This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties o...This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.展开更多
A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled functi...A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover, we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the pro- posed quasi-filled function algorithm.展开更多
A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. Th...A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the pro- posed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algo- rithm.展开更多
The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic de...The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic definitions of discrete optimization are given. Then an algorithm and the implementation of this algorithm on several test problems are showed. The computational results show the algorithm is effective.展开更多
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 f...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 objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30展开更多
In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continu...In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.展开更多
Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimiza...Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.展开更多
The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming ...The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.展开更多
In this paper,a new transformation function was proposed for finding global minimizer of discrete optimization problems.We proved that under some general assumptions the new transformation function possesses the prope...In this paper,a new transformation function was proposed for finding global minimizer of discrete optimization problems.We proved that under some general assumptions the new transformation function possesses the properties of both the tunneling functions and the filled functions.Only one parameter was included in the proposed function,and it can be adjusted easily in the realization.Numerical results demonstrate the effectiveness of the proposed method.展开更多
This paper considers discrete global optimization problems.The traditional definition of the discrete filled function is modified in this paper.Based on the modified definition,a new discrete filled function is presen...This paper considers discrete global optimization problems.The traditional definition of the discrete filled function is modified in this paper.Based on the modified definition,a new discrete filled function is presented and an algorithm for discrete global optimization is developed from the discrete filled function.Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the efficiency of the algorithm.展开更多
文摘This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.
基金Project (Nos. 10571137 and 10271073) supported by the NationalNatural Science Foundation of China
文摘A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover, we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the pro- posed quasi-filled function algorithm.
基金Project (No. 10271073) supported by the National Natural Science Foundation of China
文摘A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the pro- posed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algo- rithm.
基金Foundation item： the National Science Foundation of China（7A14178） the Science Fund of Shanghai University of Engineering Science for Young Scholars（2005Q23） the Natural Science Foundation of Education Commission of Shanghai （No.05NZ07）.
文摘The Filled Function Method is a class of effective algorithms for continuous global optimization. In this paper, a new filled function method is introduced and used to solve integer programming. Firstly, some basic definitions of discrete optimization are given. Then an algorithm and the implementation of this algorithm on several test problems are showed. The computational results show the algorithm is effective.
文摘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 objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30
文摘In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.
文摘Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.
基金This research is supported by National Natural Science Foundation of China (69874009)
文摘The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.
基金the National Natural Science Foundation of China(Nos.11471102 and 10971053).
文摘In this paper,a new transformation function was proposed for finding global minimizer of discrete optimization problems.We proved that under some general assumptions the new transformation function possesses the properties of both the tunneling functions and the filled functions.Only one parameter was included in the proposed function,and it can be adjusted easily in the realization.Numerical results demonstrate the effectiveness of the proposed method.
基金This work was supported by the National Natural Science Foundation of China(No.11471062)Ningxia Foundation for Key Disciplines of Computational Mathematics.
文摘This paper considers discrete global optimization problems.The traditional definition of the discrete filled function is modified in this paper.Based on the modified definition,a new discrete filled function is presented and an algorithm for discrete global optimization is developed from the discrete filled function.Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the efficiency of the algorithm.
基金The National Natural Science Foundation of China (10571137 and 10571116)the Great Natural Science Foundation of Henan University of Science and Technology (2005ZD006)
