A Quaternion Firefly Algorithm to Solve a Multi-row Facility Layout Problem

In this paper, a quaternion firefly algorithm is utilized to solve a multi-row facility layout design problem with the objective of minimizing the total cost of transportation. A quaternion firefly algorithm takes the motion of the firefly as a quaternion one. Consequently, the solution space is explored more accurately and the answers are of higher quality. That is, the answers are considerably better than those obtained by standard firefly algorithms. Given the necessity to cut the costs of transferring materials in the facility layout design, a layout is adopted to examine the performance of the algorithm and the solutions from the proposed algorithm are compared with those of CRAFT software, entropy algorithm, and genetic algorithm with that of a heuristic process. The results show better performance of the proposed algorithm comparing other algorithms under examination.