关键词: 牙齿正畸路径规划, 简化粒子群, 均值粒子群, 正态分布, 适应度函数

Abstract: 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.

Key words: orthodontic path planning, simplified particle swarm, mean particle swarm, normal distribution, fitness function