Enhanced Pied Kingfisher Optimization Algorithm with Hovering Scouts and Foraging Flocks Mechanisms

Population-based metaheuristic algorithms are widely used for solving nonlinear, nonconvex, constrained, and high-dimensional optimization problems. However, many swarm-based optimizers still suffer from premature convergence, loss of population diversity, and weak exploitation of multiple promising regions. To address these limitations, this study proposes the Hovering Scouts and Foraging Flocks Pied Kingfisher Optimizer (HSFFPKO), an enhanced variant of the Pied Kingfisher Optimizer (PKO). The proposed method introduces two complementary mechanisms. The Hovering Scouts mechanism applies scale-aware Gaussian probing with weak global-best guidance to restore local diversity and reduce stagnation, while the Foraging Flocks mechanism organizes the population into temporary subgroups guided by leader–centroid targets under a shrinking search radius. The performance of HSFFPKO was evaluated on the CEC 2017 benchmark suite and nine constrained engineering design problems. In the ablation study at D = 10, HSFFPKO achieved the best average rank of 1.67 and obtained 20 wins out of 30 benchmark functions. In the scalability analysis, HSFFPKO remained the best-ranked PKO variant at D = 30, D = 50, and D = 100, with average ranks of 1.37, 1.33, and 1.27, respectively. In the broad comparison with recent optimizers at D = 30, HSFFPKO obtained the best overall average rank of 2.60 and the highest number of function wins, with 11 wins out of 30 functions. The Nemenyi post-hoc test showed that HSFFPKO was statistically comparable with the strongest competitors, including BWSMA and GPSOM, while significantly outperforming several other methods. Engineering results further confirmed that HSFF-PKO is highly competitive for continuous constrained design problems, although its performance was weaker on the discrete gear-train problem. These results indicate that HSFFPKO is a scalable and competitive PKO variant for continuous numerical and engineering optimization.