Multilevel optimization strategies based on metamodel-assisted evolutionary algorithms, for computationally expensive problems

Abstract — In this paper, three multilevel optimization strate-gies are presented and applied to the design of isolated and cascade airfoils. They are all based on the same general–purpose search platform, which employs Hierarchi-cal, Distributed Metamodel–Assisted Evolutionary Algorithms (HDMAEAs). The core search engine is an Evolutionary Algo-rithm (EA) assisted by local metamodels (radial basis function networks) which, for each population member, are trained anew on a “suitable ” subset of the already evaluated solutions. The hierarchical scheme has a two–level structure, although it may accommodate any number of levels. At each level, the user may link (a) a different evaluation tool, such as low or high fidelity discipline–specific software, (b) a different optimization method, selected amongst stochastic and deterministic algo-rithms and/or (c) a different set of design variables, according to coarse and fine problem parameterizations. In the aerodynamic shape optimization problems presented in this paper, the three aforementioned techniques resort on (a) Navier–Stokes and integral boundary layer solvers, (b) evolutionary and gradient– descent algorithms where the adjoint method computes the objective function gradient and (c) airfoil parameterizations with different numbers of Bézier control points. The EAs used at any level are coarse–grained distributed EAs with a different MAEA at each deme. The three variants of the HDMAEA can be used either separately or in combination, in order to reduce the CPU cost. The optimization software runs in parallel, on multiprocessor systems