Efficient multi-objective shape optimization using proper orthogonal decomposition with variable fidelity concept

Abstract

A variable fidelity concept is introduced in a re-parameterization approach based on the proper orthogonal decomposition (POD) to efficiently solve multi-objective aerodynamic shape optimization problems. The re-parameterization approach enables to extract dominant shape deformation modes from a database of good designs and to reduce the number of design variables. The present variable fidelity approach is proposed by utilizing low-fidelity functional evaluations to select the good designs. The proposed approach is investigated in two multi-objective aerodynamic shape optimization problems of 2D airfoil in which the combinations of viscous/inviscid simulations or fine/coarse grid simulations are treated as the high/low-fidelity evaluation methods. It can be confirmed that dominant POD modes obtained from low-fidelity evaluations are qualitatively equivalent with that obtained from high-fidelity evaluations. Non-dominated solutions obtained from a conventional optimization approach can be reproduced with smaller numbers of design variables using the dominant POD modes. The computational costs to solve the multi-objective aerodynamic shape optimization problems can be dramatically reduced by introducing the variable fidelity concept.