Evolutionary optimization using a new radial basis function network and the adjoint formulation

This article aims at extending previously published ideas on the formulation and use of low-cost surrogate evaluation tools in the context of optimization methods based on evolutionary algorithms (EAs). Our goal is to minimize the cost of solving optimization problems with computationally expensive evaluations. A search algorithm is proposed which brings together computational fluid dynamics tools, namely flow and adjoint equation solvers, new radial basis function networks (RBFNs) and standard EAs. The new RBFNs involve additional control parameters which allow their training on patterns for which both responses and their gradients are available. In aerodynamic shape optimization problems, the gradient can be computed through the adjoint method. Despite the known role of adjoint methods, i.e. that of computing local search directions, in the proposed method they are used to enrich the available information for the training of the surrogate evaluation models, through providing the objective function gradient for each and every pattern. Based on a number of preselected samples, with known responses and gradients, the proposed RBFN is trained and used as the exclusive evaluation tool during the evolutionary search. A small number of cycles is required so as to capture the global optimal solution. A cycle includes the exact evaluation of the outcome of the evolutionary search, the RBFN update after retraining it on the enriched database, and a new search based on the updated RBFN. The method application is demonstrated through single- and multi-objective mathematical problems as well as the inverse design of a peripheral compressor cascade.