Performance analysis of distance metrics on the exploitation properties and convergence behaviour of the conventional firefly algorithm

The nature of the distance metric used to compare the span between two fireflies in conventional firefly algorithm can significantly enhance the exploitation properties of the algorithm and improve its convergence towards the optimum solution. Therefore, this research proposes several variants of the firefly algorithm based on different distance relations like Minkowski distance, Canberra distance, and Angular Cosine distance. To compare the performance of these variants, benchmark non-linear and non-convex objective functions are solved under the varying nature of the medium absorption coefficient and attractiveness constant. It is observed from detail analysis of results that Canberra distance provides optimal results for almost all of the benchmark functions. Furthermore, the importance of the distance metric for real-world optimization problems with very large or small magnitude of decision variables is also presented by solving a practical hydro thermal scheduling problem. It is also presented that the optimal set of parameters for a particular distance criterion may not always be optimal and better convergence results can be achieved by varying the distance metric to measure the length between the fireflies.