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Unification of filled function and Tunnelling function in Global Optimization

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Acta Mathematicae Applicatae Sinica 2007年第1期23卷 59-66页

作者： Wei Wang Yong-jian Yang Lian-sheng Zhang Department of Mathematics East China University of Science and Technology Shanghai 200237 China Department of Mathematics Shanghai University Shanghai 200444 China

In this paper, two auxiliary functions for global optimization are proposed. These two auxiliary functions possess all characters of tunnelling functions and filled functions under certain general assumptions. Thus, they can be considered as the unification of filled function and tunnelling function. Moreover, the process of tunneling or filling for global optimization can be unified as the minimization of such auxiliary functions. Result of numerical experiments shows that such two auxiliary functions are effective.

关键词： Nonlinear programming global optimization filled function tunnelling function unification

One-parameter quasi-filled function algorithm for nonlinear integer programming

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第4期6卷 305-310页

作者：尚有林韩伯顺 Department of Mathematics & Physics Henan University of Science and Technology Department of Mathematics College of Sciences Shanghai University Shanghai 200436 China Department of Mathematics College of Sciences Shanghai University

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.

关键词： Integer programming Local minimizer Global minimizer filled function Global optimization

A One-parameter filled function Method for Nonlinear Integer Programming

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Journal of Donghua University(English Edition) 2005年第4期22卷 1-4页

作者：尚有林杨永建梁玉梅 Math. Dept. Henan University of Sci. and Tech. Luoyang 471003 Math. Dept. Shanghai University Shanghai 200436

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.

关键词： integer programming local minimizer global minimizer filled function global optimization

A filled function with Adjustable Parameters for Unconstrained Global Optimization

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Chinese Quarterly Journal of Mathematics 2004年第3期19卷 232-239页

作者： SHANGYou-lin LIXiao-yan DepartmentofMathematics UniversityofScienceandTechnologyofHenanLuoyang471003China

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.

关键词： filled function global optimization global minimizer unconstrained problem basin hill

Novel Global Optimization Algorithm with a Space-Filling Curve and Integral function

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Journal of the Operations Research Society of China 2021年第3期9卷 619-640页

作者： Zhong-Yu Wang Yong-Jian Yang Department of Mathematics Shanghai UniversityShanghai 200444China

In this study,we consider the global optimization problem in a *** use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the *** on the integral function,we propose an algorithm for solving the global optimization ***,we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.

关键词： Global optimization algorithm Integral function Space-filling curve filled function

filled functionS FOR UNCONSTRAINED GLOBAL OPTIMIZATION

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Applied Mathematics(A Journal of Chinese Universities) 2000年第3期15卷 307-318页

作者： XuZheng XuChengxian FacultyofSciences Xi＇anJiaotongUniv.Xi＇an710049 FacultyofElectricalEngineering Xi＇anJiaotongUniv.Xi＇an710049

The paper is concerned with the filled functions for global optimization of a continuous function of several *** general forms of filled functions are presented for smooth and nonsmooth *** functions have either two adjustable parameters or one adjustable *** on functions and on the values of parameters are given so that the constructed functions are desired filled functions.

关键词： Global optimization filled function nonsmooth optimization basin.

AN ALGORITHM FOR FINDING GLOBAL MINIMUM OF NONLINEAR INTEGER PROGRAMMING

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Journal of Computational Mathematics 2004年第1期22卷 69-78页

作者： Wei-wenTian Lian-shengZhang DepartmentofMathematics ShanghaiUniversityBaoshan.Shanghai200436China

A filled function is proposed by ***^[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear flmction using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and ‖xI- xI^* is large, where xI - an integer point, xI^* - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled flmction and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear flmction, the new filled function improves some properties of the filled function proposed by R. Ge [2]. Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.

关键词： filled function Global integer minimizer Local integer minimizer

Improved Particle Swarm Optimization for Parameter Identification of Permanent Magnet Synchronous Motor

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Computers, Materials & Continua 2024年第5期79卷 2187-2207页

作者： Shuai Zhou Dazhi Wang Yongliang Ni Keling Song Yanming Li School of Information Science and Engineering Northeastern UniversityShenyang110819China China Northern Vehicle Research Institute Beijing100072China

In the process of identifying parameters for a permanent magnet synchronous motor,the particle swarm optimization method is prone to being stuck in local optima in the later stages of iteration,resulting in low parameter *** work proposes a fuzzy particle swarm optimization approach based on the transformation function and the filled *** approach addresses the topic of particle swarmoptimization in parameter identification from two ***,the algorithm uses a transformation function to change the form of the fitness function without changing the position of the extreme point of the fitness function,making the extreme point of the fitness function more prominent and improving the algorithm’s search ability while reducing the algorithm’s computational ***,on the basis of themulti-loop fuzzy control systembased onmultiplemembership functions,it is merged with the filled function to improve the algorithm’s capacity to skip out of the local optimal *** approach can be used to identify the parameters of permanent magnet synchronous motors by sampling only the stator current,voltage,and speed *** simulation results show that the method can effectively identify the electrical parameters of a permanent magnet synchronous motor,and it has superior global convergence performance and robustness.

关键词： Transformation function filled function fuzzy particle swarm optimization algorithm permanent magnet synchronous motor parameter identification

An Approximate Algorithm for a Class of Nonlinear Bilevel Integer Programming

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Systems Science and Systems Engineering 2002年第2期11卷 136-142页

作者： LI Lei, TENG Chun-xian, TIAN Guang-yue Harbin University of Science and Technology, Harbin, 150080, China Harbin University of Science and Technology Harbin 150080 China

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.

关键词： bilevel integer programming continuity methods simulated annealing filled function