求解非线性方程组的HHHO算法及工程应用

HHHO Algorithm for Solving Nonlinear Equations and Its Engineering Application

非线性方程组的求解具有重要的数学意义和实际意义,结合二次插值和差分进化算法的优点,提出了一种混合哈里斯鹰优化算法(HHHO)用于求解非线性方程组。先在勘探阶段采用二次插值方法,增强了算法的全局搜索能力;当算法陷入局部最优时,根据早熟机制,针对陷入局部最优的哈里斯鹰进行变异、选择操作,增强种群的多样性,避免算法陷入早熟。通过10个基准测试函数的测试,证明了HHHO算法在局部搜索能力,求解精度方面优于HHO算法,通过5个非线性方程组的求解验证上述算法在求解精度、解的求解个数上都有一定的优势。最后把HHHO算法用于求解几何约束问题和三角函数超越方程,进一步验证了算法高效的求解性能。

The solution of nonlinear equations has important mathematical and practical significance.Combined with the advantages of quadratic interpolation and differential evolution algorithm,a hybrid Harris Eagle optimization algorithm(HHHO)is proposed to solve nonlinear equations.Firstly,in the exploration stage,the quadratic interpolation method was used to enhance the global search ability of the algorithm;Secondly,when the algorithm falls into local optimization,mutation and selection operations were carried out for the Harris Eagle falling into local optimization according to the precocity mechanism,so as to enhance the diversity of the population and avoid the algorithm falling into precocity.Through the test of 10 benchmark functions,it was proved that HHHO algorithm is superior to HHO algorithm in local search ability and solution accuracy.Through the solution verification of five nonlinear equations,the algorithm has certain advantages in solution accuracy and number of solutions.Finally,HHHO algorithm was applied to solve geometric constraint problems and transcendental equations of trigonometric functions,which further verifies the efficient performance of the algorithm.