A model-assisted memetic algorithm for expensive optimization problems

This chapter proposes a new model-assisted memetic algorithm for expensive optimization problems. The algorithm follows successful optimization approaches such as a combined global-local, modelling and memetic optimization. However, compared to existing studies it offers three novelties: a statistically-sound framework for selecting optimal models during both the global and the local search, an improved trust-region framework and a procedure for improved exploration based on modifying previously found sites. The proposed algorithm uses a radial basis function neural network as a global model and performs a global search on this model. It then uses a local search with a trust-region framework to converge to a true optimum. The local search uses Kriging models and adapts them during the search to improve convergence. A rigorous performance analysis is given where the proposed algorithm is benchmarked against four reference algorithms using eight well-known mathematical test functions. The individual contribution of the components of the algorithm is also studied. Lastly, the proposed algorithm is also applied to a real-world application of airfoil shape optimization where it is also benchmarked against the four reference algorithms. Statistical analysis of all these tests highlights the beneficial combination of the proposed global and local search and shows that the proposed algorithm outperforms the reference algorithms.