A cuckoo search algorithm with scale-free population topology

The scale-free network is an important type of complex network. The node degrees in a scale-free network follow the power-law distribution. In the skeleton of a scale-free network, there exists a few nodes which own huge neighborhood size and play an important role in information transmission of the entire network, while most of the network nodes have few connections whose influences of information exchange are limited to a relatively low level. In this paper, we introduce a scale-free population topology into the cuckoo search (CS) algorithm to propose a novel variant, which is termed the scale-free cuckoo search (SFCS) algorithm. Unlike other CS algorithms where the individuals exchange information randomly, two properties of the scale-free network can improve the SFCS algorithm in two aspects: the possibility that the information of competent individuals quickly floods the whole population is reduced significantly, which guarantees population diversity; and the corrupt individuals can learn from competent individuals with greater probability, which is beneficial for convergence. Thus, SFCS can obtain a better trade-off between exploitation and exploration during the search process. To evaluate the effectiveness of the proposed SFCS, 58 benchmark functions with different dimensions (10-D, 30-D, and 50-D), and 21 real-world optimization problems are employed in our experiment. We compare SFCS with the basic CS algorithm, two CS variants, and five state-of-the-art optimization algorithms, and the experimental results and statistical analysis verify the superiority of SFCS in terms of solution quality and convergence speed. Furthermore, we compare SFCS with a scale-free fully informed particle swarm optimization algorithm (SFIPSO) and the results prove our scale-free idea is effective despite its simplicity. We also introduce the scale-free population topology into the differential evolution (DE) and the firefly algorithm (FA) and the experimental results show that the scale-free population topology enhance the search ability of the DE and FA. These lead us to believe that the scale-free population topology may be a new technique for improving the performance of the population-based algorithms.