TSI metamodels-based multi-objective robust optimization

Pietro Marco Congedo (INRIA Bordeaux Sud-Ouest, Talence, France)
Gianluca Geraci (INRIA Bordeaux Sud-Ouest, Talence, France)
Rémi Abgrall (INRIA Bordeaux Sud-Ouest, Talence, France)
Valentino Pediroda (Mechanical and Naval Engineering Department, Università di Trieste, Trieste, Italy)
Lucia Parussini (Mechanical and Naval Engineering Department, Università di Trieste, Trieste, Italy)

Engineering Computations

ISSN: 0264-4401

Publication date: 11 November 2013



This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.


ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows.


First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1− TSI )×100, where TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy.


Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.



Rémi Abgrall has been financed in part by the EU ERC Advanced Grant “ADDECCO” N. 226316. Gianluca Geraci has been fully financed by the EU ERC Advanced Grant “ADDECCO” N. 226316.


Marco Congedo, P., Geraci, G., Abgrall, R., Pediroda, V. and Parussini, L. (2013), "TSI metamodels-based multi-objective robust optimization", Engineering Computations, Vol. 30 No. 8, pp. 1032-1053. https://doi.org/10.1108/EC-01-2012-0012

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