Schemata, distributions and graphical models in evolutionary optimization

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a po or performance. First the schema theory of genetic algorithms is reformulat ed in probability theory terms. A schema defines the structure of a margina l distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algori thm, FDA, is derived. FDA uses a factorization of the distribution. The fac torization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence grap hs. For the test functions considered, the performance of FDA-in number of generations till convergence-is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.