Open Access

ARTICLE

Systematic Benchmarking of Topology Optimization Methods Using Both Binary and Relaxed Forms of the Zhou-Rozvany Problem

Jiye Zhou¹, Yun-Fei Fu², Kazem Ghabraie^1,*

1 School of Engineering, Deakin University, Geelong, VIC 3216, Australia
2 Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada

* Corresponding Author: Kazem Ghabraie. Email:

(This article belongs to the Special Issue: Topology Optimization: Theory, Methods, and Engineering Applications)

Computer Modeling in Engineering & Sciences 2025, 143(3), 3233-3251. https://doi.org/10.32604/cmes.2025.065935

Received 25 March 2025; Accepted 30 May 2025; Issue published 30 June 2025

Abstract

Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits. However, when benchmarking these methods, researchers use known solutions to only a single form of benchmark problem. This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms. A greyness measure is implemented to evaluate how far a solution is from the desired binary form. The well-known Zhou-Rozvany (ZR) problem is selected as the benchmarking problem here, making use of available global solutions for both its relaxed and binary forms. The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology (SEMDOT), well-established Solid Isotropic Material with Penalization (SIMP), and continuation methods are studied on this platform. Interestingly, in most cases, the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP. The reasons are investigated and attributed to the usage of two different regularization techniques, namely, the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP. More importantly, a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.

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Keywords

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