An optimization algorithm combining local exploitation and global exploration for computationally expensive problems

An adaptive ensemble of surrogates assisted optimization algorithm combining local exploitation and global exploration (CLEGE) for computationally expensive problems is presented in this work. At the first level, two subspaces are created to accelerate the local search. Subspace1 is a promising region determined by fuzzy c-means clustering method, and Subspace2 is a promising region around the current best solution. Subsequently, the presented local exploitation using multi-spaces reduction is carried out to alternately achieve more promising points in the original global space, Subspace1 and Subspace2. Furthermore, the estimated mean square error of Kriging will be maximized for exploring the sparsely sampled regions, once CLEGE algorithm falls into the local optimum. Tested using twenty mathematical problems and one airfoil design optimization example, CLEGE shows superior sampling capability, better search efficiency and strong stability in solving the computationally expensive optimization problems.