On the convergence and optimality of the firefly algorithm for opportunistic spectrum access

Abstract

Meta-heuristic algorithms have been proven to be efficient for engineering optimisation. However, the convergence and accuracy of such algorithms depends on the objective function and also on several choices made during algorithm design. In this paper, we focus on the firefly algorithm for optimal channel allocation in cognitive radio networks. We study the effect of various probability distributions including the Lévy alpha stable distribution for randomisation of firefly movement. We also explore various functions for converting firefly positions from the continuous space to the discrete space, as is necessary in the spectrum allocation problem. Simulation results show that in most cases, Lévy flight gives better convergence time and results for common optimisation problems such as maximising the overall channel utilisation, maximising the channel allocation for the bottleneck user and maximising proportional fairness. We also note that no single discretisation function gives both good convergence and optimality.