@book {pub4215,
	title = {Hybrid Strategy Coupling EGO and CMA-ES for the Topology Optimization of Crash Structures},
	author = {Elena Raponi AND Mariusz Bujny AND Markus Olhofer AND Simonetta Boria AND Fabian Duddeck},
	year = {2021},
	month = {July},
	abstract = {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 domain. 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.},
	publisher = {Springer, LNCS, LNAI, LNBI},
	booktitle = {Computational Intelligence. IJCCI 2019.},
	editor = {Merelo J.J., Garibaldi J., Linares-Barranco A., Warwick K., Madani K.},
	city = {Cham},
	edition = {1},
	volume = {922},
	series = {Studies in Computational Intelligence}
}