The Algebraic Differential Evolution for Permutations (ADEP) has been recently proposed as an effective evolutionary algorithm for permutation-based optimization problems. ADEP is built upon a framework that exploits the rich algebraic structure of the permutations search space. In this paper we further explore the abilities of ADEP by presenting an implementation for the Single Row Facility Layout Problem (SRFLP): a permutation problem with interesting real-world applications ranging from designing the layouts of machines in certain manufacturing systems to optimally arranging rooms in hospitals. An experimental investigation was conducted on a set of commonly adopted benchmarks and different settings ADEP were compared among them and with respect to the other methods in the literature. Interestingly, the experimental results confirm the validity of ADEP by showing its competitiveness with respect to the state-of-the-art results for the SRFLP.