增量极坐标编码的贝赛尔曲线智能优化算法

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Title:

Intelligent optimized Bezier curves based on incremental polar coordinate coding

作者:

肖琴¹, 张永韡², 汪镭³

1. 江苏科技大学 信息化建设与管理中心, 江苏 镇江 212003;
2. 江苏科技大学 电子信息学院, 江苏 镇江 212003;
3. 同济大学 电子与信息工程学院, 上海 200092

Author(s):

XIAO Qin¹, ZHANG Yongwei², WANG Lei³

1. Center of Information Construction and Management, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. Department of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
3. Coll

关键词:

隶属度函数; 贝塞尔曲线; 差分进化算法; 曲线拟合; 优化算法; 模糊分类; 模糊统计; 进化计算

Keywords:

membership function; bezier curves; differential evolution; curve fitting; optimization algorithm; fuzzy classification; fuzzy statistics; evolutionary algorithms

分类号:

TP181

DOI:

10.11992/tis.201706076

摘要:

针对基于统计的隶属度函数确定方法进行了改进，使用贝塞尔曲线作为隶属度函数的上升或下降沿，使隶属度函数可以经过统计结果规定的任意中间点。使用新的增量极坐标编码对贝塞尔曲线控制点进行表达，解决了传统贝塞尔曲线优化中的控制点约束问题。采用差分进化算法对贝塞尔曲线控制点进行优化，可智能拟合经过任意点的最佳贝塞尔曲线。算法可扩展到任意阶贝塞尔曲线，所得隶属度函数较非贝塞尔曲线方法更为合理。

Abstract:

This study improves the method of determining the statistic-based membership function for membership function selection in fuzzy classification. Bezier curves are used as the ascendant or descendant edge of the membership function, to ensure that the membership function goes through any arbitrary points stipulated in statistical results. The control points of the Bezier curves are expressed by incremental polar coordinate coding, which solves the control point constraint problem in optimization of traditional Bezier curves. In addition, the differential evolution algorithm is used to optimize the control points of Bezier curves, and this can intelligently fit the best Bezier curve that goes through any arbitrary point. Results show that the proposed algorithm can be extended to any order Bezier curve, and the obtained membership functions are more reasonable than those of the non-Bezier curve method.