In this paper a stopping criterion for a particular class of evolutionary algorithms is devised. First, a model of a generic evolutionary algorithm using iterated random maps is presented. The model allows the exploration of a connection between coupling from the past, and a stopping criterion for evolutionary algorithms. Accordingly, a method to stop a generic evolutionary algorithm is proposed. Some computational experiments are carried out to test the stopping criterion, using a modified version of coupling from the past. Empirical evidence is shown to support the suitability of the criterion.

We introduce a very large family of binary features for two-dimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classification trees. There is a feature for every possible geometric arrangement of local topographic codes. The arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial affine and nonlinear deformations. They are also partially ordered, which makes it possible to narrow the search for informative ones at each node of the tree. Different trees correspond to different aspects of shape. They are statistically and weakly dependent due to randomization and are aggregated in a simple way. Adapting the algorithm to a shape family is then fully automatic once training samples are provided. As an illustration, we classified handwritten digits from the NIST database; the error rate was 0.7 percent.