的框架，能够在无需仿真梯度信息的情况下发现高性能结构设计。然而，其成功取决于两个关键选择：定义搜索空间的几何参数化与探索该空间的优化器。本研究通过一个受连通性约束的悬臂梁柔度最小化问题，探究了这种相互作用。我们以三种几何参数化方案为基准，每种方案分别与三种代表性黑盒优化算法结合：差分进化、协方差矩阵自适应进化策略以及异方差进化贝叶斯优化，在10维、20维和50维设计空间中进行测试。结果表明，参数化质量对优化性能的影响比优化器选择更为显著：结构良好的参数化能够在不同算法中实现稳健且具有竞争力的性能，而较弱的表示则会增加对优化器的依赖性。总体而言，本研究强调了在基于黑盒优化的实际拓扑优化中几何参数化的主导作用，并表明若不考虑所诱导的设计空间，则无法公平评估算法性能与选择。