Abstract: A Hybrid Population Migration Algorithm（HPMA）, which combines the advantages of the two methods of Variable Metric Method（VMM） and Population Migration Algorithm（PMA）, is proposed to solve systems of nonlinear functions, because there are some disadvantages of VMM is sensitive to the initial value, and PMA is inaccurate due to it easily fall into local optimal. The algorithm not only explores the global search performance of PMA but also exploits the local search ability of VMM. Experimental results show that HPMA not only has solved the all kinds of systems of nonlinear functions, but has high convergence rate and strong robustness, it is a good algorithm for solving systems of nonlinear functions.

Key words: system of nonlinear functions, Variable Metric Method（VMM）, Population Migration Algorithm（PMA）, hybrid algorithm

摘要： 针对变尺度法对初始值敏感和人口迁移算法容易陷入局部极值的缺陷，结合变尺度法和人口迁移算法各自的优点，提出了一种混合人口迁移算法，用来求解非线性方程组。该混合算法不仅发挥了人口迁移算法强大的全局搜索能力，而且利用了变尺度法的局部精细搜索能力。实验结果表明，该算法不但以较高的精度求出了各种非线性方程组的解，而且鲁棒性强，收敛速度快速，是一种解决非线性方程组问题的较好方法。

关键词: 非线性方程组, 变尺度法, 人口迁移算法, 混合算法