Firefly optimization: A study on frame invariance
Christopher W. Cleghorn, Andries Petrus Engelbrecht · 2017
This paper investigates whether or not the swarm based firefly optimization algorithm is invariant under reference frame alteration, specifically, under rotation, translation, and scale changes to the reference frame. A reference frame can be seen as the perspective used to view an optimization problem. The simplest example of a reference frame alteration is that of a scale change, for example if the unit of measure in an optimization problem is in millimeters or meters. An important characteristic of any optimization algorithm is its ability to maintain a high degree of performance stability under reference frame alteration. If an algorithm's performance is in fact dependent on the reference frame, it implies existence of an optimal reference frame that should be used during the optimization process. Having to select a reference frame places a greater burden on an individual utilizing the optimization algorithm, as the choice of reference frame may have a profound impact on performance. In practice, it is unlikely that the ideal reference frame is known a priori. This paper provides theoretical proofs that the firefly optimization algorithm is invariant under rotation and translation but not invariant under scaling. Furthermore, the effects of frame alteration on the firefly optimization algorithm performance are empirically demonstrated.