增强型人工水母算法解多根方程组及工程应用

Improved Artificial Jellyfish Search Algorithm in Equations with Multiple Roots and Engineering Application

针对目前求解多根非线性方程组仍面临求解精度低、解个数不完整、收敛速度慢等问题,提出了一种增强型人工水母算法.首先引入莱维飞行和动态自适应权重因子,以避免陷入局部最优以及满足不同时期全局探索和局部开发的需求,其次采用柯西变异策略来提升算法的全局寻优性能.为测试改进算法性能,引入6个标准测试函数进行测试,实验结果表明改进算法性能优越.并对5组多根非线性方程组求解,与其他经典算法进行对比,结果表明改进算法可以有效地避免陷入局部最优,求解精度和解的数量上更具有优越性,具有较好的寻优能力;最后将算法应用于求解工程实际问题获得满意效果.

To address the problems of low solution accuracy,insufficient number of solutions and slow convergence in solving nonlinear equations with multiple roots,improved a jellyfish search algorithm is proposed.First,Levy flights and dynamic adaptive weighting factors are applied to avoid being trapped at local optima and meet the needs of global exploration and local exploitation in different periods.Then,Cauchy mutation is applied to enhance the ability of algorithms to find the global optima.Results of 6standard test functions show the superior performance of the improved algorithm.The comparison between the result of 5 sets of nonlinear equations with multiple roots calculated through the algorithm and that through classical algorithms shows that the algorithm helps avoid being trapped at local optima and performs better when it comes to the accuracy and number of solutions and the search of optima.Finally,the algorithm is used to solve engineering problems,which helps achieve satisfactory results.