Benchmarking optimization solvers for structural topology optimization

Susana Rojas Labanda, Mathias Stolpe

Research output: Contribution to journalJournal articleResearchpeer-review


The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Issue number3
Pages (from-to)527-547
Publication statusPublished - 2015


  • Benchmarking
  • Nonlinear optimization
  • Optimization methods
  • Topology optimization

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