This paper analyzes the convergence properties of the canonical genetic algorithm (CGA) with mutation, crossover and proportional reproduction applied to static optimization problems. It is proved by means of homogeneous finite Markov chain analysis that a CGA will never converge to the global optimum regardless of the initialization, crossover, operator and objective function. But variants of CGA's that always maintain the best solution in the population, either before or after selection, are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent CGA. These results are discussed with respect to the schema theorem.

We recently showed that mutations in the CNGA3 gene encoding the alpha-subunit of the cone photoreceptor cGMP-gated channel cause autosomal recessive complete achromatopsia linked to chromosome 2q11. We now report the results of a first comprehensive screening for CNGA3 mutations in a cohort of 258 additional independent families with hereditary cone photoreceptor disorders. CNGA3 mutations were detected not only in patients with the complete form of achromatopsia but also in incomplete achromats with residual cone photoreceptor function and (rarely) in patients with evidence for severe progressive cone dystrophy. In total, mutations were identified in 53 independent families comprising 38 new CNGA3 mutations, in addition to the 8 mutations reported elsewhere. Apparently, both mutant alleles were identified in 47 families, including 16 families with presumed homozygous mutations and 31 families with two heterozygous mutations. Single heterozygous mutations were identified in six additional families. The majority of all known CNGA3 mutations (39/46) are amino acid substitutions compared with only four stop-codon mutations, two 1-bp insertions and one 3-bp in-frame deletion. The missense mutations mostly affect amino acids conserved among the members of the cyclic nucleotide gated (CNG) channel family and cluster at the cytoplasmic face of transmembrane domains (TM) S1 and S2, in TM S4, and in the cGMP-binding domain. Several mutations were identified recurrently (e.g., R277C, R283W, R436W, and F547L). These four mutations account for 41.8% of all detected mutant CNGA3 alleles. Haplotype analysis suggests that the R436W and F547L mutant alleles have multiple origins, whereas we found evidence that the R283W alleles, which are particularly frequent among patients from Scandinavia and northern Italy, have a common origin.

We present four abstract evolutionary algorithms for multiobjective optimization and theoretical results that characterize their convergence behavior. Thanks to these results it is easy to verify whether or not a particular instantiation of these abstract evolutionary algorithms offers the desired limit behavior. Several examples are given.

Exploratory Landscape Analysis (ELA) subsumes a number of techniques employed to obtain knowledge about the properties of an unknown optimization problem, especially insofar as these properties are important for the performance of optimization algorithms. Where in a first attempt, one could rely on high-level features designed by experts, we approach the problem from a different angle here, namely by using relatively cheap low-level computer generated features. Interestingly, very few features are needed to separate the BBOB problem groups and also for relating a problem to high-level, expert designed features, paving the way for automatic algorithm selection.

This paper provides conditions under which e v olutionary algorithms with an elitist selection rule will converge to the global optimum of some function whose domain may be an arbitrary space. These results generalize the previously developed convergence theory for binary and Euclidean search spaces to general search spaces.