Description

R. Drechsler, B. Becker, and N. G?ckel, “A genetic algorithm for variable ordering of OBDDs,” International Workshop on Logic Synthesis, pp. P5c:5.55–5.64, 1995.

A Genetic Algorithm for Variable Ordering of OBDDs

In the realm of formal verification, logic synthesis, and computer science, the efficiency and effectiveness of digital circuit verification have long been a subject of research. A crucial aspect of this process involves the optimization of Boolean function representations, with Ordered Binary Decision Diagrams (OBDDs) being one of the most popular data structures employed. The key to leveraging OBDDs lies in the appropriate ordering of variables to achieve the most compact representation. This challenge has driven the development of innovative algorithms, among which is a genetic algorithm tailored specifically for variable ordering of OBDDs.

Developed by researchers R. Drechsler, B. Becker, and N. Gockel in 1995, this unique algorithm draws inspiration from the principles of natural evolution. By treating the process of variable ordering as a genetic optimization problem, the algorithm attempts to find the most suitable ordering of variables that minimizes the size of the resulting OBDD. In essence, the genetic algorithm applies the mechanics of natural selection and genetic variation to iteratively refine an ordering that produces the most compact OBDD.

The algorithm begins by initializing a population of candidate variable orderings. Each ordering is then evaluated based on a fitness function, which assesses the size of the OBDD resulting from the ordering. The fitness function is typically based on the number of nodes in the OBDD, with smaller orderings indicative of more compact representations. The candidate orderings undergo a series of mutation and crossover operations, akin to those occurring in natural genetic processes. Through these operations, new candidate orderings are generated, and the process is repeated until an optimal ordering is achieved.

The advantages of this genetic algorithm are multifaceted. Firstly, it allows for the exploration of a vast solution space in a relatively efficient manner. Secondly, the algorithm is capable of escaping local optima, which is particularly useful in cases where the optimal ordering is located in a region of the solution space inaccessible through traditional optimization techniques. Moreover, the genetic algorithm can be easily parallelized, making it a suitable choice for distributed computing environments.

In conclusion, the development of a genetic algorithm for the variable ordering of OBDDs has opened new avenues in the optimization of digital circuit verification. By harnessing the principles of natural evolution, this algorithm has successfully addressed the complex challenge of variable ordering, leading to more efficient and effective OBDD representations. Its innovative approach serves as a testament to the continued relevance of genetic algorithms in various fields of computer science and engineering research.

For further reading and technical exploration of the algorithm, the original paper cited by Drechsler, Becker, and Gockel in 1995 is a valuable resource.