"Vasile Alecsandri" University of Bacău Faculty of Sciences Scientific Studies and Research Series Mathematics and Informatics Vol. 19 (2009), No. 2, 241 - 256 NEW HYBRID GENETIC ALGORITHM WITH ADAPTIVE OPERATORS AND VARIABILITY TARGET FOR OPTIMIZING VARIABLE ORDER IN OBDD I. FURDU AND O. BRUDARU Abstract. Reduced Ordered Binary Decision Diagrams are one of the most powerful data structure for boolean manipulation on switching functions as top process in digital circuits design. The size of ROBDDs is very sensitive to the ordering choices of input variables. A new genetic algorithm is described for optimizing the variable order. It uses adaptive operators and includes a mechanism based on information energy for controlling the variability of the population. Experimental investigations of the performance of this genetic algorithm are described. 1. INTRODUCTION The OBDD size is given by the number of its nonterminal nodes. A smaller number of nodes imply a smaller circuit design, whereas a bad ordering can lead to an exponential growth in the size of OBDD. The existing variable ordering methods [10, 12, 18] include static variable ordering techniques and dynamic variable ordering techniques. Most of static techniques are used to determine good initial variable orders before constructing the OBDD of a function and they are usually based on a breadth- first or depth-first traversal of a circuit [11, 13] from its outputs to inputs. Dynamic techniques are based on a process of improving the variable order and the size of an already built OBDD [4, 19, 22]. The Rudell’s sifting algorithm and window permutation algorithm [21, 24] are the most popular dynamic techniques. In experimental studies, it turned out that methods based on genetic algorithms yield better results than other techniques. Even the runtime for genetic reordering algorithms were brought down to a reasonable level, they are still not competitive to deterministic reordering heuristics like window permutation or sifting [16]. Keywords and phrases: BDD, OBDD Optimisation, GA (2000) Mathematics Subject Classification: 06E30, 94C10, 68W35