A Microcanonical Optimization Algorithm for BDD Minimization Problem

Abstract

Reduced ordered binary decision diagrams (ROBDDs) have become widely used for CAD applications such as logic synthesis, formal verification, and etc. The size of RDBDDs for a Boolean function is very sensitive to the ordering choices of input variables and the problem of finding a minimum-size variable ordering is known to be NP-complete. In this paper, we propose a new ROBDD minimization algorithm based on the microcanonical optimization (MO). MO iteratively applies an initialization phase and a sampling phase to combinatorial optimization problems. In the proposed MO-based algorithm, the initialization phase is replaced with the existing Sifting algorithm known to be a very fast local search algorithm to find a minimum-size ROBDD. We derived equations for the proposed MO-based algorithm parameters empirically. The algorithm has been experimented on well known benchmark circuits and the experiments show that, even with slightly better solutions, the run time of the algorithm is 24% and 48% of the Genetic and SA algorithms', respectively, on average. The proposed MO-based algorithm is a good candidate for the large size problems that cannot be attacked by exact algorithms when a near-optimal solution is required.