Simulation and Optimization of Multi-Phase Terminal Trajectory for Three-Dimensional Anti-Ship Missiles Based on Hybrid MOPSO

In high-dynamic battlefield environments, anti-ship missiles must perform intricate attitude adjustments and energy management within time constraints to hit a target accurately. Traditional optimization methods face challenges due to the high speed, flexibility, and varied constraints inherent to anti-ship missiles. To overcome these challenges, this research introduces a three-dimensional (3D) multi-stage trajectory optimization approach based on the hybrid multi-objective particle swarm optimization algorithm (MOPSO-h). A multi-stage optimization model is developed for terminal trajectory, dividing the flight process into three stages: cruising, altitude adjustment, and penetration dive. Dynamic equations are formulated for each stage, incorporating real-time observations and overload constraints and ensuring the trajectory remains smooth, continuous, and compliant with physical limitations. The proposed algorithm integrates an adaptive hybrid mutation strategy, effectively balancing global search with local exploitation, thus preventing premature convergence. The simulation results demonstrate that, in typical scenarios, the mean miss distance optimized by MOPSO-h remains no greater than 2.34 m, while the terminal landing angle is consistently no less than 85.68°. Furthermore, MOPSO-h enables the missile’s cruise altitude and speed, driven by multiple models, to maintain long-term stability, ensuring that the maneuver overload adheres to physical constraints. This research provides a rigorous and practical solution for anti-ship missile trajectory design and engagement with shipborne air defense systems in high-dynamic environments, achieved through a multi-stage collaborative optimization mechanism and error analysis.