Modified firefly algorithm using quaternion representation

•We use quaternions for the representation of individuals in firefly algorithm.•Quaternion representation enhance the performance of the firefly algorithm.•Quaternion representation improves the original firefly algorithm. Quaternions are a number system, which extends complex numbers. They are especially useful in areas where fast rotation calculations are needed, e.g., programming video games or controllers of spacecraft. This paper proposes to use quaternion for the representation of individuals in firefly algorithm so as to enhance the performance of the firefly algorithm and to avoid any stagnation. The preliminary results of our experiments after optimizing a test-suite consisting of ten standard functions, showed that the proposed firefly algorithms using quaternion’s representation improved the results of the original firefly algorithm.