The one-dimensional Ising model: Mutation versus recombination

The investigation of genetic and evolutionary algorithms on Ising model problems gives much insight into how these algorithms work as adaptation schemes. The onedimensional Ising model with periodic boundary conditions has been considered as a typical example with a clear building block structure suited well for two-point crossover. It has been claimed that GAs based on recombination and appropriate diversity-preserving methods by far outperform EAs based on mutation only. Here, a rigorous analysis of the expected optimization time proves that mutation-based EAs are surprisingly effective. The (1 + λ) EA with an appropriate λ-value is almost as efficient as typical GAs. Moreover, it is proved that specialized GAs do even better and this holds for two-point crossover as well as for one-point crossover.