Even Search in a Promising Region for Constrained Multi-Objective Optimization

Fei Ming; Wenyin Gong; Yaochu Jin

doi:10.1109/JAS.2023.123792

Volume 11 Issue 2

Feb. 2024

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(2): 474-486

F. Ming, W. Gong, and Y. Jin, “Even search in a promising region for constrained multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 474–486, Feb. 2024. doi: 10.1109/JAS.2023.123792

Citation:

F. Ming, W. Gong, and Y. Jin, “Even search in a promising region for constrained multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 474–486, Feb. 2024. doi: 10.1109/JAS.2023.123792

Citation:

PDF( 1800 KB)

Even Search in a Promising Region for Constrained Multi-Objective Optimization

doi: 10.1109/JAS.2023.123792

Fei Ming^,,
Wenyin Gong^{,
,},
Yaochu Jin^{,
,}

Funds: This work was partly supported by the National Natural Science Foundation of China (62076225)

More Information

Author Bio:
Fei Ming received the B.Sc. degree in computer science from China University of Geosciences in 2019. He is currently a Ph.D. candidate with the School of Computer Science, China University of Geosciences. His current research interests include evolutionary multiobjective optimization methods and their applications

Wenyin Gong (Member, IEEE) received the B.Eng., M.Eng. and Ph.D. degrees in computer science from China University of Geosciences, in 2004, 2007 and 2010, respectively. He is currently a Professor with School of Computer Science, China University of Geosciences. His research interests include evolutionary algorithms, evolutionary optimization, and their applications. Professor Gong has published over 80 research papers in journals and international conferences. He served as a Referee for over 30 international journals, such as IEEE Transactions on Evolutionary Computation, IEEE Transactions on Cybernetics, IEEE Transactions on Systems, MAN, and Cybernetics: Systems, IEEE Computational Intelligence Magazine, ACM Transactions on Intelligent Systems and Technology, Information Sciences, European Journal of Operational Research, Applied Soft Computing, Journal of Power Sources, etc. He currently serves as Associate Editor of Expert Systems With Applications, International Journal of Bio-Inspired Computation, Memetic Computing, etc

Yaochu Jin (Fellow, IEEE) received the B.Sc., M.Sc., and Ph.D. degrees in automatic control from Zhejiang University, in 1988, 1991 and 1996, respectively, and the Dr.-Ing, degree in neuroinformatics from Ruhr University Bochum, Germany in 2001. He joined the Westlake University in October 2023 as a Chair Professor of Al, leading the Trustworthy and General Al Laboratory. He was an Alexander von Humboldt Professor for Al with the Faculty of Technology, Bielefeld University, Germany from 2021 to 2023, and a Distinguished Chair, Professor in Computational Intelligence with the Department of Computer Science, University of Surrey, UK. He was a “Finland Distinguished Professor” with the University of JyvÃskyla, Finland, “Changjiang Distinguished Visiting Professor” with Northeastern University, China, and “Distinguished Visiting Scholar”, University of Technology Sydney, Australia. His main research interests include multi-objective and data-driven evolutionary optimization, evolutionary multi-objective learning, trustworthy Al, and evolutionary developmental Al. Professor Jin is presently the President of the IEEE Computational Intelligence Society and the Editor-in-Chief of Complex & Intelligent Systems. He is the recipient of the 2018, 2021 and 2023 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 Clarivate as “a Highly Cited Researcher” from 2019 to 2023 consecutively. He is a Member of Academia Europaea and Fellow of IEEE
Corresponding author: Wenyin Gong, e-mail: wygong@cug.edu.cn; Yaochu Jin, e-mail: jinyaochu@westlake.edu.cn
¹ Overfit in this work indicates that a method performs extremely well on some problems but unusable (i.e., cannot find a desirable number of applicable solutions) on others.
² Evidence can be found in Secion IV, where we perform various experiments to test performances of different CMOEAs on different CMOPs. The results clearly reveal that some CMOEAs using a specific or complicated strategy (e.g., BiCo and MFOSPEA2) perform very well on one kind of CMOP but cannot handle other features of CMOPs.
³ Detailed discussions and analyses on all experimental results can be found in the supplementary file at: https: //wewnyin.github.io/wenyingong/Publication/CMOES-supp.pdf.
⁴ Dimensions of m and n of the selected benchmarks are reported in Table S-I in the Supplementary file.
Received Date: 2023-06-18
Accepted Date: 2023-07-25

Available Online: 2023-11-23

Abstract

Abstract

In recent years, a large number of approaches to constrained multi-objective optimization problems (CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly fine-tuned strategy or technique might overfit some problem types, resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties. First, the constrained Pareto front (CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance (i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search, which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
- Constrained multi-objective optimization,
- even search,
- evolutionary algorithms,
- promising region,
- real-world problems

FullText(HTML)

¹ Overfit in this work indicates that a method performs extremely well on some problems but unusable (i.e., cannot find a desirable number of applicable solutions) on others.
² Evidence can be found in Secion IV, where we perform various experiments to test performances of different CMOEAs on different CMOPs. The results clearly reveal that some CMOEAs using a specific or complicated strategy (e.g., BiCo and MFOSPEA2) perform very well on one kind of CMOP but cannot handle other features of CMOPs.
³ Detailed discussions and analyses on all experimental results can be found in the supplementary file at: https: //wewnyin.github.io/wenyingong/Publication/CMOES-supp.pdf.
⁴ Dimensions of m and n of the selected benchmarks are reported in Table S-I in the Supplementary file.

References(31)

References

[1]	Z. Ma and Y. Wang, “Shift-based penalty for evolutionary constrained multiobjective optimization and its application,” IEEE Trans. Cyber., vol. 53, no. 1, pp. 18–30, Jan. 2023. doi: 10.1109/TCYB.2021.3069814
[2]	Y. Hua, Q. Liu, K. Hao, and Y. Jin, “A survey of evolutionary algorithms for multi-objective optimization problems with irregular Pareto fronts,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 303–318, 2021.
[3]	Z. Liu and Y. Wang, “Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces,” IEEE Trans. Evolutionary Computation, vol. 23, no. 5, pp. 870–884, 2019.
[4]	K. Li, R. Chen, G. Fu, and X. Yao, “Two-archive evolutionary algorithm for constrained multiobjective optimization,” IEEE Trans. Evolutionary Computation, vol. 23, no. 2, pp. 303–315, 2019. doi: 10.1109/TEVC.2018.2855411
[5]	Y. Tian, Y. Zhang, Y. Su, X. Zhang, K. C. Tan, and Y. Jin, “Balancing objective optimization and constraint satisfaction in constrained evolutionary multiobjective optimization,” IEEE Trans. Cyber., vol. 52, no. 9, pp. 9559–9572, Sept. 2022. doi: 10.1109/TCYB.2020.3021138
[6]	J. Liang, K. Qiao, K. Yu, B. Qu, C. Yue, W. Guo, and L. Wang, “Utilizing the relationship between unconstrained and constrained Pareto fronts for constrained multiobjective optimization,” IEEE Trans. Cyber., vol. 53, no. 6, pp. 3873–3886, Jun. 2023. doi: 10.1109/TCYB.2022.3163759
[7]	Z. Fan, W. Li, X. Cai, H. Li, C. Wei, Q. Zhang, K. Deb, and E. Goodman, “Push and pull search for solving constrained multi-objective optimization problems,” Swarm and Evolutionary Computation,, vol. 44, pp. 665–679, 2019. doi: 10.1016/j.swevo.2018.08.017
[8]	Z. Sun, H. Ren, G. G. Yen, T. Chen, J. Wu, H. An, and J. Yang, “An evolutionary algorithm with constraint relaxation strategy for highly constrained multiobjective optimization,” IEEE Trans. Cyber., vol. 53, no. 5, pp. 3190–3204, May 2023. doi: 10.1109/TCYB.2022.3151974
[9]	J. Yuan, H.-L. Liu, and Z. He, “A constrained multi-objective evolutionary algorithm using valuable infeasible solutions,” Swarm and Evolutionary Computation, vol. 68, p. 101020, 2022.
[10]	F. Ming, W. Gong, L. Wang, and C. Lu, “A tri-population based coevolutionary framework for constrained multi-objective optimization problems,” Swarm and Evolutionary Computation, vol. 70, p. 101055, 2022.
[11]	D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evolutionary Computation, vol. 1, no. 1, pp. 67–82, 1997. doi: 10.1109/4235.585893
[12]	Y. Tian, T. Zhang, J. Xiao, X. Zhang, and Y. Jin, “A coevolutionary framework for constrained multiobjective optimization problems,” IEEE Trans. Evolutionary Computation, vol. 25, no. 1, pp. 102–116, 2021.
[13]	R. Jiao, B. Xue, and M. Zhang, “A multiform optimization framework for constrained multiobjective optimization,” IEEE Trans. Cyber., vol. 53, no. 8, pp. 5165–5177, Aug. 2023. doi: 10.1109/TCYB.2022.3178132
[14]	K. Yu, J. Liang, B. Qu, Y. Luo, and C. Yue, “Dynamic selection preference-assisted constrained multiobjective differential evolution,” IEEE Trans. Systems,Man,and Cyber.: Systems, vol. 52, no. 5, pp. 2954–2965, 2022.
[15]	Z. Ma, Y. Wang, and W. Song, “A new fitness function with two rankings for evolutionary constrained multiobjective optimization,” IEEE Trans. Systems,Man,and Cyber.: Systems, vol. 51, no. 8, pp. 5005–5016, 2021.
[16]	J. Zhou, J. Zou, J. Zheng, S. Yang, D. Gong, and T. Pei, “An infeasible solutions diversity maintenance epsilon constraint handling method for evolutionary constrained multiobjective optimization,” Soft Computing, vol. 25, no. 13, pp. 8051–8062, 2021.
[17]	C. Qin, F. Ming, W. Gong, and Q. Gu, “Constrained multi-objective optimization via two archives assisted push-pull evolutionary algorithm,” Swarm and Evolutionary Computation, vol. 75, p. 101178, 2022. doi: 10.1016/j.swevo.2022.101178
[18]	Y. Tian, R. Cheng, X. Zhang, and Y. Jin, “PlatEMO: A MATLAB platform for evolutionary multi-objective optimization,” IEEE Computational Intelligence Magazine, vol. 12, pp. 73–87, 2017.
[19]	Z. Ma and Y. Wang, “Evolutionary constrained multiobjective optimization: Test suite construction and performance comparisons,” IEEE Trans. Evolutionary Computation, vol. 23, no. 6, pp. 972–986, 2019.
[20]	Z. Fan, W. Li, X. Cai, H. Huang, Y. Fang, Y. Yugen, J. Mo, C. Wei, and E. Goodman, “An improved epsilon constraint-handling method in MOEA/D for CMOPS with large infeasible regions,” Soft Computing, vol. 23, pp. 12491–12510, 2019.
[21]	Z. Fan, W. Li, X. Cai, H. Li, C. Wei, Q. Zhang, K. Deb, and E. Goodman, “Difficulty adjustable and scalable constrained multiobjective test problem toolkit,” Evolutionary Computation, vol. 28, no. 3, pp. 339–378, 2020.
[22]	A. Kumar, G. Wu, M. Z. Ali, Q. Luo, R. Mallipeddi, P. N. Suganthan, and S. Das, “A benchmark-suite of real-world constrained multiobjective optimization problems and some baseline results,” Swarm and Evolutionary Computation, vol. 67, p. 100961, 2021.
[23]	Z.-Z. Liu, B.-C. Wang, and K. Tang, “Handling constrained multiobjective optimization problems via bidirectional coevolution,” IEEE Trans. Cyber., vol. 52, no. 10, pp. 10163–10176, Oct. 2022. doi: 10.1109/TCYB.2021.3056176
[24]	H. Ishibuchi, R. Imada, N. Masuyama, and Y. Nojima, “Comparison of hypervolume, IGD and IGD+ from the viewpoint of optimal distributions of solutions,” in Proc. Evolutionary Multi-Criterion Optimization, 2019, pp. 332–345.
[25]	E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach,” IEEE Trans. Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999.
[26]	H. Ishibuchi, L. M. Pang, and K. Shang, “Difficulties in fair performance comparison of multi-objective evolutionary algorithms [research frontier],” IEEE Computational Intelligence Magazine, vol. 17, no. 1, pp. 86–101, 2022.
[27]	Z. Lv, L. Wang, Z. Han, and J. Zhao, “Surrogate-assisted particle swarm optimization algorithm with Pareto active learning for expensive multiobjective optimization,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 838–849, 2019.
[28]	Y. Tian, L. Si, X. Zhang, K. C. Tan, and Y. Jin, “Local modelbased Pareto front estimation for multiobjective optimization,” IEEE Trans. Systems,Man,and Cyber.: Systems, vol. 53, no. 1, pp. 623–634, Jan. 2023. doi: 10.1109/TSMC.2022.3186546
[29]	Y. Tian, H. Chen, H. Ma, X. Zhang, K. Tan, and Y. Jin, “Integrating conjugate gradients into evolutionary algorithms for large-scale continuous multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, p. 1801–1817, 2022.
[30]	W. Li, X. Yao, K. Li, R. Wang, and T. Zhang, “Coevolutionary framework for generalized multimodal multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 7, pp. 1544–1556, 2022.
[31]	Y. Tian, Y. Feng, X. Zhang, and C. Sun, “A fast clustering based evolutionary algorithm for super-large-scale sparse multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 1048–1063, 2023. doi: 10.1109/JAS.2022.105437

Supplements(1)

Supplements

JAS-2023-0595-supp.pdf

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(8) / Tables(1)

Get Citation

PDF

XML

Article Metrics

Article views (501) PDF downloads(110)

Highlights

A promising region concept that includes the CPF and possesses good properties
An even search method utilizing valuable solutions in the promising region to search the CPF
A new two-stage CMOEA that implements the even search method

Even Search in a Promising Region for Constrained Multi-Objective Optimization

doi: 10.1109/JAS.2023.123792

Abstract

References

Supplements

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content