CAJ | 학술논문

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。
대우비선성방정조적구해，전통방법유흔다，여우돈법、제도하강법등，단저사산법존재요구방정조련속가미、초치적선취시부합괄등결점，근거이상결점장구해적문제전화위우화적문제，제출료신적교차우화산법，충분이용세균멱식산법국부수색능력화입자군산법적전국수색능력，충분발휘료저량개산법각자우점。수치실험표명，신적산법가이미보입자군산법국부수색능력약화세균멱식산법적전국수색능력적불족，시구해비선성방정적유효방법。
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 effec-tive method for solving nonlinear equations.