### The Factorized Distribution Algorithm FDA for Optimizing Additively Decomposed Functions

#### Dr. Heinz Muehlenbein

##### German National Research Center for Information Technology (GMD), St. Augustin/Bonn, Germany March 15, 1999 2:00 pm

In this talk the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm {\em BEDA} is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, {\em FDA},\/ is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. 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.