基于改进精英克隆选择算法的B样条曲线逼近方法

B-spline curve approximation method based on an improved elitist clonal selection algorithm

提出一种改进的精英克隆选择算法(ECSA)来实现B样条曲线逼近的自动节点配置。为了提高算法搜索效率和求解质量,设计了自适应混沌变异算子,同时提出了基于抗体浓度和抗原亲和力矢量矩的抗体重选择策略,再以贝叶斯信息准则(BIC)为亲和力度量来权衡拟合优良性和计算复杂度,改进的算法在深度搜索和广度寻优之间取得了平衡,可以自动且精确地计算内节点数量和位置,从而完成数据点的B样条曲线逼近工作。仿真和实验结果表明,提出的方法不仅可以高效精确地实现对存在连续、不连续、尖点等特征含噪复杂数据的自动B样条曲线逼近,而且相比于现有研究,具有更好的全局收敛性和收敛速度。

In this paper,an improved elitist clonal selection algorithm(ECSA)is proposed to realize the automatic knot adjustment of the B-spline curve approximation.In order to improve the search efficiency and solution quality of the algorithm,an adaptive chaotic mutation operator is designed,and an antibody reselection strategy based on the antibody concentration and antigen affinity vectorial moment is proposed.Then Bayesian Information Criterion(BIC)is used as the affinity metric to weigh and judge the goodness of fitting and computational complexity.Further,the improved algorithm achieves a balance between depth search and breadth optimization,and can automatically and accurately calculate the number and locations of internal knots,thus the B-spline curve approximation of the data points is completed.Simulation and experiment results show that the proposed algorithm not only can efficiently and accurately realize the automatic B-spline curve approximation of the noisy complex data with the features of continuity,discontinuity and cusps,but also possesses better global convergence and convergence speed compared with current researches.