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Comparison between two multi objective optimization algorithms : PAES and MGDA. Testing MGDA on Kriging metamodels

Adrien Zerbinati 1 Jean-Antoine Désidéri 1, * Régis Duvigneau 1 
* Corresponding author
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 [4], NSGA-II [3], etc), have been proposed in the literature and proved to be successful to identify the Pareto set. However, these derivative-free algorithms are very demanding in 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 presently. 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 the steepest-descent method and compared with PAES by numerical experiments. Using MGDA on a multi objective optimization problem requires the evaluation of a large number of points with regard to criteria, and their gradients. In the particular case of CFD problems, each point evaluation is very costly. Thus here we also propose to construct metamodels and to calculate approximate gradients by local finite differences.
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Adrien Zerbinati, Jean-Antoine Désidéri, Régis Duvigneau. Comparison between two multi objective optimization algorithms : PAES and MGDA. Testing MGDA on Kriging metamodels. Repin, S. and Tiihonen, T. and Tuovinen, T. Numerical Methods for Differential Equations, Optimization, and Technological Problems, 27, Springer Dordrecht, pp.237-252, 2013, Computational Methods in Applied Sciences, 978-94-007-5288-7. ⟨10.1007/978-94-007-5288-7⟩. ⟨hal-00765314⟩

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