Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Ye Tian; Haowen Chen; Haiping Ma; Xingyi Zhang; Kay Chen Tan; Yaochu Jin

doi:10.1109/JAS.2022.105875

Volume 9 Issue 10

Oct. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(10): 1801-1817

Y. Tian, H. W. Chen, H. P. Ma, X. Y. Zhang, K. C. Tan, and Y. C. Jin, “Integrating conjugate gradients into evolutionary algorithms for large-scale continuous multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1801–1817, Oct. 2022. doi: 10.1109/JAS.2022.105875

Citation:

Y. Tian, H. W. Chen, H. P. Ma, X. Y. Zhang, K. C. Tan, and Y. C. Jin, “Integrating conjugate gradients into evolutionary algorithms for large-scale continuous multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1801–1817, Oct. 2022. doi: 10.1109/JAS.2022.105875

Citation:

Y. Tian, H. W. Chen, H. P. Ma, X. Y. Zhang, K. C. Tan, and Y. C. Jin, “Integrating conjugate gradients into evolutionary algorithms for large-scale continuous multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1801–1817, Oct. 2022. doi: 10.1109/JAS.2022.105875

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Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

doi: 10.1109/JAS.2022.105875

Ye Tian^1
,,
Haowen Chen^1
,,
Haiping Ma^1
,,
Xingyi Zhang^{2
,
,},
Kay Chen Tan^3
,,
Yaochu Jin^4
,

1.
Information Materials and Intelligent Sensing Laboratory of Anhui Province, Institutes of Physical Science and Information Technology, Anhui University, and also with the Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230601, China
2.
Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei 230601, China
3.
Department of Computing, The Hong Kong Polytechnic University, Hong Kong SAR, China
4.
Faculty of Technology, Bielefeld University, Bielefeld 33619, Germany

Funds: This work was supported in part by the National Key Research and Development Program of China (2018AAA0100100), the National Natural Science Foundation of China (61906001, 62136008, U21A20512), the Key Program of Natural Science Project of Educational Commission of Anhui Province (KJ2020A0036), and Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research, Germany

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Author Bio:
Ye Tian received the B.Sc., M.Sc., and Ph.D. degrees from Anhui University in 2012, 2015, and 2018, respectively. He is an Associate Professor with the Institutes of Physical Science and Information Technology, Anhui University. His research interests include evolutionary computation and its applications. He is the recipient of the 2018 and 2021 IEEE Transactions on Evolutionary Computation Outstanding Paper Award, the 2020 IEEE Computational Intelligence Magazine Outstanding Paper Award, and the 2022 IEEE Computational Intelligence Society Outstanding Ph.D. Dissertation Award

Haowen Chen received the B.Sc. degree from Hebei Agricultural University in 2020, where she is currently pursuing the M.Sc. degree with the Institutes of Physical Science and Information Technology, Anhui University. Her research interests include evolutionary computation and mathematical programming

Haiping Ma received the B.E. degree from Anhui University in 2008 and the Ph.D. degree from University of Science and Technology of China in 2013. She is a Lecturer with the Institutes of Physical Science and Information Technology, Anhui University. Her research interests include data mining and multi-objective optimization methods and their applications

Xingyi Zhang (Senior Member, IEEE) received the B.Sc. degree from Fuyang Normal College in 2003, and the M.Sc. and Ph.D. degrees from Huazhong University of Science and Technology in 2006 and 2009, respectively. He is a Professor with the School of Artificial Intelligence, Anhui University. His research interests include unconventional models and algorithms of computation, evolutionary multi-objective optimization, and logistic scheduling. He is the recipient of the 2018 and 2021 IEEE Transactions on Evolutionary Computation Outstanding Paper Award and the 2020 IEEE Computational Intelligence Magazine Outstanding Paper Award

Kay Chen Tan (Fellow, IEEE) received the B.Eng. (First Class Hons.) degree in electronics and electrical engineering and the Ph.D. degree from the University of Glasgow, UK, in 1994 and 1997, respectively. He is currently a Chair Professor of the Department of Computing at The Hong Kong Polytechnic University, Hong Kong, China. He has published over 200 refereed articles and six books, and holds one US patent on surface defect detection. Prof. Tan is currently the Vice-President (Publications) of IEEE Computational Intelligence Society, USA. He has served as the Editor-in-Chief of IEEE Transactions on Evolutionary Computation from 2015−2020 and IEEE Computational Intelligence Magazine from 2010−2013, and currently serves as the Editorial Board Member of over 10 journals. He is currently an IEEE Distinguished Lecturer Program (DLP) Speaker and Chief Co-Editor of Springer Book Series on Machine Learning: Foundations, Methodologies, and Applications

Yaochu Jin (Fellow, IEEE) received the B.Sc., M.Sc., and Ph.D. degrees from Zhejiang University in 1988, 1991, and 1996, respectively, and the Dr.-Ing. degree from Ruhr University Bochum, Germany, in 2001.He is an Alexander von Humboldt Professor for artificial intelligence, Chair of Nature Inspired Computing and Engineering, Faculty of Technology, Bielefeld University, Germany. He is also a Distinguished Chair, Professor in Computational Intelligence, Department of Computer Science, University of Surrey, UK. He was a “Finland Distinguished Professor” of University of Jyväskylä, Finland, “Changjiang Distinguished Visiting Professor”, Northeastern University, and “Distinguished Visiting Scholar”, University of Technology Sydney, Australia. His research interests include evolutionary optimization, evolutionary learning, trustworthy machine learning, and evolutionary developmental systems.Prof. Jin is presently the Editor-in-Chief of Complex & Intelligent Systems. He was the Editor-in-Chief of the IEEE Transactions on Cognitive and Developmental Systems in 2016−2021 and an IEEE Distinguished Lecturer in 2013–2015 and 2017–2019, the Vice President for Technical Activities of the IEEE Computational Intelligence Society (2015–2016). He is the recipient of the 2018 and 2021 IEEE Transactions on Evolutionary Computation Outstanding Paper Award, and the 2015, 2017, and 2020 IEEE Computational Intelligence Magazine Outstanding Paper Award. He was named by the Web of Science as “a Highly Cited Researcher” from 2019 to 2021 consecutively. He is a Member of Academia Europaea
Corresponding author: Xingyi Zhang, e-mail: xyzhanghust@gmail.com
Received Date: 2022-03-20
Revised Date: 2022-04-13
Accepted Date: 2022-04-24

Available Online: 2022-06-23

Abstract

Abstract

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
- Conjugate gradient,
- differential evolution,
- evolutionary computation,
- large-scale multi-objective optimization,
- mathematical programming

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References

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This work deeply integrates evolutionary computation (EC) with mathematical programming (MP)
This work customizes a hybrid algorithm for large-scale multi-objective optimization
The proposed algorithm inherits the good convergence of MP and good diversity of EC
The proposed algorithm is verified on time-varying ratio error estimation tasks
The proposed algorithm is verified on intensity-modulated radiotherapy tasks

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

doi: 10.1109/JAS.2022.105875

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