IEEE/CAA Journal of Automatica Sinica
Citation: | K. Qiao, J. Liang, K. Yu, X. Ban, C. Yue, B. Qu, and P. Suganthan, “Constraints separation based evolutionary multitasking for constrained multi-objective optimization problems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 8, pp. 1819–1835, Aug. 2024. doi: 10.1109/JAS.2024.124545 |
Constrained multi-objective optimization problems (CMOPs) generally contain multiple constraints, which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions, thus they propose serious challenges for solvers. Among all constraints, some constraints are highly correlated with optimal feasible regions; thus they can provide effective help to find feasible Pareto front. However, most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints, and do not consider judging the relations among constraints and do not utilize the information from promising single constraints. Therefore, this paper attempts to identify promising single constraints and utilize them to help solve CMOPs. To be specific, a CMOP is transformed into a multitasking optimization problem, where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively. Besides, an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships. Moreover, an improved tentative method is designed to find and transfer useful knowledge among tasks. Experimental results on three benchmark test suites and 11 real-world problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.
[1] |
Y. Xu, L. Liu, N. Gu, D. Wang, and Z. Peng, “Multi-ASV collision avoidance for point-to-point transitions based on heading-constrained control barrier functions with experiment,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1494–1497, 2023. doi: 10.1109/JAS.2022.105995
|
[2] |
Y. Zhang, M. Fei, Q. Sun, D. Du, A. Rakić, and K. Li, “A multi-objective and multi-constraint optimization model for cyber-physical power systems considering renewable energy and electric vehicles,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1498–1500, 2023. doi: 10.1109/JAS.2022.106037
|
[3] |
Y. Zhu, B. Qiao, Y. Dong, B. Qu, and D. Wu, “Multiobjective dynamic economic emission dispatch using evolutionary algorithm based on decomposition,” IEEE Trans. Electrical and Electronic Engineering, vol. 14, no. 9, pp. 1323–1333, 2019. doi: 10.1002/tee.22933
|
[4] |
Q. Yu, C. Yang, G. Dai, L. Peng, and X. Chen, “Synchronous wireless sensor and sink placement method using dual-population coevolutionary constrained multi-objective optimization algorithm,” IEEE Trans. Indus. Inform., vol. 19, no. 6, pp. 7561–7571, 2023. doi: 10.1109/TII.2022.3211853
|
[5] |
H. Hu, X. Sun, B. Zeng, D. Gong, and Y. Zhang, “Enhanced evolutionary multi-objective optimization-based dispatch of coal mine integrated energy system with flexible load,” Applied Energy, vol. 307, p. 118130, 2022. doi: 10.1016/j.apenergy.2021.118130
|
[6] |
S.-Z. Zhou, Z.-H. Zhan, Z.-G. Chen, S. Kwong, and J. Zhang, “A multi-objective ant colony system algorithm for airline crew rostering problem with fairness and satisfaction,” IEEE Trans. Intelligent Transportation Systems, vol. 22, no. 11, pp. 6784–6798, 2021. doi: 10.1109/TITS.2020.2994779
|
[7] |
S. Gupta, S. Singh, R. Su, S. Gao, and J. C. Bansal, “Multiple elite individual guided piecewise search-based differential evolution,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 135–158, 2023. doi: 10.1109/JAS.2023.123018
|
[8] |
K. Qiao, J. Liang, K. Yu, W. Guo, C. Yue, B. Qu, and P. Suganthan, “Benchmark problems for large-scale constrained multi-objective optimization with baseline results,” Swarm and Evolutionary Computation, vol. 86, p. 101504, 2024. doi: 10.1016/j.swevo.2024.101504
|
[9] |
Y. Hao, C. Zhao, Y. Zhang, Y. Cao, and Z. Li, “Constrained multi-objective optimization problems: Methodologies, algorithms and applications,” Knowledge-Based Systems, vol. 299, p. 111998, 2024. doi: 10.1016/j.knosys.2024.111998
|
[10] |
N. D. Lagaros, M. Kournoutos, N. A. Kallioras, and A. N. Nordas, “Constraint handling techniques for metaheuristics: A state-of-the-art review and new variants,” Optimization and Engineering, vol. 24, no. 4, pp. 2251–2298, 2023. doi: 10.1007/s11081-022-09782-9
|
[11] |
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002. doi: 10.1109/4235.996017
|
[12] |
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
|
[13] |
W. Long, H. Dong, P. Wang, Y. Huang, J. Li, X. Yang, and C. Fu, “A constrained multi-objective optimization algorithm using an efficient global diversity strategy,” Complex & Intelligent Systems, vol. 9, no. 2, pp. 1455–1478, 2023.
|
[14] |
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 multi-objective optimization,” IEEE Trans. Cybern., vol. 53, no. 6, pp. 3873–3886, 2023. doi: 10.1109/TCYB.2022.3163759
|
[15] |
K. Qiao, J. Liang, K. Yu, C. Yue, H. Lin, D. Zhang, and B. Qu, “Evolutionary constrained multiobjective optimization: Scalable high-dimensional constraint benchmarks and algorithm,” IEEE Trans. Evolutionary Computation, pp. 1–15, 2023. doi: 10.1109/TEVC.2023.3281666
|
[16] |
K. Qiao, K. Yu, B. Qu, J. Liang, C. Yue, and X. Ban, “Feature extraction for recommendation of constrained multi-objective evolutionary algorithms,” IEEE Trans. Evolutionary Computation, vol. 27, no. 4, pp. 949–963, 2023. doi: 10.1109/TEVC.2022.3186667
|
[17] |
P. Calégari, F. Guidec, P. Kuonen, and D. Kobler, “Parallel island-based genetic algorithm for radio network design,” J. Parallel and Distributed Comput., vol. 47, no. 1, pp. 86–90, 1997. doi: 10.1006/jpdc.1997.1397
|
[18] |
C. Bao, D. Gao, W. Gu, L. Xu, and E.D. Goodman, “A new adaptive decomposition-based evolutionary algorithm for multi-and many-objective optimization,” Expert Systems Applica., vol. 213, pp. 119080, 2023. doi: 10.1016/j.eswa.2022.119080
|
[19] |
J.-Y. Li, Z.-H. Zhan, K. C. Tan, and J. Zhang, “Dual differential grouping: A more general decomposition method for large-scale optimization,” IEEE Trans. Cybern., vol. 53, no. 6, pp. 3624–3638, 2023. doi: 10.1109/TCYB.2022.3158391
|
[20] |
E. Osaba, J. Del Ser, and P. N. Suganthan, “Evolutionary multitask optimization: Fundamental research questions, practices, and directions for the future,” Swarm and Evolutionary Computation, vol. 75, p. 101203, 2022. doi: 10.1016/j.swevo.2022.101203
|
[21] |
E. Osaba, J. Del Ser, A. D. Martinez, and A. Hussain, “Evolutionary multitask optimization: A methodological overview, challenges, and future research directions,” Cognitive Computation, vol. 14, no. 3, pp. 927–954, 2022. doi: 10.1007/s12559-022-10012-8
|
[22] |
S. Wang and X. Tan, “Determining seeds with robust influential ability from multi-layer networks: A multi-factorial evolutionary approach,” Knowledge-Based Systems, vol. 246, p. 108697, 2022. doi: 10.1016/j.knosys.2022.108697
|
[23] |
X. Ma, Y. Zheng, Z. Zhu, X. Li, L. Wang, Y. Qi, and J. Yang, “Improving evolutionary multitasking optimization by leveraging inter-task gene similarity and mirror transformation,” IEEE Comput. Intelli. Magazine, vol. 16, no. 4, pp. 38–53, 2021. doi: 10.1109/MCI.2021.3108311
|
[24] |
Y. Chen, J. Zhong, L. Feng, and J. Zhang, “An adaptive archive-based evolutionary framework for many-task optimization,” IEEE Trans. Emerging Topics in Computational Intelligence, vol. 4, no. 3, pp. 369–384, 2019.
|
[25] |
H. Sun, P. Chen, Z. Hu, and L. Wei, “Multi-objective evolutionary multitasking algorithm based on cross-task transfer solution matching strategy,” ISA Trans., vol. 138, pp. 504–520, 2023. doi: 10.1016/j.isatra.2023.03.015
|
[26] |
K. Qiao, J. Liang, K. Yu, M. Wang, B. Qu, C. Yue, and Y. Guo, “A self-adaptive evolutionary multi-task based constrained multi-objective evolutionary algorithm,” IEEE Trans. Emerging Topics in Computa tional Intelligence, vol. 7, no. 4, pp. 1098–1112, 2023. doi: 10.1109/TETCI.2023.3236633
|
[27] |
E. Osaba, J. D. Ser, A. D. Martinez, and A. Hussain, “Evolutionary multitask optimization: a methodological overview, challenges, and future research directions,” Cognitive Computation, vol. 14, no. 3, pp. 927–954, 2022. doi: 10.1007/s12559-022-10012-8
|
[28] |
K. Qiao, J. Liang, Z. Liu, K. Yu, C. Yue, and B. Qu, “Evolutionary multitasking with global and local auxiliary tasks for constrained multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 10, pp. 1–14, 2023.
|
[29] |
L. Bao, Y. Qi, M. Shen, X. Bu, J. Yu, Q. Li, and P. Chen, “An evolutionary multitasking algorithm for cloud computing service composition,” in Proc. World Congr. Services, 2018, pp. 130–144.
|
[30] |
K. Chen, B. Xue, M. Zhang, and F. Zhou, “An evolutionary multitasking-based feature selection method for high-dimensional classification,” IEEE Trans. Cybern., vol. 52, no. 7, pp. 7172–7186, 2022. doi: 10.1109/TCYB.2020.3042243
|
[31] |
Y. Feng, L. Feng, Y. Hou, and K. C. Tan, “Large-scale optimization via evolutionary multitasking assisted random embedding,” in Proc. IEEE Congr. Evolut. Comput., 2020, pp. 1–8.
|
[32] |
Y. Wu, P. Gong, M. Gong, H. Ding, Z. Tang, Y. Liu, and W. Ma, Q. Miao, “Evolutionary multitasking with solution space cutting for point cloud registration,” IEEE Trans. Emerging Topics in Computational Intelligence, vol. 8, no. 1, pp. 110–125, 2024. doi: 10.1109/TETCI.2023.3290009
|
[33] |
K. Qiao, K. Yu, B. Qu, J. Liang, H. Song, and C. Yue, “An evolutionary multitasking optimization framework for constrained multi-objective optimization problems,” IEEE Trans. Evolutionary Computation, vol. 26, no. 2, pp. 263–277, 2022. doi: 10.1109/TEVC.2022.3145582
|
[34] |
Z. Fan, Y. Fang, W. Li, X. Cai, C. Wei, and E. Goodman, “MOEA/D with angle-based constrained dominance principle for constrained multi-objective optimization problems,” Applied Soft Comput., vol. 74, pp. 621–633, 2019. doi: 10.1016/j.asoc.2018.10.027
|
[35] |
W. Ning, B. Guo, Y. Yan, X. Wu, J. Wu, and D. Zhao, “Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm,” Engineering Optimization, vol. 49, no. 10, pp. 1645–1664, 2017. doi: 10.1080/0305215X.2016.1271661
|
[36] |
Z. Ma, Y. Wang, and W. Song, “A new fitness function with two rankings for evolutionary constrained multiobjective optimization,” IEEE Trans. Systems, Man, Cybern.: Systems, vol. 51, no. 8, pp. 5005–5016, 2021. doi: 10.1109/TSMC.2019.2943973
|
[37] |
K. Yu, J. Liang, B. Qu, Y. Luo, and C. Yue, “Dynamic selection preference-assisted constrained multiobjective differential evolution,” IEEE Trans. Systems, Man, Cybern.: Systems, vol. 52, no. 5, pp. 2954–2965, 2022. doi: 10.1109/TSMC.2021.3061698
|
[38] |
Q. Zhu, Q. Zhang, and Q. Lin, “A constrained multiobjective evolutionary algorithm with detect-and-escape strategy,” IEEE Trans. Evolutionary Computation, vol. 24, no. 5, pp. 938–947, 2020. doi: 10.1109/TEVC.2020.2981949
|
[39] |
H. Tang, F. Yu, J. Zou, S. Yang, and J. Zheng, “A constrained multi-objective evolutionary strategy based on population state detection,” Swarm and Evolutionary Computation, vol. 68, pp. 100978–100992, 2022. doi: 10.1016/j.swevo.2021.100978
|
[40] |
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. doi: 10.1109/TEVC.2020.3004012
|
[41] |
J. Zou, R. Sun, S. Yang, and J. Zheng, “A dual-population algorithm based on alternative evolution and degeneration for solving constrained multi-objective optimization problems,” Information Sciences, vol. 579, pp. 89–102, 2021. doi: 10.1016/j.ins.2021.07.078
|
[42] |
F. Ming, W. Gong, L. Wang, and C. Lu, “A tri-population based co-evolutionary framework for constrained multi-objective optimization problems,” Swarm and Evolutionary Computation, vol. 70, pp. 101055–101070, 2022. doi: 10.1016/j.swevo.2022.101055
|
[43] |
M. Ming, A. Trivedi, R. Wang, D. Srinivasan, and T. Zhang, “A dual-population-based evolutionary algorithm for constrained multiobjective optimization,” IEEE Trans. Evolutionary Computation, vol. 25, no. 4, pp. 739–753, 2021. doi: 10.1109/TEVC.2021.3066301
|
[44] |
H. Ma, H. Wei, Y. Tian, R. Cheng, and X. Zhang, “A multi-stage evolutionary algorithm for multi-objective optimization with complex constraints,” Information Sciences, vol. 560, pp. 68–91, 2021. doi: 10.1016/j.ins.2021.01.029
|
[45] |
K. Deb and R. B. Agrawal, “Simulated binary crossover for continuous search space,” Complex Systems, vol. 9, no. 2, pp. 115–148, 1995.
|
[46] |
K. Deb and M. Goyal, “A combined genetic adaptive search (geneas) for engineering design,” Computer Science and Informatics, vol. 26, pp. 30–45, 1996.
|
[47] |
Z. Fan, W. Li, X. Cai, H. Huang, Y. Fang, Y. You, 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, no. 23, pp. 12491–12510, 2019. doi: 10.1007/s00500-019-03794-x
|
[48] |
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. doi: 10.1109/TEVC.2019.2896967
|
[49] |
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
|
[50] |
R. Jiao, S. Zeng, C. Li, S. Yang, and Y.-S. Ong, “Handling constrained many-objective optimization problems via problem transformation,” IEEE Trans. Cybernetics, vol. 51, no. 10, pp. 4834–4847, 2021. doi: 10.1109/TCYB.2020.3031642
|
[51] |
B.-C. Wang, Z.-Y. Shui, Y. Feng, and Z. Ma, “Evolutionary algorithm with dynamic population size for constrained multiobjective optimization,” Swarm and Evolutionary Computation, vol. 73, p. 101104, 2022. doi: 10.1016/j.swevo.2022.101104
|
[52] |
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. doi: 10.1162/evco_a_00259
|
[53] |
Y. Tian, R. Cheng, X. Zhang, and Y. Jin, “Platemo: A matlab platform for evolutionary multi-objective optimization [educational forum],” IEEE Computational Intelligence Magazine, vol. 12, no. 4, pp. 73–87, 2017. doi: 10.1109/MCI.2017.2742868
|
[54] |
J. Liang, X. Ban, K. Yu, K. Qiao, and B. Qu, “Constrained multiobjective differential evolution algorithm with infeasible-proportion control mechanism,” Knowledge-Based Systems, vol. 250, p. 109105, 2022. doi: 10.1016/j.knosys.2022.109105
|
[55] |
H. Ishibuchi, H. Masuda, Y. Tanigaki, and Y. Nojima, “Modified distance calculation in generational distance and inverted generational distance,” in Evolutionary Multi-Criterion Optimization, A. Gaspar-Cunha, C. Henggeler Antunes, and C. C. Coello, Eds., Berlin, Germany: Springer, 2015, pp. 110–125.
|
[56] |
A. P. Guerreiro, C. M. Fonseca, and L. Paquete, “The hypervolume indicator: Computational problems and algorithms,” ACM Comput. Surveys, vol. 54, no. 6, pp. 1–42, 2021.
|
[57] |
H. Ishibuchi, R. Imada, N. Masuyama, and Y. Nojima, “Comparison of hypervolume, igd and igd+ from the viewpoint of optimal distributions of solutions,” in Evolutionary Multi-Criterion Optimization, K. Deb, E. Goodman, C. A. Coello Coello, K. Klamroth, K. Miettinen, S. Mostaghim, and P. Reed, Eds., Berlin, Germany: Springer, 2019, pp. 332–345.
|
[58] |
Q. Zhang, A. Zhou, S. Zhao, P. N. Suganthan, W. Liu, and S. Tiwari, “Multiobjective optimization test instances for the CEC 2009 special session and competition,” in Proc. Special Session Perfor. Assessment of Multi-Object. Optimization Algori., 2008, vol. 264, pp. 1–8.
|
[59] |
C. Dai, X. Sun, H. Hu, Y. Zhang, and D. Gong, “A constraint adaptive multi-tasking differential evolution algorithm: Designed for dispatch of integrated energy system in coal mine,” Tsinghua Science and Technology, vol. 29, no. 2, pp. 368–385, 2024. doi: 10.26599/TST.2023.9010067
|
[60] |
Y. Wang, H. Hu, X. Sun, Y. Zhang, and D. Gong, “Unified operation optimization model of integrated coal mine energy systems and its solutions based on autonomous intelligence,” Applied Energy, vol. 328, p. 120106, 2022. doi: 10.1016/j.apenergy.2022.120106
|
[61] |
A. Kumar, G. Wu, M. Z. Ali, Q. Luo, R. Mallipeddi, P. N. Suganthan, and S. Das, “A benchmark-suite of real-world constrained multi-objective optimization problems and some baseline results,” Swarm and Evolutionary Computation, vol. 67, p. 100961, 2021. doi: 10.1016/j.swevo.2021.100961
|
![]() |
![]() |