The advancement of industrialization has spurred the development of innovative swarm intelligence algorithms, with Lion Swarm Optimization (LSO) notable for its robustness, parallelism, simplicity, and efficiency. While LSO excels in single-objective optimization, its multi-objective variants face challenges such as poor initialization, local optima entrapment, and so on. This study proposes Dynamic Multi-Objective Lion Swarm Optimization with Multi-strategy Fusion (MF-DMOLSO) to address these limitations. MF-DMOLSO comprises three key components: initialization, swarm position update, and external archive update. The initialization unit employs chaotic mapping for uniform population distribution. The position update unit enhances behavior patterns and step size formulas for cub lions, incorporating crowding degree sorting, Pareto non-dominated sorting, and Levy flight to improve convergence speed and global search capabilities. Reference points guide convergence in higher-dimensional spaces, maintaining population diversity. An adaptive cold-hot start strategy generates a population responsive to environmental changes. The external archive update unit re-evaluates solutions based on non-domination and diversity to form the new population. Evaluations on benchmark functions showed MF-DMOLSO surpassed multi-objective particle swarm optimization, non-dominated sorting genetic algorithm II, and multi-objective lion swarm optimization, exceeding 90% accuracy for two-objective and 97% for three-objective problems. Compared to non-dominated sorting genetic algorithm III, MF-DMOLSO showed a 60% improvement. Applied to 6R robot trajectory planning, MF-DMOLSO optimized running time and maximum acceleration to 8.3s and 0.3pi rad/s^2, achieving a set coverage rate of 70.97% compared to 2% by multi-objective particle swarm optimization, thus improving efficiency and reducing mechanical dither.

翻译：工业化进程的推进促进了新型群体智能算法的发展，其中狮群优化算法因其鲁棒性、并行性、简洁性与高效性而备受关注。尽管该算法在单目标优化中表现优异，但其多目标变体仍面临初始化质量差、易陷入局部最优等挑战。本研究提出基于多策略融合的动态多目标狮群优化算法以解决这些局限。该算法包含三个核心模块：初始化模块、群体位置更新模块和外部档案更新模块。初始化模块采用混沌映射实现种群均匀分布；位置更新模块通过引入拥挤度排序、帕累托非支配排序和莱维飞行机制，改进幼狮行为模式与步长公式，从而提升收敛速度与全局搜索能力；参考点策略引导高维空间中的收敛方向，维持种群多样性；自适应冷热启动策略生成能响应环境变化的种群。外部档案更新模块基于非支配性与多样性对解进行重评估以形成新种群。在基准函数上的测试表明，本算法在多目标粒子群优化、非支配排序遗传算法II及多目标狮群优化对比中均表现更优，双目标问题精度超过90%，三目标问题精度超过97%；相较于非支配排序遗传算法III，本算法性能提升达60%。在6R机器人轨迹规划应用中，本算法将运行时间与最大加速度分别优化至8.3秒与0.3π rad/s²，其集合覆盖率达到70.97%（多目标粒子群优化仅为2%），有效提升了运动效率并降低了机械抖动。