GFPSMA: An improved algorithm based on flower pollination, slime mould, and game inspiration for global optimization

Metaheuristic algorithms have garnered much attention among researchers owing to their robustness, adaptability, independence from a predetermined initial solution, and lack of reliance on gradient computations. The flower pollination algorithm (FPA) and the slime mould algorithm (SMA) are efficient methodologies for addressing global optimization challenges. Nonetheless, tackling large-scale global problems using a single algorithm often proves challenging due to inherent limitations in its mechanism. One effective approach to mitigating this limitation is to hybrid the two algorithms employing suitable strategies. We proposed a hybrid algorithm (GFPSMA) based on FPA and SMA. First, to address the global exploration issue of FPA, a method was proposed that utilized the golden section mechanism to enhance information exchange between random individuals and the best individual. Second, to improve the reliability of the random search phase in SMA, an adaptive step-size strategy was introduced. Furthermore, a dual-competition mechanism, inspired by gaming concepts, was introduced to enhance the integration of the two algorithms. Finally, an elite learning method with adjustment conditions was employed to refine the localization of the best individual. To assess the performance advantage of GFPSMA, 39 benchmark functions were employed, comparing GFPSMA with FPA and SMA along with their six variants, six variants of other metaheuristic algorithms, three CEC competition algorithms, totaling 17 algorithms, and strategic algorithms for testing. Experimental results demonstrated the favorable performance advantage of GFPSMA. Additionally, the feasibility and practicality of GFPSMA were demonstrated in four engineering problems. Keywords: hybrid algorithms; flower pollination algorithm; slime mould algorithm; competitive mechanism; householder elite learning; global search