求解箱式约束全局优化问题的新的填充函数

屈德强, 吴丹, 尚有林

doi:10.13371/j.cnki.chin.q.j.m.2020.04.003

数学季刊 >

2020 , Vol. 35 >Issue 4: 354 - 362

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.04.003

求解箱式约束全局优化问题的新的填充函数

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School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China

QU De-qiang (1996-), male, native of Nanyang, Henan, postgraduate student of Henan University of Science and Technology, engages in operations research and cybernetics; WU Dan (1981-), female, native of Luoyang, Henan, lecturer of Henan University of Science and Technology, engages in operations research and cybernetics and systems science and engineering; SHANG You-lin (1963-), male, native of Luoyang, Henan, professor of Henan University of Science and Technology, engages in operations research, cybernetics, systems science and engineering.

收稿日期: 2020-07-06

网络出版日期: 2021-01-06

基金资助

Supported by National Natural Science Foundation of China (Grant No. 11471102, 11701150, 12071112); Basic research projects for key scientific research projects in Henan Province (Grant No. 20ZX001).

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A New Filled Function for Global Optimization Problems with Box Constraints

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School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China

Received date: 2020-07-06

Online published: 2021-01-06

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11471102, 11701150, 12071112); Basic research projects for key scientific research projects in Henan Province (Grant No. 20ZX001).

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摘要

本文考虑利用辅助函数法求解箱式约束全局优化问题。首先，提出了一个新的与目标函数具有相同局部极小点的无参数填充函数。该填充函数的局部极小点是目标函数更优的局部极小点，基于这一特征设计的填充函数方法，目标函数只需要被极小化一次。改变了传统填充函数法目标函数和填充函数交替极小化的算法框架，能有效减少算法的迭代次数，加快寻找全局极小点的速度。随后进一步讨论了填充函数的理论性质，并建立了相应的算法。最后，通过数值实验验证了算法的可行性和有效性。

关键词： 全局最优化; 无参数填充函数; 局部极小点

本文引用格式

屈德强, 吴丹, 尚有林 . 求解箱式约束全局优化问题的新的填充函数[J]. 数学季刊, 2020 , 35(4) : 354 -362 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.003

Abstract

In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed. By the character that having same local minimizers, and these minimizers are all better than the current minimizer of the objective function, it does not need to minimize the objective function except for the first iteration in the filled function method. It changes the frame of conventional filled function methods that objective function and filled function are minimized alternately, and can effectively reduce the iterations of the algorithm and accelerate the speed of global optimization. And then the theoretical properties of the filled function are discussed and the corresponding algorithm is established. Finally, numerical experiments are made and comparisons on several test problems are shown which exhibit the feasibility and effectiveness of the algorithm.

Key words： Global Optimization; Non-Parameter Filled Function; Local Minimizer

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