The filled function method is an efficient approach for finding a global minimizer of global optimization problems. This paper introduces a new filled function which overcomes the drawbacks of sensitivity to parameters, containing exponential or logarithmic terms, discontinuity and non-differentiability for some previous filled functions. It proposes a filled function without any parameters to be adjusted. This filled function has no exponential or logarithmic terms which make the filled function numerically unstable. Also it is continuously differentiable, so gradient information is available in order to use effective local minimization algorithms. Theories of the proposed filled function are investigated and an algorithm for unconstrained global optimization is presented. Numerical results on many test problems with large number of variables are reported. A comparison with some existing algorithms shows that this algorithm is efficient and reliable.

中文翻译：

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一种用于求解无约束全局优化问题的新的无参数填充函数

填充函数法是一种寻找全局优化问题的全局极小值的有效方法。本文介绍了一种新的填充函数，它克服了对参数敏感的缺点，包含指数或对数项、不连续性和不可微性，这是一些以前的填充函数。它提出了一个填充函数，无需调整任何参数。这个填充函数没有指数或对数项，这使得填充函数在数值上不稳定。而且它是连续可微的，因此可以使用梯度信息以使用有效的局部最小化算法。研究了所提出的填充函数的理论，并提出了一种无约束全局优化算法。报告了许多具有大量变量的测试问题的数值结果。与一些现有算法的比较表明，该算法是高效可靠的。