Investigating the Interplay of Parameterization and Optimizer in Gradient-Free Topology Optimization: A Cantilever Beam Case Study

• URL: http://arxiv.org/abs/2601.22241v2
• Date: Mon, 02 Feb 2026 11:12:21 GMT
• Title: Investigating the Interplay of Parameterization and Optimizer in Gradient-Free Topology Optimization: A Cantilever Beam Case Study
• Authors: Jelle Westra, Iván Olarte Rodríguez, Niki van Stein, Thomas Bäck, Elena Raponi,
• Abstract summary: This study investigates the interplay through a minimization problem for a cantilever beam subject to a connectivity constraint.<n>We benchmark three geometric parameterizations, each combined with three representative BBO algorithms.<n>Results reveal that parameterization quality has a stronger influence on optimization performance than choice.
• Score: 1.7414095108022616
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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