A multilevel approach to single- and multiobjective aerodynamic optimization

An optimization platform with multilevel structure, which is capable of efficiently solving design-optimization problems in aerodynamics, is proposed. The multilevel structure relies on a two-way regular exchange of information between successive search levels. Each level can be associated with a different evaluation software, different problem parameterization and/or different search tool, for the minimization of the same objective function(s). The combination of some or all of the aforementioned strategies is possible, although beyond the scope of this paper. The basic optimization tool, which is associated with at least one of the levels, is a metamodel-assisted evolutionary algorithm; candidate solutions that have previously been examined are memorized and serve to train radial basis function networks, operating as local surrogate evaluation models. To handle multiobjective optimization problems with different search techniques at each level, we hybridize an evolutionary algorithm that computes the front of Pareto optimal solutions at the lower level(s) with a gradient-based method at the upper level, for the purpose of refinement through local search. In aerodynamic optimization, the adjoint method is used to compute the gradient of the objective function. For the gradient method to apply to a front of solutions rather than a single individual, an approximation of the SPEA-2 utility function gradient needs to be devised. The multilevel platform is demonstrated on mathematical problems as well as the design of isolated and compressor cascade airfoils.