The Ising model: Simple evolutionary algorithms as adaptation schemes

The investigation of evolutionary algorithms as adaptation schemes has a long history starting with Holland (1975). The Ising model from physics leads to a variety of different problem instances and it is interesting to investigate how simple evolutionary algorithms cope with these problems. A theoretical analysis is known only for the Ising model on the ring and partially for the Ising model on the two-dimensional torus. Here, the two-dimensional torus, the d-dimensional hypercube, and graphs consisting of two cliques connected by some bridges are investigated experimentally. Many hypotheses are confirmed by rigorous statistical tests.