Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

Aijuan Song; Guohua Wu; Witold Pedrycz; Ling Wang

doi:10.1109/JAS.2021.1004278

Volume 9 Issue 1

Jan. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(1): 75-89

A. J. Song, G. H. Wu, W. Pedrycz, and L. Wang, “Integrating variable reduction strategy with evolutionary algorithms for solving nonlinear equations systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 75–89, Jan. 2022. doi: 10.1109/JAS.2021.1004278

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A. J. Song, G. H. Wu, W. Pedrycz, and L. Wang, “Integrating variable reduction strategy with evolutionary algorithms for solving nonlinear equations systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 75–89, Jan. 2022. doi: 10.1109/JAS.2021.1004278

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Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

doi: 10.1109/JAS.2021.1004278

Aijuan Song^1
,,
Guohua Wu^{1
,
,},
Witold Pedrycz^{2, 3, 4
,},
Ling Wang^5
,

1.
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
2.
Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada
3.
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4.
Systems Research Institute, Polish Academy of Sciences, Warsaw 01447, Poland
5.
Department of Automation, Tsinghua University, Beijing 100084, China

Funds: This work was supported by the National Natural Science Foundation of China (62073341), and in part by the Natural Science Fund for Distinguished Young Scholars of Hunan Province (2019JJ20026)

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Author Bio:
Aijuan Song received the B.E. degree from Central South University, China, in 2019. Currently, she is a master student at the School of Traffic & Transportation Engineering, Central South University. Her research interests include computational intelligence, multiobjective evolutionary algorithms, planning and scheduling

Guohua Wu received the B.S. degree in information systems and the Ph.D degree in operations research from National University of Defense Technology, China, in 2008 and 2014, respectively. During 2012 and 2014, he was a Visiting Ph.D Student at University of Alberta, Edmonton, Canada. He is currently a Professor at the School of Traffic and Transportation Engineering, Central South University, Changsha, China. His current research interests include planning and scheduling, computational intelligence and machine learning. He has authored more than 80 referred papers including those published in IEEE TCYB, IEEE TSMCA and IEEE TITS. He serves as an Associate Editor of Swarm and Evolutionary Computation Journal, an editorial board member of International Journal of Bio-Inspired Computation, and a Guest Editor of Information Sciences and Memetic Computing. He is a regular reviewer of more than 20 journals including IEEE TEVC, IEEE TCYB, IEEE TSMCA and Information Sciences

Witold Pedrycz received the M.Sc. degree in computer science, the Ph.D. degree in computer engineering, and the D.Sci. degree in systems science from the Silesian University of Technology, Gliwice, Poland, in 1977, 1980, and 1984, respectively. He is a Professor and the Canada Research Chair (CRC-Computational Intelligence) with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada, and also with the Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. He is also with the Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland. In 2012, he was elected a Fellow of the Royal Society of Canada. His current research interests include computational intelligence, knowledge discovery and data mining, pattern recognition, knowledge-based neural networks, and software engineering. He has published numerous papers in the above areas. He is an Editor-in-Chief of Information Sciences. He currently serves as an Associate Editor of IEEE Transactions on Fuzzy Systems and IEEE Transactions on Systems, Man and Cybernetics: System and is a member of a number of editorial boards of other international journals

Ling Wang received the B.Sc. degree in automation and the Ph.D. degree in control theory and control engineering from Tsinghua University, Beijing, China, in 1995 and 1999, respectively. Since 1999, he has been with the Department of Automation, Tsinghua University, where he became a Full Professor in 2008. He has authored five academic books and over 260 refereed papers. His current research interests include intelligent optimization and production scheduling. He was a Recipient of the National Natural Science Fund for Distinguished Young Scholars of China, the National Natural Science Award (Second Place) in 2014, the Science and Technology Award of Beijing City in 2008, the Natural Science Award (First Place in 2003 and Second Place in 2007) nominated by the Ministry of Education of China. He is currently the Editor-in-Chief of the International Journal of Automation and Control and an Associate Editor of the IEEE Transactions on Evolutionary Computation
Corresponding author: Guohua Wu, e-mail: guohuawu@csu.edu.cn
¹ The statistical tests reported in this paper are calculated by the KEEL3.0 software [32].
² http://faculty.csu.edu.cn/guohuawu/zh_CN/zdylm/193832/list/index.htm
³ Except for VR-DR-JADE, DR-JADE, and MONES, the data of other seven compared methods are from the literature [20] and the detailed results of the eleven methods are reported in the supplementary file².
⁴ The date of DR-JADE comes from [20].
Received Date: 2021-03-27
Accepted Date: 2021-05-21

Available Online: 2023-03-29

Abstract

Abstract

Nonlinear equations systems (NESs) are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots. Evolutionary algorithms (EAs) are one of the methods for solving NESs, given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run. Currently, the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs. By contrast, problem domain knowledge of NESs is investigated in this study, where we propose the incorporation of a variable reduction strategy (VRS) into EAs to solve NESs. The VRS makes full use of the systems of expressing a NES and uses some variables (i.e., core variable) to represent other variables (i.e., reduced variables) through variable relationships that exist in the equation systems. It enables the reduction of partial variables and equations and shrinks the decision space, thereby reducing the complexity of the problem and improving the search efficiency of the EAs. To test the effectiveness of VRS in dealing with NESs, this paper mainly integrates the VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE) according to the integration framework of the VRS and EA, respectively. Experimental results show that, with the assistance of the VRS, the EA methods can produce better results than the original methods and other compared methods. Furthermore, extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.
- Evolutionary algorithm (EA),
- nonlinear equations systems (ENSs),
- problem domain knowledge,
- variable reduction strategy (VRS)

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¹ The statistical tests reported in this paper are calculated by the KEEL3.0 software [32].
² http://faculty.csu.edu.cn/guohuawu/zh_CN/zdylm/193832/list/index.htm
³ Except for VR-DR-JADE, DR-JADE, and MONES, the data of other seven compared methods are from the literature [20] and the detailed results of the eleven methods are reported in the supplementary file².
⁴ The date of DR-JADE comes from [20].

References(43)

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Variable reduction strategy was proposed to reduce nonlinear equations systems
A framework of variable reduction strategy and evolutionary algorithms was presented
Variable reduction strategy enables a better performance of an original algorithm
A better algorithm and a reduction scheme with more reduced variables perform better

Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

doi: 10.1109/JAS.2021.1004278

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