A Class of Parameter-Free Filled Functions for Unconstrained Global Optimization

The deficiencies of existing filled functions have been extensively reviewed in the literature. Their use of an exponent function, the existence of adjustable parameters, their discontinuities, and their difficulty in determining an initial minimization point are significant issues that must be addressed. Although a new generation of filled functions, i.e., parameter-free filled functions, has been proposed, these filled functions still include an exponential term or some discontinuous points in their feasible domains. In this paper, these two adverse effects were diminished by providing a more general form, a new parameter free, and nonexponential filled function, which is continuously differentiable. The results of the analysis demonstrated that, under a specific condition, the properties of the filled functions presented in this paper meet the definition of a filled function. A comparison of numerical results confirmed that the proposed filled function performs better compared to some other parametric and nonparametric filled functions.