Genetic Algorithms for the Variable Ordering Problem of Binary Decision Diagrams

Abstract

Ordered binary decision diagrams (BDDs) yield a data structure for switching functions that has been proven to be very useful in many areas of computer science. The major problem with BDD-based calculations is the variable ordering problem which addresses the question of finding an ordering of the input variables which minimizes the size of the BDD-representation. In this paper, we discuss the use of genetic algorithms to improve the variable ordering of a given BDD. First, we explain the main features of an implementation and report on experimental studies. In this context, we present a new crossover technique that turned out to be very useful in combination with sifting as hybridization technique. Second, we provide a definition of a distance graph which can serve as formal framework for efficient schemes for the fitness evaluation.