Filled function method is one of deterministic methods for solving global minimization problems. Filled function algorithm method generally contains of two main phases. First phase is to obtain local minimizer of objective function, second is to obtain minimizer or saddle point of filled function. In the second phase, vector direction plays an important role on finding stationary point of filled function, by assist in escaping from neighborhood of current minimizer of objective function of the first phase. In this paper, we introduce parameter free filled function and some typical vector direction to be applied in filled function algorithm. The algorithm method is implemented into some benchmark test functions. General computational and numerical results are presented to show the performance of each vector direction on filled function method for solving two dimensional unconstrained global optimization problems.

#2Fusheng Bai(CNU: Chongqing Normal University)H-Index: 7

An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm.

#2Pu Li(HAUST: Henan University of Science and Technology)H-Index: 1

Last. Hailing Xie(HAUST: Henan University of Science and Technology)H-Index: 1

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Many real life problems can be modeled as nonlinear global optimization problems. Such problems often have multiple local minima and thus require global optimization methods. One of the more recent global optimization tools is known as the filled function method which is a promising way used in unconstrained global optimization. Several filled functions with one or two parameters have already been suggested in the literatures. A new parameter-free filled function different from An [2004, Journal...

Last. Huaqun Liu(SHU: Shanghai University)H-Index: 1

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The filled function method is considered as an efficient method to find the global minimum of multidimensional functions. A number of filled functions were proposed recently, most of which have one or two adjustable parameters. However, there is no efficient criterion to choose the parameter appropriately. In this paper, we propose a filled function without parameter. And this function includes neither exponential terms nor logarithmic terms so it is superior to the traditional ones. Theories of...

Last. Mei-lin Chen(SHU: Shanghai University)H-Index: 1

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The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the obj...

#2Chi-Kong Ng(CUHK: The Chinese University of Hong Kong)H-Index: 6

Last. Wei-Wen Tian(SHU: Shanghai University)H-Index: 2

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A novel filled function is suggested in this paper for identifying a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Theoretical and numerical properties of the proposed filled function are investigated and a solution algorithm is proposed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

#1Xian Liu(U of A: University of Alberta)H-Index: 20

Several filled functions were reported to seek the global minimum of multimodal functions of multiple variables. This paper proposes an alternative formulation that may reduce the negative definite effect of the Hessian of a filled function proposed before. Furthermore, a class of mitigators is defined and applied to improve the computational characteristics of filled functions. Results of numerical experiments on typical testing functions are also reported.

#1Xian Liu(U of A: University of Alberta)H-Index: 20

The Filled Function Method is an approach to finding global minima of multidimensional nonconvex functions. The traditional filled functions have features that may affect the computability when applied to numerical optimization. This paper proposes a new filled function. This function needs only one parameter and does not include exponential terms. Also, the lower bound of weight factor a is usually smaller than that of one previous formulation. Therefore, the proposed new function has better co...

The concept of a filled function is introduced. We construct a particular filled function and analyze its properties. An algorithm for global minimization is generated based on the concept and properties of the filled function. Some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm. The advantages and disadvantages are analyzed and further research directions are discussed.

Global optimization problem still becomes a challenges due to the problem on locating the global optimum of multimodal function. How to reach the better minimizer from the current minimizer and how to decide that the obtained minimizer is the desired one are both major challenges on solving global optimization problem. Filled function method is one of the recent considered deterministic easy applied methods which concerned to the mentioned problems. The basic concept of filled function method is...

Global optimization problem still becomes an interest due to the challenge of locating the global optimum of nonlinear objective function with multiple local minima. Two challenges on solving global optimization problem are; firstly how to reach the better minimizer from the current minimizer, and secondly how to decide that the obtained minimizer is the desired global minimizer. One of the recent considered deterministic easy applied methods, which concerned in the mentioned problems, is the fi...