求解非线性方程组的蛙跳和 BFGS 混合算法

摘要

Shuffled Frog Leaping Algorithm ( SFLA) is characterized by simplicity , few control parameters required , and easily be used.However, SFLA would easily trap into local optimum and have a low convergent precision when being used to address complex problems .As the traditional numerical optimization method , BFGS is of good local optimum ability .In order to improve the performance of SFLA , a new algorithm called SFLA based on BFGS is proposed , which combines the advantages of the meth-ods of BFGS and SFLA , is put forward to solve systems of nonlinear functions .The experiment results show that the proposed al-gorithm is of the advantages of robustness , higher precision and faster speed by test of three systems of nonlinear functions .It is a good algorithm for solving systems of nonlinear functions .%混合蛙跳算法具有算法简单、控制参数少、易于实现等优点，但缺乏良好的局部细化搜索能力，使得求解精度不高。借鉴BFGS算法强的局部搜索能力，将BFGS算法与混合蛙跳算法有机融合，形成性能更优的混合优化算法，并用来求解非线性方程组。通过3个非线性方程组的实验表明，该混合算法收敛精度较高，收敛速度较快，是一种较好的求解非线性方程组的方法。