基于理想点法的双目标优化算法
A Bi-Objective Optimization Algorithm Based on the Ideal Point Method
摘要: 现有的四元数曲线能量优化方法主要集中于单目标策略，而忽略了不同能量函数间的内在冲突。首先介绍了曲线的拉伸能，弯曲能和扭曲能等能量函数，然后提出了一种基于理想点法的双目标能量优化方法，最后以G2连续的含参单位四元数曲线为例，验证了该方法在平滑姿态轨迹构造中的有效性。实验结果表明，该方法能有效权衡不同能量函数，相较于单目标能量优化方法，其生成的姿态轨迹在综合性能上得到显著提升。
Abstract: Existing energy optimization methods for quaternion curves mainly focus on single-objective strategies, overlooking the inherent conflicts among different energy functionals. This paper introduces energy functionals for curves, such as stretching, bending, and twisting energy, and then proposes a bi-objective energy optimization method based on the ideal point method. The effectiveness of this approach in constructing smooth attitude trajectories is validated using a class of G2 continuous parametric unit quaternion curves as an example. Experimental results demonstrate that our method can effectively balance different energy functionals, leading to a significant improvement in the overall performance of the generated attitude trajectories compared to single-objective optimization methods.
文章引用：梁爱华, 王倩. 基于理想点法的双目标优化算法[J]. 应用数学进展, 2026, 15(1): 112-121. https://doi.org/10.12677/aam.2026.151012

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