Fig. 3

Qualitative analysis result of KSHHO. Each row corresponds to one test function \(\:{F}_{i}\).From left to right: (1) the 3D surface plot of \(\:{F}_{i}\), illustrating the function landscape; (2) the search history, where black dots represent visited candidate solutions and the red dot marks the best solution found; (3) the trajectories of agents over iterations, showing convergence behavior in the decision space; and (4) the average fitness curve of all agents, reflecting convergence in the objective space.