Modified bat algorithm with quaternion representation

This paper introduces a modified bat algorithm using quaternion representation of individuals. Quaternions are a number system, which extends complex numbers. They are successfully applied to problems of theoretical physics and to those areas needing fast rotation calculations. We propose the application of quaternions in optimization, more precisely, we have been using quaternions for representation of individuals in bat algorithm belonging to a swarm intelligence family. It is expected that the problems with stagnation in swarm intelligence should be reduced or even eliminated. We believe that this representation could successfully be applied also to the other swarm intelligence and evolutionary algorithms.