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运筹学学报 >

2021 , Vol. 25 >Issue 1: 89 - 95

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.01.008

 

全局优化问题的一个新的无参数填充函数

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  • 1. 河南科技大学数学与统计学院, 河南洛阳 471003
尚有林 E-mail: mathshang@sina.com

收稿日期: 2019-10-08

  网络出版日期: 2021-03-05

基金资助

国家自然科学基金(12071112);国家自然科学基金(11701150);国家自然科学基金(11471102);河南省高等学校重点科研项目计划基础研究专项(20ZX001)

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A new parameterless filled function for global optimization problems

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  • 1. School of Mathematics and Statistics, Henan University of Science andTechnology, Luoyang 471003, Henan, China

Received date: 2019-10-08

  Online published: 2021-03-05

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摘要

求全局最优化问题的填充函数算法被提出以来，参数的选取和调整一直是制约算法有效性的因素。如何在实际的计算过程中选取合适的参数，直接影响和决定了运算速度和效率。因此，构造不含参数的填充函数就显得极为重要。提出一个新的无参数的填充函数，对其理论性质进行了分析，并给出相应的填充函数算法，数值计算验证了算法的有效性。

关键词： 全局最优化; 填充函数; 无参数; 确定性算法

本文引用格式

屈德强, 尚有林, 詹悦, 吴丹 . 全局优化问题的一个新的无参数填充函数[J]. 运筹学学报, 2021 , 25(1) : 89 -95 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.01.008

Abstract

Since the filled function algorithm for global optimization problems has been proposed, the selection and adjustment of parameters have always been the factors that restrict the effectiveness of the algorithm. How to select appropriate parameters in the actual calculation process directly affects and determines the operation speed and efficiency. Therefore, constructing a filled function without parameters is extremely important. This paper proposes a new parameterless filled function, and gives the corresponding filled function algorithm.Through numerical experiments and comparison with existing literature, numerical experiments verify the effectiveness of the algorithm.

Key words： global optimization; filled function; parameterless; deterministic algorithm

参考文献

1 Ge R P . A filled function method for finding a global minimizer ofa function of several variables[J]. Mathematical Programming, 1990, 46 (1): 191- 204.
2 Ge R P , Qin Y F . A class of filled function for finding globalminimizers of a function of several variables[J]. Journal ofOptimization Theory and Applications, 1987, 54 (2): 241- 252.
3 Ge R P , Huang H . A continuous approach to nonlinear integer programming[J]. Applied Mathematics and Computation, 1989, 34, 39- 60.
4 Liu X . Finding global minima with a computable filled function[J]. Journal of global Optimization, 2001, 19 (2): 151- 161.
5 Liu X . Several filled functions with mitigators[J]. Applied Mathematics and Computation, 2002, 133 (2-3): 375- 387.
6 李博, 鲁殿军. 一个新的单参数填充函数算法[J]. 工程数学学报, 2015, 32 (2): 269- 270.
7 LIN Hongwei , LI Huirong . A new filled function with one parameter to solve global optimization[J]. Open Journal of Optimization, 2015, 4, 10- 20.
8 尚有林. 非线性全局优化中填充函数方法的研究[D]. 上海: 上海大学, 2005.
9 Zhang Y , Zhang L , Xu Y . New filled functions for nonsmooth global optimization[J]. Applied Mathematical Modelling, 2009, 33 (7): 3114- 3129.
10 王伟祥, 尚有林, 王朵. 求解带箱子集约束的非光滑全局优化问题的填充函数方法[J]. 运筹学学报, 2019, 23 (01): 28- 34.
11 石礼堂, 陈伟. 非线性无约束优化问题的滤子填充函数算法[J]. 运筹学学报, 2017, 24 (1): 35- 44.
12 茅嘉, 杨永建. 一个无参数的填充函数算法[J]. 应用数学与计算数学学报, 2010, 21 (01): 55- 64.
13 吴波, 高岳林. 全局优化问题的一个无参数填充函数算法[J]. 数学的实践与认识, 2017, 47 (4): 170- 174.
14 胡铨, 王薇. 求解带箱式约束全局优化问题的滤子填充函数方法[J]. 运筹学学报, 2016, 20 (3): 57- 67.
15 Lin H , Gao Y , Wang X , et al. A filled function which has thesame local minimizer of the objective function[J]. Optimization Letters, 2019, 13 (1): 761- 776.
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