Evolutionary tunneling and periodicity across the Big Valley distribution

Abstract

We demonstrate that there are strong patterns of periodicity in terms of how local optima are distributed across search spaces that can help to explain the "Big Valley" distribution of local optima. Examples of periodicity can be found by looking at several Partition Crossover events simultaneously and grouping together those that are nearer to each other in Hamming space. All of the local optima associated with one Partition Crossover event can be evaluated using a single linear equation. When looking at many Partition Crossover events simultaneously, linearity is preserved over complete and partially preserved recombining components.