Epistasis-tunable test functions with known maximum constructed with sinusoidal bases

Epistasis-tunable fitness landscapes are useful to evaluate the performance of a genetic algorithm (GA). Such landscapes have generally been produced within the framework of Walsh polynomials or general parametric interaction models. This paper attempts a novel way by constructing test functions with sinusoidal basis functions. It is remarked that, for a GA with a binary encoding, a linearly separable fitness function, i.e., a zero-epistasis fitness function, can be expressed as the sum of periodical basis functions whose frequencies are exponential to 2, and the sinusoidal bases with such frequencies are much more suitable than those with other integral frequencies to construct epistasis-tunable test functions. A kind of test functions are accordingly produced, the merits of which are: both the locations and values of their global maxima are trivially known; and their degrees of epistasis are smoothly tunable simply by changing the locations of the global maxima.