Preference incorporation to solve many-objective airfoil design problems

In this paper, we assess the convenience of applying a previously proposed interactive method to solve three aerodynamic airfoil shape optimization problems with 2, 3, and 6 objectives, respectively. The expensive simulations required to evaluate the objective functions makes these problems an excellent example in which the use of interactive methods is very advantageous. First, the search can be focused on the decision maker's region of interest, saving this way, valuable function evaluations. Second, the preference relation used in the interactive method helps to deal with a large number of objectives since it is able to rank incomparable nondominated solutions. The experimental evaluation reveals that in the three problems studied, the interactive method achieved a better final solution than a traditional a posteriori method with no preferences. Nevertheless, in the problem with 6 objectives, only 3 of them were improved. A possible explanation for this is that local optima become harder to overcome when the size of the region of interest is very small. Additional experiments confirmed that the convergence is deteriorated if very small regions of interest are used.