Comparison of multiobjective gradient-based methods for structural shape optimization

Abstract : This work aims at formulating a shape optimization problem within a multiobjective optimization framework and approximating it by means of the so-called Multiple-Gradient Descent Algorithm (MGDA), a gradient-based strategy that extends classical Steepest-Descent Method to the case of the simultaneous optimization of several criteria. We describe several variants of MGDA and we apply them to a shape optimization problem in linear elasticity using a numerical solver based on IsoGeometric Analysis (IGA). In particular, we study a multiobjective gradient-based method that approximates the gradients of the functionals by means of the Finite Difference Method; kriging-assisted MGDA that couples a statistical model to predict the values of the objective functionals rather than actually computing them; a variant of MGDA based on the analytical gradients of the functionals extracted from the NURBS -based parametrization of the IGA solver. Some numerical simulations for a test case in computational mechanics are carried on to validate the methods and a comparative analysis of the results is presented.
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Rapport
[Research Report] RR-8511, INRIA. 2014, pp.26
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  • HAL Id : hal-00967601, version 1

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Matteo Giacomini, Jean-Antoine Désidéri, Régis Duvigneau. Comparison of multiobjective gradient-based methods for structural shape optimization. [Research Report] RR-8511, INRIA. 2014, pp.26. 〈hal-00967601〉

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