非线性方程组的增强型部分强化算法求解与应用
Improved Partial Reinforcement Optimization Algorithm for Solving Nonlinear Equations and Application
张伟 1莫愿斌2
作者信息
- 1. 广西民族大学人工智能学院,广西 南宁 530006
- 2. 广西民族大学人工智能学院,广西 南宁 530006;广西民族大学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
- 折叠
摘要
针对非线性方程组求解存在求解准确度低、求解个数不全、收敛速度慢等问题,提出了 一种融合改进Circle混沌映射、柯西变异以及正切飞行算子的改进部分强化优化算法用于求解方程组.首先初始化种群时加入改进Circle混沌序列,增加种群的复杂性;其次,对当前最优解采用柯西变异扰动策略,提升算法跳出局部最优的概率;最后,在刺激阶段加入正切飞行算子,提高算法在不同时期全局探索和局部开发的需求.通过6个标准测试函数的测试和8组多根非线性方程组的求解,实验结果表明改进算法在鲁棒性,寻优精度和收敛性等方面都优于其他算法.将算法用于工程上的三角函数超越方程求解,也获得好的效果.
Abstract
In view of the problems of low solution accuracy,incomplete number of solutions,and slow convergence speed in solving nonlinear equations,an Improved Partial Reinforcement Optimization Algorithm that integrates improved Circle chaos mapping,Cauchy mutation,and tangent flight operator is proposed for solving equation set.An improved Circle chaos sequence is first added when initializing the population to increase the complexity of the population.A Cauchy mutation perturbation strategy is then used for the current optimal solution to improve the probability of the algorithm jumping out of the local optimum.Finally,a tangent flight operator is added in the stimulation stage to improve the needs of global exploration and local development of algorithms in different periods.Through the testing of 6 standard test functions and the solution of 8 sets of multi-root nonlinear equations,the experimental results show that the improved algorithm is superior to other algorithms in terms of robustness,optimization accuracy and convergence.The algorithm is used to solve trigonometric transcendental equations in engineering and also achieves good results.
关键词
部分强化优化算法/非线性方程组/Circle混沌/正切飞行算子/柯西变异Key words
partial reinforcement optimization algorithm/nonlinear equations/circle chaos/tangent flight operator/Cauchy mutation引用本文复制引用
基金项目
广西自然科学基金(2019GXNSFAA1850117)
广西民族大学科研项目(2021MDKJ004)
出版年
2024
NETL
NSTL
万方数据