基于改进PSO算法的B样条曲线拟合

B spline curve fitting based on improved PSO algorithm

节点向量的确定对B样条曲线最终拟合效果有着重要影响。粒子群优化(PSO)算法在优化节点向量时存在易于陷入局部极值的问题,导致曲线拟合效果较差。针对这一问题,提出一种改进的PSO算法—GBPSO算法。在PSO算法中引入天牛须搜索(BAS)策略增强算法的局部搜索能力,引入交叉和变异操作增强算法的全局搜索能力。首先通过罚函数的方法建立B样条曲线拟合问题的数学模型,然后使用GBPSO算法优化节点向量,最后得到误差较小的拟合曲线。通过对4个实例的仿真以及与另外3种算法的实验数据对比,验证了所提算法的有效性。

The determination of the knot vector has an important influence on the final fitting effect of the B-spline curve.The particle swarm optimization(PSO)algorithm is easy to fall into the local extreme value when optimizing the knot vector,resulting in poor curve fitting effect.In response to this problem,an improved genetic-beetle particle swarm optimization(GBPSO)algorithm is proposed.In the GBPSO,the long-horned beard search strategy is introduced to enhance the local search ability of the algorithm,and crossover and mutation operations are used to enhance the global search ability of the algorithm.Firstly,the mathematical model of B-spline curve fitting problem is established by the method of penalty function,and then the knot vector is optimized by GBPSO algorithm,and finally the fitting curve with smaller error is obtained.The effectiveness of the proposed algorithm is verified by the simulation of four examples and the comparison with the experimental data of the other three algorithms.