Hybrid butter-flower algorithm: Novel metaheuristic optimization algorithm

This study presents the Hybrid Butter-Flower Algorithm (HBFA), an innovative metaheuristic optimization approach that combines the strengths of the Sunflower Optimization Algorithm (SOA) and the Butterfly Optimization Algorithm (BOA) to improve convergence speed, accuracy, and robustness. While proficient in exploration, SOA may lack the aggressive exploitation required for swift convergence, potentially slowing down solution refinement. However, BOA might experience premature convergence in challenging milieu that results in demurrer in local optima. HBFA handles these challenges by amalgamating SOA’s unique exploration nuances with BOA’s effectual exploitation techniques, assuring an optimum exchange between orbicular and localized search. The algorithm is assessed on 23 unimodal and multimodal standard functions and six constrained mechanical design optimization problems with real-world applications. The performance of HBFA is benchmarked against nine state-of-the-art optimization methods, including PSO, SSA, and HSA, based on metrics such as best solution, average solution, and convergence rate. The results demonstrate that HBFA attains the highest performance efficiency (96.69 %), accomplishing all competitive algorithms by epochal margins, with amelioration ranging from 21 % to 63 % over conventional approaches. Notably, the proposed HBFA is 83.25 % faster in finding the optimal solution than other algorithms without falling for premature convergence and local optima. The superiority of HBFA is further validated through Wilcoxon signed-rank and Friedman statistical tests, with an average p-value of 3.14E-10, confirming its statistically significant advantage. Given to its adaptive nature and rapid convergence, HBFA emerges as a powerful tool for addressing complex optimization challenges in engineering, artificial intelligence, and industrial applications.