Metamodel assisted multiobjective optimisation strategies and their application in airfoil design

In this paper various metamodel-assisted multiobjective evolutionary algorithms (M-MOEA) for optimisation with time-consuming function evaluations are proposed and studied. Gaussian field (Kriging) models fitted by results from previous evaluations are used in order to pre-screen candidate solutions and decide whether they should be rejected or evaluated precisely. The approximations provide upper and lower bound estimations for the true function values. Three different rejection principles are proposed, discussed and integrated into recent MOEA variants (NSGA-II and epsilon-MOEA). Experimental studies on a theoretical test case and in airfoil design demonstrate the improvements in diversity of solutions and convergence to the pareto fronts that can be achieved by using metamodels for pre-screening.