数学季刊 >

2021 , Vol. 36 >Issue 2: 188 - 195

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.007

求解全局优化问题的一种新的非参数填充函数

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  • 1. School of Science, Hebei University of Technology, Tianjin 300401, China; 2. School of Mathematics
    and Statistics, Henan University of Science and Technology, Luoyang 471000, China
LIU Jin-zan (1996-), male, native of Shangqiu, Henan, postgraduate student of Hebei University of Technology, engages in operations research and cybernetics; QU De-qiang (1996-), male, native of Nanyang, Henan, postgraduate student of Henan University of Science and Technology, engages in operations research and cybernetics.

收稿日期: 2020-12-24

  网络出版日期: 2021-03-01

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A New Non-Parameter Filled Function for Global Optimization Problems

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  • 1. School of Science, Hebei University of Technology, Tianjin 300401, China; 2. School of Mathematics
    and Statistics, Henan University of Science and Technology, Luoyang 471000, China
LIU Jin-zan (1996-), male, native of Shangqiu, Henan, postgraduate student of Hebei University of Technology, engages in operations research and cybernetics; QU De-qiang (1996-), male, native of Nanyang, Henan, postgraduate student of Henan University of Science and Technology, engages in operations research and cybernetics.

Received date: 2020-12-24

  Online published: 2021-03-01

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摘要

 In the paper, to solve the global optimization problems, we propose a novel
parameter-free filled function. Based on the non-parameter filled function, a new filled
function algorithm is designed. In the algorithm, the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free. In
addition, in the region lower than the current local minimizer of the objective function, the
filled function is continuously differentiable which enables any gradient descent method
to be used as a local search method in the algorithm. Through numerical experiments by
solving two test problems, the effectiveness of the algorithm is verified.

关键词：  Global optimization; Non-parameter filled function; Box constraint

本文引用格式

刘金赞, 屈德强 . 求解全局优化问题的一种新的非参数填充函数[J]. 数学季刊, 2021 , 36(2) : 188 -195 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.007

Abstract

 In the paper, to solve the global optimization problems, we propose a novel
parameter-free filled function. Based on the non-parameter filled function, a new filled
function algorithm is designed. In the algorithm, the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free. In
addition, in the region lower than the current local minimizer of the objective function, the
filled function is continuously differentiable which enables any gradient descent method
to be used as a local search method in the algorithm. Through numerical experiments by
solving two test problems, the effectiveness of the algorithm is verified.

Key words：  Global optimization; Non-parameter filled function; Box constraint

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