A complex network-based firefly algorithm for numerical optimization and time series forecasting

The firefly algorithm (FA) has gained widespread attention and has been widely applied because of its simple structure, few control parameters and easy implementation. As the traditional FA lacks a mutation mechanism, it tends to fall into local optima, leading to premature convergence, thus affecting the optimization accuracy. To address these limitations, from the perspective of population diversity, a complex network-based FA (CnFA) with scale-free properties is proposed in this paper. The scale-free properties of complex networks effectively ensure the diversity of populations to guide the populations in their search, thus avoiding random interactions of information among populations that could lead to superindividuals controlling the entire population. The property of the power-law distribution of nodes in complex networks is exploited to effectively avoid the premature convergence of the FA and falling into local optima. To verify the search performance of CnFA, we compared the FA and its variants, as well as multiple competitive approaches, on 30 different-dimension benchmark function optimization tasks and two time series prediction tasks. The experimental results and statistical analysis show that CnFA achieves satisfactory performance due to the better balance between exploitation and exploration in the search process. Additionally, we extended the proposed method to two other population-based algorithms, and the experimental results verify that the complex network -based mechanism can enhance the performance of not only the FA but also other population-based evolutionary algorithms.(c) 2023 Elsevier B.V. All rights reserved.