Application of Metamodel-assisted Multiple-gradient Descent Algorithm (mgda) to Air-cooling Duct Shape Optimization

MGDA stands for Multiple-Gradient Descent Algorithm was introduced in [1]. In a previous report [2], MGDA was tested on several analytical test cases and also compared with a well-known Evolution Strategy algorithm, Pareto Archived Evolution Strategy (PAES) [3]. 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.