Abstract: Traditional methods for solving nonlinear equations, such as Newton’s method, gradient descent method and so on,but they are required continuous differentiable, initial value selection. Aiming at above faults, the solution of the problem is transformed to an optimization problem. A new crossover foraging algorithm which is made full use of the ability of local search and particle swarm algorithm bacterial search ability, giving full play to the advantages of the two algorithms is proposed. Numerical experiments result shows that the new algorithm can make up for the lack of local search ability of particle swarm optimization algorithm and bacterial foraging algorithm global searching ability. This algorithm is an effective method for solving nonlinear equations.

Key words: local optimization, crossover, nonlinear equations

摘要： 对于非线性方程组的求解，传统方法有很多，如牛顿法、梯度下降法等，但这些算法存在要求方程组连续可微、初值的选取是否合适等缺点，根据以上缺点将求解的问题转化为优化的问题，提出了新的交叉优化算法，充分利用细菌觅食算法局部搜索能力和粒子群算法的全局搜索能力，充分发挥了这两个算法各自优点。数值实验表明，新的算法可以弥补粒子群算法局部搜索能力弱和细菌觅食算法的全局搜索能力的不足，是求解非线性方程的有效方法。

关键词: 局部优化, 交叉, 非线性方程