A New Filled Function for Global Optimization Problems with Box Constraints

QU De-qiang, WU Dan, SHANG You-lin

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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.

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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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

Cite this article

QU De-qiang, WU Dan, SHANG You-lin . A New Filled Function for Global Optimization Problems with Box Constraints[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(4) : 354 -362 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.003

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