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The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems. [ABSTRACT FROM AUTHOR]

This paper intends to develop a new integral filled function method with four properties. First, the proposed filled function is non-exponential and non-logarithmic. This property is aimed at avoiding the overflow effect during the computational stage. Second, our method does not contain parameters, so the possibility of non-converging iterations can be prevented. Third, the filled function proposed in this paper is continuously differentiable. By this property, any local minimization procedures can be applied. Finally, the suggested filled function is dependent on the objective function, and thus it can provide any information for locating a minimum of the filled function. To show that the proposed method is competitive, a comparison has been made with one of the deterministic approaches, namely the DIRECT method. [ABSTRACT FROM AUTHOR]

This study aims to provide a non-limiting factor auxiliary function in a general form. This function, under some assumptions, is proven to fulfill the properties of filling functions. The properties of the proposed method, which include continuously differentiable and the absence of any limiting factor, provide an advantage during numerical experiments for solving some global optimization problems. A numerical comparison was performed, and the results confirmed that our filling function has several advantages compared with other filling functions. Moreover, numerical computational results demonstrate the reliability and effectiveness of the proposed filling function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]