Application of MGDA to domain partitioning

Jean-Antoine Désidéri 1
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 : This report is a sequel to several publications in which a {\em Multiple-Gradient Descent Algorithm (MGDA)} has been proposed and tested for the treatment of multi-objective differentiable optimization. The method was originally introduced in \cite{JAD09:MGDA}, and again formalized in \cite{JAD12:MGDA-CRAS}. Its efficacy to identify the Pareto front has been demonstrated in \cite{JAD11:MGDA-PAES}, in comparison with an evolutionary strategy. Finally, recently, a variant, {\em MGDA II}, has been proposed in which the descent direction is calculated by a direct procedure \cite{JAD12:MGDA2}. In this new report, the efficiency of the algorithm is tested in the context of a simulation by domain partitioning, as a technique to match the different interface components concurrently. For this, the very simple testcase of the finite-difference discretization of the Dirichlet problem over a square is considered. The study aims at assessing the performance of {\em MGDA} in a discretized functional setting. One of the main teachings is the necessiy, here found imperative, to normalize the gradients appropriately.
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Jean-Antoine Désidéri. Application of MGDA to domain partitioning. [Research Report] RR-7968, INRIA. 2012, pp.34. ⟨hal-00694039v2⟩

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