A hybrid FA–FPA optimization strategy delivering structural, economic and numerical efficiency in cellular beam design

Purpose The purpose of this study is to introduce a novel hybrid algorithm by integrating features of the firefly (FA) algorithm and the flower pollination (FPA) algorithm to optimize the design of cellular beams. The hybrid algorithm was tested on beams of 300, 500, and 700 cm lengths under simply supported conditions, considering structural failure modes. Its performance was compared with three methods, showing clear superiority in obtaining optimal solutions across multiple independent runs. Design/methodology/approach Individual metaheuristic algorithms often exhibit performance limitations when applied to diverse optimization problems. To overcome these limitations, a hybrid approach was developed, combining the strong global search capabilities of the FPA algorithm with the effective exploratory capabilities of the FA algorithm. The stability and efficiency of its performance were also assessed using multiple independent runs (50 runs) through sensitivity analyses, processing time, standard deviation and coefficient of variation (CV) and interquartile range (IQR). Its structural relevance was validated through an evaluation of its performance in determining the four basic cross-section dimensions. Findings The results consistently showed superior solutions with improved stability and reduced cost, demonstrating its effectiveness in improving structural design with statistically significant improvements in solution stability. Originality/value A new hybrid algorithm was developed and its efficiency was evaluated through comprehensive analyses and comparative benchmarking against both established metaheuristic algorithms. The hybrid algorithm demonstrated superiority supported by non-parametric statistical analysis over its parent algorithms, in addition to its superiority over the improved ray optimization (IRO) algorithm. This research presents a practical hybrid algorithm framework for solving complex structural design optimization problems while improving the quality of solutions, enhancing efficiency and reducing computational cost.