基于改进粒子群优化算法的牙齿正畸路径规划方法

针对虚拟口腔正畸治疗系统中牙齿移动路径规划问题，提出了一种基于正态分布的简化均值粒子群的牙齿正畸路径规划方法。首先建立了单颗牙齿及整体牙齿的数学模型，并根据牙齿运动的特性，将牙齿正畸路径规划问题转化为带约束的优化问题；其次，在简化粒子群算法的基础上，引入正态分布及均值粒子群的思想，提出了一种基于正态分布的简化均值粒子群优化（NSMPSO）算法；最后，从平移路径长度、旋转角度、碰撞检测以及牙齿在单阶段的移动量、旋转量这五个方面构造了高安全性的适应度函数，实现了牙齿正畸移动路径的规划。将NSMPSO与基本粒子群优化（PSO）算法、均值粒子群优化（MPSO）算法和动态调整惯性权重的简化均值粒子群优化（DSMPSO）算法进行对比，结果表明，改进的算法在Sphere、Griewank和Ackley这三大基准测试函数上均在50次迭代内趋于稳定收敛，且均具有最快的收敛速度和最高的收敛精度。通过Matlab中的仿真实验，验证了利用该数学模型和改进算法求得的最优路径安全可靠，可以为医生提供辅助诊断。

Orthodontic path planning based on improved particle swarm optimization algorithm

Concerning the problem of tooth movement path planning in virtual orthodontic treatment system, a method of tooth movement path planning based on simplified mean particle swarm with normal distribution was proposed. Firstly, the mathematical models of single tooth and whole teeth were established. According to the characteristics of tooth movement, the orthodontic path planning problem was transformed into a constrained optimization problem. Secondly, based on the simplified particle swarm optimization algorithm, a Simplified Mean Particle Swarm Optimization based on the Normal distribution (NSMPSO) algorithm was proposed by introducing the idea of normal distribution and mean particle swarm optimization. Finally, a fitness function with high security was constructed from five aspects:translation path length, rotation angle, collision detection, single-stage tooth moving amount and rotation amount, so as to realize the orthodontic movement path planning. NSMPSO was compared with basic Particle Swarm Optimization (PSO) algorithm, the mean Particle Swarm Optimization (MPSO) algorithm and the Simplified Mean Particle Swarm Optimization with Dynamic adjustment of inertia weight(DSMPSO) algorithm. Results show that on Sphere, Griewank and Ackley, these three benchmark test functions, this improved algorithm tends to be stable and convergent within 50 iteration times, and has the fastest convergence speed and the highest convergence precision. Through the simulation experiments in Matlab, the optimal path obtained by the mathematical models and the improved algorithm is verified to be safe and reliable, which can provide assisted diagnosis for doctors.