Computing with Haar functions
Sami Khuri · 1997
Walsh functions are orthogonal, rectangular functions that take values \\Sigma1 and form a convenient basis for the expansion of genetic algorithm fitness functions. Since their introduction into genetic algorithms [2, 8], they have been used to compute the average fitness values of schemata, to decide whether functions are hard or easy for genetic algorithms, and to design deceptive functions for the genetic algorithm. In [10], Haar functions were introduced as an alternative to Walsh functions and it was shown that Haar functions are in general more computationally advantageous. This paper revisits Haar functions, albeit with a slight variation to [10]'s definition, uses the functions to construct fully deceptive functions for the genetic algorithm (as was done with Walsh functions [5]), and studies fast Haar transforms and fast Walsh-Haar transforms. 1 Introduction Orthonormal bases have captured the attention of researchers in a variety of fields. In wavelet theory, "orthonormal w...