Filled function methods have been considered as an effective approach for solving global optimization problems. However, most filled functions have the drawbacks of discontinuity, non-differentiability, and they could be sensitive to parameters and have exponential or logarithmic terms which may reduce their efficiency. In this paper, we propose a continuously differentiable filled function without parameters and exponential/logarithmic terms to overcome these problems. The continuous differentiability of the presented filled function makes its minimization an easy process and allows using efficient indirect local search methods. The proposed filled function has no parameters to adjust. Adjustment of the parameters is not an easy task, since the parameters may take different values for different problems. Moreover, the new filled function is numerically stable, since there are no exponential or logarithmic terms. Theoretical features of the considered filled function are investigated and a new algorithm for unconstrained global optimization problems is designed. The numerical results show that this method can successfully be used to solve global optimization problems, with a large number of variables. Furthermore, we extend the proposed filled function method to solve systems of nonlinear equations. Finally, some test problems for systems of nonlinear equations are reported, with satisfactory numerical results.

填充函数方法已被认为是解决全局优化问题的有效方法。然而，大多数填充函数具有不连续性、不可微性的缺点，并且它们可能对参数敏感并且具有指数或对数项，这可能会降低它们的效率。在本文中，我们提出了一种无参数和指数/对数项的连续可微填充函数来克服这些问题。所呈现的填充函数的连续可微性使其最小化成为一个简单的过程，并允许使用高效的间接局部搜索方法。提议的填充函数没有要调整的参数。参数的调整不是一件容易的事，因为对于不同的问题，参数可能取不同的值。而且，新的填充函数在数值上是稳定的，因为没有指数或对数项。研究了所考虑的填充函数的理论特征，并设计了一种用于无约束全局优化问题的新算法。数值结果表明，该方法可以成功地用于求解具有大量变量的全局优化问题。此外，我们将所提出的填充函数方法扩展到求解非线性方程组。最后，报告了一些非线性方程组的测试问题，并取得了令人满意的数值结果。数值结果表明，该方法可以成功地用于求解具有大量变量的全局优化问题。此外，我们将所提出的填充函数方法扩展到求解非线性方程组。最后，报告了一些非线性方程组的测试问题，并取得了令人满意的数值结果。数值结果表明，该方法可以成功地用于求解具有大量变量的全局优化问题。此外，我们将所提出的填充函数方法扩展到求解非线性方程组。最后，报告了一些非线性方程组的测试问题，并取得了令人满意的数值结果。