竞选优化算法求解非线性方程组的应用研究

Research on application of election-survey optimization algorithm for solving nonlinear equations

针对非线性方程组的求解在工程上具有广泛的实际意义,经典的数值求解方法存在其收敛性依赖于初值而实际计算中初值难确定的问题,将复杂非线性方程组的求解问题转化为函数优化问题,引入竞选优化算法进行求解。同时竞选优化算法求解时无需关心方程组的具体形式,可方便求解几何约束问题。通过对典型非线性测试方程组和几何约束问题实例的求解,结果表明了竞选优化算法具有较高的精确性和收敛性,是应用于非线性方程组求解的一种可行和有效的算法。

Aimed at the widespread practical significance of solving nonlinear equations in engineering,classic numerical methods are highly sensitive to the initial guess,but it is difficult to find a suitable good initial guess in practical operation,the problem of solving sophisticated nonlinear equation group is transformed to the problem of function optimization,and then,election-survey optimization algorithm is introduced to achieve the optimal result for the problem.Meanwhile the composition of the functions is of little concern,and the algorithm is convenient to solve geometric constraint problems.Numerical simulation experiments of standard nonlinear test equation groups and solving of geometric constraint problems show that election-survey optimization algorithm has higher convergence speed and more precise solution,and it is a feasible and effective approach in solving systems of nonlinear equations problems.