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

2026-01-29

AI Summary

This study investigates the interplay between geometric parameterization and optimizer selection in gradient-free topology optimization, where their relative impact on performance remains unclear. Using compliance minimization of a cantilever beam as a benchmark, the authors systematically evaluate three geometric parameterization schemes in conjunction with three gradient-free black-box optimization algorithms—Differential Evolution, CMA-ES, and Heteroscedastic Evolutionary Bayesian Optimization—across varying design space dimensions. The findings reveal that the quality of geometric parameterization exerts a far greater influence on optimization performance than the choice of optimizer: high-quality parameterizations consistently yield robust and competitive results across all algorithms, whereas poor parameterizations significantly increase reliance on specific optimizers. This work underscores the decisive role of design space structure in algorithm evaluation.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• topology optimization
• gradient-free optimization
• parameterization
• black-box optimization
• cantilever beam

Innovation

• gradient-free optimization
• topology optimization
• geometric parameterization
• black-box optimization
• design space structure