Hybrid Strategy Coupling EGO and CMA-ES for Structural Topology Optimization in Statics and Crashworthiness

Elena Raponi, Mariusz Bujny, Markus Olhofer, Simonetta Boria, Fabian Duddeck

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Topology Optimization (TO) represents a relevant tool in the design of mechanical structures and, as such, it is currently used in many industrial applications. However, many TO optimization techniques are still questionable when applied to crashworthiness optimization problems due to their complexity and lack of gradient information. The aim of this work is to describe the Hybrid Kriging-assisted Level Set Method (HKG-LSM) and test its performance in the optimization of mechanical structures consisting of ensembles of beams subjected to both static and dynamic loads. The algorithm adopts a low-dimensional parametrization introduced by the Evolutionary Level Set Method (EA-LSM) for structural Topology Optimization and couples the Efficient Global Optimization (EGO) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to converge towards the optimum within a fixed budget of evaluations. It takes advantage of the explorative capabilities of EGO ensuring a fast convergence at the beginning of the optimization procedure, as well as the flexibility and robustness of CMA-ES to exploit promising regions of the search space Precisely, HKG-LSM first uses the Kriging-based method for Level Set Topology Optimization (KG-LSM) and afterwards switches to the EA-LSM using CMA-ES, whose parameters are initialized based on the previous model. Within the research, a minimum compliance cantilever beam test case is used to validate the presented strategy at different dimensionalities, up to 15 variables. The method is then applied to a 15-variables 2D crash test case, consisting of a cylindrical pole impact on a rectangular beam fixed at both ends. Results show that HKG-LSM performs well in terms of convergence speed and hence represents a valuable option in real-world applications with limited computational resources.

Original languageEnglish
Title of host publicationComputational Intelligence - 11th International Joint Conference, IJCCI 2019, Revised Selected Papers
EditorsJuan Julián Merelo, Jonathan Garibaldi, Alejandro Linares-Barranco, Kevin Warwick, Kurosh Madani
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages30
ISBN (Print)9783030705930
StatePublished - 2021
Event11th International Joint Conference on Computational Intelligence, IJCCI 2019 - Vienna, Austria
Duration: 17 Sep 201919 Sep 2019

Publication series

NameStudies in Computational Intelligence
ISSN (Print)1860-949X
ISSN (Electronic)1860-9503


Conference11th International Joint Conference on Computational Intelligence, IJCCI 2019


  • Crashworthiness optimization
  • Evolution strategies
  • Hybrid methods
  • Kriging
  • Level set method
  • Moving morphable components
  • Surrogate modeling
  • Topology optimization


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