单纯形法的改进萤火虫算法及其在非线性方程组求解中的应用

Title:

Improved firefly algorithm based on simplex method and its application in solving non-linear equation groups

作者:

莫愿斌^1,2, 马彦追¹, 郑巧燕¹, 袁伟军²

1. 广西民族大学 信息科学与工程学院, 广西 南宁 530006;
2. 广西混杂计算与集成电路设计分析重点实验室, 广西 南宁 530006

Author(s):

MO Yuanbin^1,2, MA Yanzhui¹, ZHENG Qiaoyan¹, YUAN Weijun²

1. College of Information Science and Engineering, Guangxi University for Nationalities, Nanning 530006, China;
2. Guangxi Key Laboratory of Mixed Computing Integrated Circuit Design and Analysis, Nanning 530006, China

关键词:

萤火虫算法; 单纯形法; 函数优化; 非线性方程组

Keywords:

firefly algorithm; simplex method; function optimization; non-linear equation groups

分类号:

TP18

DOI:

10.3969/j.issn.1673-4785.201309075

文献标志码:

A

摘要:

萤火虫算法(FA)是一种基于群体搜索的启发式随机优化算法,其模拟自然界中萤火虫利用发光的生物学特性而表现出来的社会性行为。针对萤火虫算法存在着收敛速度慢、易陷入局部最优、求解精度低等不足,利用单纯形法局部搜索速度快和萤火虫算法全局寻优的特点,提出一种基于单纯形法的改进型萤火虫算法(SMFA)。通过对标准测试函数以及非线性方程组的实验仿真,并与其他算法进行的对比分析表明,改进后的算法在函数优化方面有较强的优势,在一定程度上有效地避免了陷入局部最优,提高了搜索的精度。

Abstract:

The firefly algorithm (FA) is a heuristic random optimization algorithm based on groupization. It simulates the social behavior of firefly in the natural environment represented in its biological characteristics of shining. FA has disadvantages in global searching, such as slow convergence speed, high possibility of being trapped in local optimum and low solving precision. An improved FA based on the simplex method is proposed. The proposed method combines the characteristics of speedy local search of simplex method with the global optimization of firefly algorithm. The simplex method modifies the firefly, which is located at poor positions through its reflection, expansion and compression operation. However, it improves the diversity of individuals and avoids falling into local optimum and improves the precision of the algorithm. The results showed that through simulations of standard benchmark functions and nonlinear functions and contrasted with other algorithms, the improved algorithm has a strong advantage in function optimization. It also avoids trapping in local optimum and improves the calculation accuracy to a certain extent.