Abstract—A new methodology for deriving surrogate models for solving black-box optimization problems has been developed in this study. A discrete Fourier series was derived from the conventional Fourier series formulation and principles associated with the discrete Fourier transform, and used for the reformulation of black-box objective functions as continuous functions. A stochastic global optimization technique known as Particle Swarm Optimization (PSO) was then applied to locate the global optimal solutions of the continuous functions derived. The methodology was applied to the solution of a black-box optimization problem that was simulated on the basis of the Himmelblau function.
Index Terms—Black-box optimization, discrete Fourier series, global optimization, particle swarm optimization, surrogate models
E. W. C. Lim is with the Department of Chemical & Biomolecular Engineering, National University of Singapore (e-mail: chelwce@nus.edu.sg).
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Cite: Eldin Wee Chuan Lim, "Application of Discrete Fourier Series for Surrogate Modeling,"
International Journal of Chemical Engineering and Applications vol. 3, no. 6, pp. 369-399, 2012.
