基于人工蜂群算法的非线性方程组求解研究

Research on the Solving Method Based on Artificial Bee Colony Algorithm for Nonlinear Equations

为了更有效地求解复杂的非线性方程组,引入了人工蜂群算法。考虑到人工蜂群算法后期表现出的收敛速度慢、容易陷入局部最优值的缺点,提出了一种新的人工蜂群优化算法(IABC)。新算法对工蜂进行邻域搜索产生新解的方法进行了改进,引入了尝试次数,修改了向新食物源靠拢的递进步长,加快了原有算法的收敛速度。试验结果表明,改进算法较好地平衡了全局搜索能力和局部搜索能力,是一种求解非线性方程组的高效算法。

To solve the complex nonlinear equations more effectively, the artificial bee colony （ ABC ） algorithm is introduced. Considering the demerit of artificial bee colony algorithm, i. e. , easily to fall into local optimum value because of the slow late convergence speed, an improved artificial bee colony （ IABC ） optimized algorithm is proposed. The new algorithm improves the method for producing new solution when bees are doing neighborhood search, introduces the number of attempts, modifies the progressive step moving to a new food resource, and accelerates the original convergence speed. The test result indicates that the improved algorithm well balances the global and local seeking capability, so it is a highly efficient algorithm for solving nonlinear equations.