基于改进多粒子群的牙齿正畸路径规划

牙齿矫治路径规划是虚拟牙齿正畸系统的重要组成部分。针对多目标高维度的路径规划问题， 提出一种改进多粒子群的路径规划方法。首先，采用多粒子群对牙齿路径规划问题进行建模和设计，解决牙齿 正畸维度过高的问题；其次，考虑不同类别牙齿的生理重建难度，基于 Beta 曲线和牙弓深度优化不同粒子群 的惯性参数 w，精细化传统正畸系统的矫治过程；最后，通过修改位置更新上下限缩小路径搜索范围，减少正 畸过程中的碰撞同时优化正畸效果。实验结果表明，该方法效率比单粒子群模型整体提升了约 38%，更符合临 床正畸过程，矫治后更接近理想的正畸效果。

Orthodontic path planning based on improved multi-PSO

Orthodontic path planning is an integral part of a virtual orthodontic system. Aiming at the multi-objective and high-dimensional path planning problem, an improved multi-particle swarm optimization (PSO) path planning method was proposed. Firstly, the multi-PSO was utilized to model and design the tooth path planning to solve the problem of the overly high orthodontic dimension. Secondly, the difficulties in physiological reconstruction of different types of teeth were considered based on Beta curve and dental arch depth, and the inertia parameter w of different particle swarms was optimized to refine the orthodontic treatment process of the traditional orthodontic system. Finally, the upper and lower limits of position updating were modified to narrow the path search range, reduce the collision during orthodontic process, and optimize the orthodontic effect. The experimental results show that this method is 38% more efficient than the single particle swarm optimization model, which is more consistent with clinical orthodontic treatment, and is more likely to achieve the ideal orthodontic effect after treatment.