带权重的改进天牛须算法解方程组及工程应用

Improved beetle antennae search algorithm with position weight solving equations and engineering application

针对求解方程组时解值精度低、个数不全和收敛速度慢的问题,提出一种带位置权重的黄金分割自适应的天牛须算法(GRBAS)。将黄金分割法缩短搜索区间的优势结合天牛须算法,天牛左右两须作为黄金分割边界,插值选择更好区间缩短搜索范围;引入位置权重改变天牛的位置,使算法避免易陷入局部收敛的缺陷;为后期在小范围内能更精确搜索,加入步长自适应。通过求解10个标准测试函数、3个线性方程组和3个非线性方程组,表明算法有良好优化性能。将算法用于求解工程上三角函数超越方程,获得满意效果。

Aiming at the problems of low precision,incomplete number and low convergence speed in solving equations,a self-adaptive beetle antennae search algorithm based on golden ratio with position weight(GRBAS)to solve equations.The advantages of the golden ratio method were combined to determine the region of search in the traditional beetle antennae search algorithm.The position of left and right antennae of beetle was regarded as the golden ratio boundary,and by interpolating between the two antennae,the search range of the beetle was shortened.The position weight was introduced to change the position of the beetle to avoid the defect of local convergence.To search more accurately in the later small-scale search,the adaptive step size was added to the algorithm.Through 10 standard test functions,the improved algorithm was used to solve 3 linear equations and 3 nonlinear equations.The results show that the proposed algorithm has good performance.The algorithm is applied to solve the transcendental equations of trigonometric function in engineering and satisfactory results are obtained.