@article {2020,
	title = {A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems},
	journal = {SIAM Journal on Scientific Computing},
	volume = {43},
	year = {2021},
	chapter = {B831},
	abstract = {<p>In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions {\textendash} Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov {\textendash} and finally we apply it to an aeronautical shape optimization problem.</p>},
	doi = {https://doi.org/10.1137/20M1345219},
	url = {https://arxiv.org/abs/2006.07282},
	author = {Nicola Demo and Marco Tezzele and Gianluigi Rozza}
}
@conference {2019,
	title = {Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces},
	booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019},
	year = {2019},
	abstract = {<p>We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.</p>},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075390244\&partnerID=40\&md5=3e1f2e9a2539d34594caff13766c94b8},
	author = {Marco Tezzele and Nicola Demo and Gianluigi Rozza}
}
@conference {demo2018shape,
	title = {Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition},
	booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research},
	year = {2018},
	publisher = {IOS Press},
	organization = {IOS Press},
	chapter = {212},
	address = {Trieste, Italy},
	abstract = {Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship.},
	doi = {10.3233/978-1-61499-870-9-212},
	url = {http://ebooks.iospress.nl/publication/49229},
	author = {Nicola Demo and Marco Tezzele and Gianluca Gustin and Gianpiero Lavini and Gianluigi Rozza}
}
