*The One-Dimensional Ising Model: Mutation versus Recombination*

                    Simon Fischer and Ingo Wegener

*Abstract.* The investigation of genetic and evolutionary algorithms on Ising
model problems gives much insight into how these algorithms work as
adaptation schemes.  The one-dimensional 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+lambda)EA with an appropriate lambda-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.

*Keywords:* Ising model, evolutionary algorithms, randomized local
search, expected optimization time