Preference-driven Kriging-based multiobjective optimization method with a novel multipoint infill criterion and application to airfoil shape design

Abstract

Multipoint infill sampling has emerged recently as a promising tool to enhance the efficiency of the adaptive Kriging-based optimization method for computational expensive multiobjective problems. However, the number of infill samples in each iteration in the open literature is up to 10. A novel multipoint infill criterion is proposed on the basis of Expected Angle-Penalized Length Improvement (EAPLI). One of its distinct features is that it makes the number of infill samples in each iteration increase tenfold along with a fair convergence speed by using multiple reference vectors to search for multiple infill points. Its implementation involves several major elements: firstly, angle-penalized length based improvement is established for each reference vector; then maximizing EAPLI is conducted for all vectors to obtain sufficient candidate infill points; finally, multiple infill points are selected from the candidate pool according to the candidate niche counts. Experimental results on benchmark test problems show that the proposed EAPLI criterion is highly competitive in comparison with other criteria. Then the performance of EAPLI using different numbers of multiple infill points, from several to tens and even a hundred, is studied. The other distinct feature of EAPLI is, the distribution of reference vectors can be manipulated to include the designer's preferences to perform preference-driven optimization, which can reduce searches towards solutions violating the preferences and thus further enhance the optimization efficiency. A preference-driven airfoil shape optimization method is established by integrating the EAPLI, free-form deformation method, and a flow solver. It is used to optimize the NACA0012 airfoil, by which the non-dominated solutions are fairly driven into the preferred subspaces with significant gains in both objectives of lift/drag coefficient ratio and drag coefficient simultaneously.