Pyramid: A Hierarchical Approach to Scaling down Population Size in Genetic Algorithms

We present Pyramid, a Hierarchical Genetic Algorithm that decomposes problems by first tackling simpler versions of them, before automatically scaling up to more difficult versions while also reducing the population size. Pyramid takes its name from the architectural phenomenon of the Mayan pyramid in Chichen-Itza, which, although constructed from the bottom up, operates in a top down manner through interactions with the sun. This gives a two stage approach: initially we create our pyramid of experiments, with the most complex fitness functions at the bottom, and with increasingly more simplified/decomposed version as we move up through the pyramid. Runs start at the top of the pyramid and populations descend through it, decreasing in size, being exposed to increasingly complex fitness functions, until, at the bottom layer, we have small populations with the original full fitness function. We conduct experiments comparing the performance of Pyramid for a suite of difficult unimodal and multimodal functions. The experimental results show that in three of four cases, Pyramid achieves the same or better fitness scores as standard algorithms, with substantially fewer evaluations, and that in two cases it actually performs statistically significantly better.