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1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621

Abstract : In multi-objective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies PAES, NSGA-II, etc, have been proposed in the literature and proved to be successful to identify the Pareto set. However, these derivative-free algorithms are very remanding in terms of computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced here. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm MGDA is defined as a generalization of steepest-descent method and compared with PAES by numerical experiments.

keyword : performances Pareto front Pareto optimality Optimization gradient descent

Autor: Adrien Zerbinati - Jean-Antoine Desideri - Régis Duvigneau -



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