The Factorized Distribution Algorithm for additively decomposed functions

FDA (the Factorized Distribution Algorithm) is an evolutionary algorithm that combines mutation and recombination by using a distribution. First the distribution is estimated from a set of selected points. It is then used to generate new points for the next generation. In general a distribution defined for n binary variables has 2ⁿ parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exists an algorithm that factors the distribution into conditional and marginal distributions, each of which can he computed in polynomial time. The scaling of FDA is investigated theoretically and numerically. The scaling depends on the ADF structure and the specific assignment of function values. Difficult functions on a chain or a tree structure are optimized in about O(n√n) function evaluations. More standard genetic algorithms are not able to optimize these functions. FDA is not restricted to exact factorizations. It also works for approximate factorizations