A multi-strategy Hippopotamus Optimization algorithm for dynamic parameter identification of robotic manipulators

The Hippopotamus Optimization (HO) algorithm is a recent swarm-intelligence metaheuristic with three structural limitations: rank-blind updates that waste evaluations on poorly-ranked individuals; a single-magnitude escape operator that cannot leave narrow multi-modal traps; and no elite re-evaluation under stochastic fitness. This paper proposes the Fitness-Ranked Hippopotamus Optimization (FHO) algorithm, which replaces HO’s update pipeline with three rank-driven mechanisms: fitness-contrast directional learning (FCDL), fitness-rank differential search (FRDS), and fitness-rank guided mutation (FRGM), together with a per-iteration elite-preservation step. FHO is validated on five CEC configurations (CEC2017 at D = 30/50/100, CEC2019, and CEC2022; 109 function instances) against 22 competitors, including LSHADE, CMA-ES, and four 2025–2026 optimisers, under each suite’s official evaluation budget with 30 runs. On the 51-function aggregate FHO attains Friedman mean rank 4.83, third of 23 behind the state-of-the-art non-swarm optimisers LSHADE (1.57) and CMA-ES (3.50); it is the strongest swarm- and social-inspired algorithm in the pool and outranks both Hippopotamus-family algorithms. At D = 100 it rises to second (3.97), overtaking CMA-ES, and it beats HO on 27–28 of 29 functions across dimensions. A controlled ablation confirms all three mechanisms contribute. Applied to robust tuning of the 20-dimensional fractional-order PID controller of a hardware-identified four-degree-of-freedom (4-DOF) manipulator under ±20% uncertainty against 11 competitors, FHO sits inside the top statistical clique on unseen plants (Wilcoxon p ≥ 0.50) and is the most reliable of that clique’s high-variance members, with the narrowest score spread and no catastrophic-failure tails.

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