Application of Metamodel-Assisted Multiple-Gradient Descent Algorithm (MGDA) to Air-Cooling Duct Shape Optimization

Adrien Zerbinati (1) , Jean-Antoine Désidéri (1) , Régis Duvigneau (1)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

MGDA stands for Multiple-Gradient Descent Algorithm, which was introduced in a previous report. MGDA was tested on several analytical test cases and also compared with a well-known Evolution Strategy algorithm, Pareto Archived Evolution Strategy (PAES). Using MGDA in a multi-objective optimization problem requires the evaluation of a substantial number of points with regard to criteria, and their gradients. In industrial test cases, in which computing the objective functions is CPU demanding, a variant of the method was to be found. Here, a metamodel-assisted MGDA is proposed and tested. The MGDA is assisted by a Kriging surrogate model construction. A first database is computed as an Latin Hypercube Sampling (LHS) distribution in the admissible design space, which is problem-dependent. Then, MGDA leads each database point to a non dominated set of the surrogate model. In this way, each function computation is made on the surrogate model at a negligible computational cost.

Domaines: Analyse numérique [cs.NA]

Adrien Zerbinati, Jean-Antoine Désidéri, Régis Duvigneau. Application of Metamodel-Assisted Multiple-Gradient Descent Algorithm (MGDA) to Air-Cooling Duct Shape Optimization. ECCOMAS - European Congress on Computational Methods in Applied Sciences and Engineering - 2012, Sep 2012, Vienna, Austria. ⟨hal-00742948⟩