Global Optimization for Noisy Expensive Black-Box Multi-Modal Functions Via Radial Basis Function Surrogate

This study proposes a new surrogate global optimization algorithm that solves problems with expensive black-box multi-modal objective functions subject to homogeneous evaluation noise. Specifically, we propose a new radial basis function (RBF) surrogate to approximate noisy functions and extend the Stochastic Response Surface method, which was developed for deterministic problems, to optimize noisy functions. Instead of conducting multiple replications at each point to mitigate the influence of noise, we only do a single observation at every sampled point and regularize the RBF surrogate by penalizing the bumpiness. The proposed algorithm sequentially identifies a new point for the expensive function evaluation from a set of randomly generated candidate points using both exploitation and exploration. Numerical studies show that the proposed noisy RBF surrogate can produce reliable approximations for noisy functions, and the proposed algorithm is effective and competitive in solving the global optimization problems with noisy evaluations.