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.
[1] THIND S K,CHATTERJEE A,ARSHAD F,et al. A clinical comparative evaluation of periodontally accelerated osteogenic orthodontics with piezo and surgical bur:An interdisciplinary approach[J]. Journal of Indian Society of Periodontology,2018,22(4):328-333. [2] ILIADI A,KOLETSI D,ELIADES T. Forces and moments generated by aligner-type appliances for orthodontic tooth movement:a systematic review and meta-analysis[J]. Orthodontics and Craniofacial Research,2019,22(4):248-258. [3] YU X,CHENG X,DAI N,et al. Study on digital teeth selection and virtual teeth arrangement for complete denture[J]. Computer Methods and Programs in Biomedicine,2017,155:53-60. [4] 吴婷, 张礼兵. 3维牙颌模型牙齿分割的路径规划方法[J]. 中国图象图形学报,2018,23(1):84-94. (WU T,ZHANG L B. Tooth segmentation on 3D dental meshes based on path planning[J]. Journal of Image and Graphics,2018,23(1):84-94.) [5] HADDANI H,ELMOUTAOUAKKIL A,BENZEKRI F,et al. Quantification of 3d tooth movement after a segmentation using a watershed 3d method[C]//Proceedings of the 5th International Conference on Multimedia Computing and Systems. Piscataway:IEEE, 2016:7-11. [6] LI Y,JACOX L A,LITTLE S H,et al. Orthodontic tooth movement:The biology and clinical implications[J]. The Kaohsiung Journal of Medical Sciences,2018,34(4):207-214. [7] KENNEDY J,EBERHART R. Particle swarm optimization[C]//Proceedings of the 1995 International Conference on Neural Networks. Piscataway:IEEE,1995:1942-1948. [8] HAN H,LU W,HOU Y,et al. An adaptive-PSO-based self-organizing RBF neural network[J]. IEEE Transactions on Neural Networks and Learning Systems,2018,29(1):104-117. [9] INDADUL KHAN,SOVA PAL,MANAS KUMAR MAITI. A hybrid PSO-GA algorithm for traveling salesman problems in different environments[J]. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2019,27(5):693-717. [10] 韩明, 刘教民, 吴朔媚, 等. 粒子群优化的移动机器人路径规划算法[J]. 计算机应用,2017,37(8):2258-2263.(HAN M, LIU J M,WU S M,et al. Path planning algorithm of mobile robot based on particle swarm optimization[J]. Journal of Computer Applications,2017,37(8):2258-2263.) [11] CHENG Y,ZHOU Z,JIANG J,et al. Path planning for support jammers formation in penetration operation based on improved PSO-GA[C]//Proceedings of the 2nd International Conference on Image,Vision and Computing. Piscataway:IEEE,2017:1090-1096. [12] SETYAWAN N,KADIR R E A,JAZIDIE A. Adaptive Gaussian parameter particle swarm optimization and its implementation in mobile robot path planning[C]//Proceedings of the 2017 International Seminar on Intelligent Technology and Its Applications. Piscataway:IEEE,2017:238-243. [13] 刘洁, 赵海芳, 周德廉. 一种改进量子行为粒子群优化算法的移动机器人路径规划[J]. 计算机科学,2017,44(11A):133-138. (LIU J,ZHAO H F,ZHOU D L. Improved quantum behaved particle swarm optimization algorithm for mobile robot path planning[J]. Computer Science,2017,44(11A):133-138.) [14] LIU Z,XU J,CHENG Q,et al. Trajectory planning with minimum synthesis error for industrial robots using screw theory[J]. International Journal of Precision Engineering and Manufacturing, 2018,19(2):183-193. [15] DEEP K,BANSAL J C. Mean particle swarm optimisation for function optimisation[J]. International Journal of Computational Intelligence Studies,2009,1(1):72-92. [16] 胡旺, 李志蜀. 一种更简化而高效的粒子群优化算法[J]. 软件学报, 2007,18(4):861-868. (HU W,LI Z S. A simpler and more effective particle swarm optimization algorithm[J]. Journal of Software,2007,18(4):861-868.) [17] 李占利, 付敬鼎, 李洪安, 等. 虚拟正畸治疗中的错位牙齿自动排列方法[J]. 图学学报,2019,40(2):225-234.(LI Z L,FU J D,LI H A,et al. Automatic alignment method for malocclusion in virtual orthodontics treatment[J]. Journal of Graphics,2019,40(2):225-234.)
2020, Vol. 40 
