Genetic Algorithms as Reshufflers and the Anti-Mutation Operator

The goal of this paper is to study the dynamics of a genetic algorithm in a more visual, intuitive way than statistical methods do. Rather than modeling the genetic algorithm mathematically, we try to describe how the GA scans through the search space, and how genotypes move through the search space as genetic operators are applied to them. We find that standard genetic operators can be described as reshufflers that divide the search space into a number of decks, then move individuals around decks following precise rules. Mutation, in particular, can be described as depending on a deterministic parity rule. We incidentally derive integer equations for the genetic algorithm that translate mutation and crossover into simple arithmetic operations on integers. We then investigate alternative genetic algorithms by modifying the rules that we found, especially the parity rule that governs mutation. The resulting operators are compared to standard mutation over various test problems.