Utilizing the Honeybees Mating-Inspired Firefly Algorithm to Extract Parameters of the Wind Speed Weibull Model

Abstract

This study introduces a novel adjustment to the firefly algorithm (FA) through the integration of rare instances of cannibalism among fireflies, culminating in the development of the honeybee mating-based firefly algorithm (HBMFA). The IEEE Congress on Evolutionary Computation (CEC) 2005 benchmark functions served as a rigorous testing ground to evaluate the efficacy of the new algorithm in diverse optimization scenarios. Moreover, thorough statistical analyses, including two-sample t-tests and fitness function evaluation analysis, the algorithm’s optimization capabilities were robustly validated. Additionally, the coefficient of determination, used as an objective function, was utilized with real-world wind speed data from the SR-25 station in Brazil to assess the algorithm’s applicability in modeling wind speed parameters. Notably, HBMFA achieved superior solution accuracy, with enhancements averaging 0.025% compared to conventional FA, despite a moderate increase in execution time of approximately 18.74%. Furthermore, this dominance persisted when the algorithm’s performance was compared with other common optimization algorithms. However, some limitations exist, including the longer execution time of HBMFA, raising concerns about its practical applicability in scenarios where computational efficiency is critical. Additionally, while the new algorithm demonstrates improvements in fitness values, establishing the statistical significance of these differences compared to FA is not consistently achieved, which warrants further investigation. Nevertheless, the added value of this work lies in advancing the state-of-the-art in optimization algorithms, particularly in enhancing solution accuracy for critical engineering applications.