Supply of Order-1 Building Blocks for Functions Linearly Combined of Sinusoidal Bases with Integral Frequencies

摘要

In line with the theory of schema sampling, a hypothesis could be made that sufficient supply of low-order building blocks (BBs) was one of the necessary conditions for a genetic algorithm(GA) to work. A consequential question of this hypothesis regards, when a certain fitness function is optimized with a commonly used GA, whether it is rare or common that there are plenty of low-order BBs. It is remarked that, when a base-m encoded GA is applied to a fitness function that is linearly combined of sinusoidal basis functions with integral frequencies, it is unlikely to obtain order-1 BBs with fixed positions at multiple loci, i.e., it is rare that there are plenty of order-1 BBs. However, if a considerable part of the sinusoidal basis functions are with frequencies exponential to a positive integer m, a base-m encoding can provide relatively more order-1 BBs compared with the encodings with cardinalities other than m.