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

TL;DR

This paper examines how the choice of geometric parameterization and optimizer affects the effectiveness of gradient-free topology optimization for a cantilever beam, emphasizing the importance of parameterization quality over optimizer selection.

Contribution

It systematically benchmarks different parameterizations and algorithms, demonstrating the dominant influence of parameterization quality on optimization success in topology optimization.

Findings

Parameterization quality strongly influences optimization performance.

Well-structured parameterizations lead to robust results across algorithms.

Weaker representations increase dependency on optimizer choice.

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.