Fast Non-Dominated Sorting Tuna Swarm Optimization Algorithm (FNS-TSO): Time-Energy-Impact Multi-Objective Optimization of Underwater Manipulator Trajectories

To achieve time–energy–impact multi-objective optimization in the trajectory control of underwater manipulators, this paper proposes a Fast Non-Dominated Sorting Tuna Swarm Optimization algorithm (FNS-TSO). The algorithm integrates a fast non-dominated sorting mechanism into the Tuna Swarm Optimization algorithm, improves initialization through Optimal Latin Hypercubic Sampling (OLHS) to enhance population distribution uniformity, and incorporates a nonlinear dynamic weight to refine the spiral foraging strategy, thereby strengthening algorithmic robustness. To verify FNS-TSO’s effectiveness, we conducted comparative evaluations using standard test functions against three established algorithms: Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Jellyfish Search Optimization (MOJSO), and the Non-Dominated-Sorting Genetic Algorithm (NSGA-II). Results demonstrate superior overall performance, particularly regarding convergence speed and solution diversity, with solution set distributions showing enhanced uniformity. In practical implementation, we applied FNS-TSO to the multi-objective optimization of an underwater manipulator using quintic spline curves for trajectory planning. Simulation outcomes reveal respective reductions of 11.03% in total operation time, 19.02% in energy consumption, and 24.69% in mechanical impacts, with the optimized manipulator achieving stable point-to-point motion transitions.