Quantum Differential Evolution Algorithm for Variable Ordering Problem of Binary Decision Diagram

Abstract

This paper presents a new variable ordering method called QDEBDD to reduce the size of Binary Decision Diagram (BDD). The size of BDD is very reliant on the order of function variables. Unfortunately, the search for the best variables ordering has been showed NP-difficult. In this work, the variable ordering problem is cast as an optimization problem for which a new framework relying on quantum computing is proposed. The contribution consists in defining an appropriate quantum representation scheme that allows applying successfully on BDD problem some quantum computing principles. This representation scheme is embedded within a Differential Evolution Algorithm leading to an efficient hybrid framework which achieves better balance between exploration and exploitation capabilities of the search process.