Which random is the best random? A study on sampling methods in Fourier surrogate modeling

Global optimization problems can be effectively solved by means of Computational Intelligence methods. However, there are several areas in which the effectiveness of these algorithms can be hampered by the computational costs of the fitness evaluations, or by specific features of the fitness landscape that can be characterized by noise and by the presence of several (even infinite) local optima. These issues bring about the necessity of defining specific techniques to replace the original problem with a surrogate representation. Fourier surrogate modeling represents a novel and effective approach to generate smoother, and possibly easier to explore, fitness landscapes, and to reduce the computational effort. Fourier surrogates require an initial sampling of the search space that must be performed to calculate the Fourier transforms. In this paper we investigate the impact on the quality of the surrogate models of the hyper-parameters of the methodology, and of several methods that can be employed for the initial sampling of the fitness landscape (i.e., pseudorandom numbers, low discrepancy sequences, a logistic map in chaotic regime, true random positions generated by a quantum computer, and point packing). Our results show that semistructured approaches like quasi-random sequences and point packing can outperform the other sampling methods.