A sigmoid attractiveness based improved firefly algorithm and its applications in IIR filter design

Abstract

Recently, a novel population-based optimisation algorithm, namely firefly algorithm (FA), which mimics the flashing and attraction behaviour of fireflies, has shown promising performance in solving global optimisation problems. However, the preliminary studies have shown that FA often gets stuck in local optima. In this paper, we investigate the reasons why the FA suffers from getting stuck in local optima; and then propose an improved firefly algorithm (IFA). These improvements are twofold: first, a sigmoid-based attractiveness is employed to reformulate its definition and strengthen its local refinement ability; second, a dynamic step parameter tuning strategy is designed to adjust the random search intensity and narrow the search space iteratively to strengthen its global search ability. The empirical results indicate IFA can well balance between the global exploration and the local exploitation, and provides the best solutions, at least the competitive results, for most of 12 global optimisation problems over other FA variants. Besides, by employing IFA to solve well-known infinite impulse response filter design problems, we evaluate the effectiveness and efficiency of IFA. The experimental results and comparisons show that IFA performs better than, at least as competent again, other meta-heuristics in terms of the solution accuracy, solution robustness, and convergence rate.