Exact search-space size for the refactoring scheduling problem

Ouni et al. “Maintainability defects detection and correction: a multi-objective approach” proposed a search-based approach for generating optimal refactoring sequences. They estimated the size of the search space for the refactoring scheduling problem using a formulation that is incorrect; the search space is estimated to be too much larger than it is. We provide in this paper the exact expression for computing the number of possible refactoring sequences of a software system. This could be useful for researchers and practitioners interested in developing new approaches to automate refactoring.