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Decision space information driven algorithm for dynamic multiobjective optimization with a changing number of objectives

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Abstract

Dynamic multiobjective optimization problems (DMOPs) with a changing number of objectives receive little attention, but they exist widely in real life. These type of dynamics not only lead to expansion or contraction of Pareto optimal front/set (PF/PS) manifold, but also pose great challenges to balancing diversity and convergence. However, the current dynamic response mechanism has difficulty adapting these kind of problems. To tackle these problems, a decision space information driven algorithm (DSID) is proposed. Once the number of objectives changes, an individual guidance strategy based on manifold learning (IGSML) is introduced to identify solutions suitable for changes. Then IGSML produces excellent solutions by learning the manifold of these solutions. Meanwhile, a variable layering reconstruction strategy (VLRS) is proposed to divide the decision variables into three layers: convergence, diversity and multi-functional variables. Afterwards, VLRS takes into account the different degrees of influence of variables at different layers in the process of objective change, and makes targeted operations on different variables to quickly respond to changes. These two strategies cooperate with each other to balance the diversity and convergence. Comprehensive experiments are conducted on 15 benchmark functions with a varying number of objectives. Simulation results verify the efficacy of the proposed algorithm.

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Data availability

The datasets used in this paper are available from the corresponding author on reasonable request.

References

  1. Chen Renzhi, Li Ke, Yao Xin (2018) Dynamic multi-objectives optimization with a changing number of objectives. IEEE Trans Evol Comput 22(1):157–171

    Google Scholar 

  2. Yang Xu, Li Hongru, Xia Yu (2022) A dynamic multi-swarm cooperation particle swarm optimization with dimension mutation for complex optimization problem. Int J Mach Learn Cybern 13:2581–2608

    Google Scholar 

  3. Zhang H, Ding J, Jiang M, Tan KC, Chai T (2022) Inverse gaussian process modeling for evolutionary dynamic multiobjective optimization. IEEE Trans Cybern 52:11240–11253

    Google Scholar 

  4. Ziyu Hu, Wei Zhihui, Sun Hao, Yang Jingming, Wei Lixin (2021) Optimization of metal rolling control using soft computing approaches: a review. Arch Comput Methods Eng 28:405–421

    Google Scholar 

  5. CRB Azevedo and AFR Ara\(\acute{\rm{u}}\)jo (2011) Generalized immigration schemes for dynamic evolutionary multiobjective optimization. In IEEE Congress on Evolutionary Computation, New Orleans, LA, USA, pages 2033–2040

  6. Huang L, Suh IH, Abraham A (2011) Dynamic multi-objective optimization based on membrane computing for control of time-varying unstable plants. Inf Sci 181:2370–2391

    Google Scholar 

  7. Ma Xuemin, Yang Jingming, Sun Hao, Ziyu Hu, Wei Lixin (2021) Feature information prediction algorithm for dynamic multi-objective optimization problems. Eur J Oper Res 295:965–981

    MathSciNet  Google Scholar 

  8. Ziyu H, Wei Z, Ma X, Sun H, Yang J (2020) Multi-parameter deep-perception and many-objective autonomous-control of rolling schedule on high speed cold tandem mill. ISA Trans 102:193–207

    Google Scholar 

  9. Orouskhani M, Teshnehlab M, Nekoui MA (2019) Evolutionary dynamic multi-objective optimization algorithm based on borda count method. Int J Mach Learn Cybern 10:1931–1959

    Google Scholar 

  10. Ziyu H, Jingming Y, Hao S, Lixin W, Zhiwei Z (2017) An improved multi-objective evolutionary algorithm based on environmental and history information. Neurocomputing 222:170–182

    Google Scholar 

  11. Xie Y, Qiao J, Wang D, Yin B (2021) A novel decomposition-based multiobjective evolutionary algorithm using improved multiple adaptive dynamic selection strategies. Inf Sci 556:472–494

    MathSciNet  Google Scholar 

  12. Ruochen L, Ping Y, Jiangdi L (2021) A dynamic multi-objective optimization evolutionary algorithm for complex environmental changes. Knowl Based Syst 216:106612

    Google Scholar 

  13. Azzouz R, Bechikh S, Said LB (2017) A dynamic multi-objective evolutionary algorithm using a change severity-based adaptive populationmanagement strategy. Soft Comput 21:885–906

    Google Scholar 

  14. Liang Z, Zheng S, Zhu Z, Yang S (2019) Hybrid of memory and prediction strategies for dynamic multiobjective optimization. Inf Sci 485:200–218

    Google Scholar 

  15. Zou F, Yen GG, Zhao C (2021) Dynamic multiobjective optimization driven by inverse reinforcement learning. Inf Sci 575:468–484

    MathSciNet  Google Scholar 

  16. Zhang K, Shen C, Liu X, Yen GG (2020) Multiobjective evolution strategy for dynamic multiobjective optimization. IEEE Trans Evol Comput 24:974–988

    Google Scholar 

  17. Deb K, Udaya Bhaskara Rao N, Karthik S (2007) Dynamic multi-objective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling. In Proceedings of the 4th international conference on Evolutionary multi-criterion optimization. Springer, Berlin., volume 4403, pages 803–817

  18. Liu R, Li J, Fan J, Mu C, Jiao L (2017) A coevolutionary technique based on multi-swarm particle swarm optimization for dynamic multi-objective optimization. Eur J Oper Res 261:1028–1051

    MathSciNet  Google Scholar 

  19. Zou J, Li Q, Yang S, Zheng J, Peng Z, Pei T (2019) A dynamic multiobjective evolutionary algorithm based on a dynamic evolutionary environment model. Swarm Evol Comput 44:247–259

    Google Scholar 

  20. Jiang Shouyong, Yang Shengxiang (2017) A steady-state and generational evolutionary algorithm for dynamic multi-objective optimization. IEEE Trans Evol Comput 21(1):65–82

    Google Scholar 

  21. Zhang Qingyang, Yang Shengxiang, Jiang Shouyong, Wang Ronggui, Li Xiaoli (2020) Novel prediction strategies for dynamic multi-objective optimization. IEEE Trans Evol Comput 24:260–274

    Google Scholar 

  22. Ma Xuemin, Yang Jingming, Sun Hao, Ziyu Hu, Wei Lixin (2021) Multiregional co-evolutionary algorithm for dynamic multiobjective optimization. Inf Sci 545:1–24

    MathSciNet  Google Scholar 

  23. Hu Y, Jinhua Z, Shouyong J, Shengxiang Y, Juan Z (2023) Handling dynamic multiobjective optimization environments via layered prediction and subspace-based diversity maintenance. IEEE Trans Cybern 53:2572–2585

    Google Scholar 

  24. Sun Hao, Cao Anran, Ziyu Hu, Li Xiaxia, Zhao Zhiwei (2021) A novel quantile-guided dual prediction strategies for dynamic multi-objective optimization. Inf Sci 579:751–775

    MathSciNet  Google Scholar 

  25. Li Xiaxia, Yang Jingming, Sun Hao, Ziyu Hu, Cao Anran (2021) A dual prediction strategy with inverse model for evolutionary dynamic multiobjective optimization. ISA Trans 117:196–209

    Google Scholar 

  26. Xie Huipeng, Zou Juan, Yang Shengxiang, Zheng Jinhua, Junwei Ou, Yaru Hu (2021) A decision variable classification-based cooperative coevolutionary algorithm for dynamic multiobjective optimization. Inf Sci 560:307–330

    MathSciNet  Google Scholar 

  27. Zhou Aimin, Jin Yaochu, Zhang Qingfu (2013) A population prediction strategy for evolutionary dynamic multiobjective optimization. IEEE Trans Cybern 44(1):40–53

    Google Scholar 

  28. Cao Leilei, Lihong Xu, Goodman Erik D, Li Hui (2019) Decomposition-based evolutionary dynamic multiobjective optimization using a difference model. Appl Soft Comput J 76:473–490

    Google Scholar 

  29. Rong Miao, Gong Dunwei, Zhang Yong, Jin Yaochu, Pedrycz Witold (2019) Multidirectional prediction approach for dynamic multiobjective optimization problems. IEEE Trans Cybern 49(9):3362–3374

    Google Scholar 

  30. Feng L, Zhou W, Liu W, Ong Y-S, Tan KC (2020) Solving dynamic multiobjective problem via autoencoding evolutionary search. IEEE Trans Cybern 52:1–14

    Google Scholar 

  31. Jinhua Zheng, Yubing Zhou, Juan Zou, Shengxiang Yang, Junwei Ou, Yaru Hu (2021) A prediction strategy based on decision variable analysis for dynamic multi-objective optimization. Swarm Evol Comput 60:100786

    Google Scholar 

  32. Guan Sheng-Uei, Chen Qian, Mo Wenting (2005) Evolving dynamic multi-objective optimization problems with objective replacement. Artif Intell Rev 23:267–293

    Google Scholar 

  33. Wei Zhihui, Yang Jingming, Ziyu Hu, Sun Hao (2020) An adaptive decomposition evolutionary algorithm based on environmental information for many-objective optimization. ISA Trans 111:108–120

    Google Scholar 

  34. Wang Chen, Wang Yi, Wang Kesheng, Yang Yang, Tian Yingzhong (2019) An improved biogeography/complex algorithm based on decomposition for many-objective optimization. Int J Mach Learn Cybern 10:1961–1977

    Google Scholar 

  35. Deb Kalyanmoy, Pratap Amrit, Agarwal Sameer, Meyarivan Tamt (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197

    Google Scholar 

  36. Coello CAC, van Veldhuizen DA, and Lamont G.B. (2007) Evolutionary algorithms for solving multiobjective problems. Springer-Verlag, New York

    Google Scholar 

  37. Zhang Qingfu, Zhou Aimin, Jin Yaochu, Li Hui (2008) Rm-meda: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans Evol Comput 12:41–63

    Google Scholar 

  38. Wang Handing, Jiao Licheng, Yao Xin (2015) \(\text{ Two}_{-}\)arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19(4):524–541

    Google Scholar 

  39. Zhang Hu, Zhou Aimin, Song Shenmin, Zhang Qingfu, Gao Xiao-Zhi, Zhang Jun (2016) A self-organizing multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20(5):792–806

    Google Scholar 

  40. Cuevas Erik, Galvez Jorge (2019) An optimization algorithm guided by a machine learning approach. Int J Mach Learn Cybern 10:2963–2991

    Google Scholar 

  41. Liang Zhengping, Kaifeng Hu, Ma Xiaoliang, Zhu Zexuan (2021) A many-objective evolutionary algorithm based on a two-round selection strategy. IEEE Trans Cybern 51(3):1417–1429

    Google Scholar 

  42. Wei Cao, Wei Zhan, and ZhiQiang Chen. Ml-moea/som: A manifold-learning-based multiobjective evolutionary algorithm via self-organizing maps. In The International Conference on Fuzzy System and Data Mining. Shanghai, China., volume 9, pages 391–406, 2016

  43. Haykin SS, Gwynn R (2009) Neural networks and learning machines, vol 3. China Machine Press

  44. Li Ke, Deb Kalyanmoy, Zhang Qingfu, Kwong Sam (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19:694–716

    Google Scholar 

  45. Zhang Xingyi, Tian Ye, Cheng Ran, Jin Yaochu (2018) A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans Evol Comput 22(1):97–112

    Google Scholar 

  46. Ma L, Huang M, Yang S, Wang R, Wang X (2022) An adaptive localized decision variable analysis approach to large-scale multiobjective and many-objective optimization. IEEE Trans Cybern 52:6684–6696

    Google Scholar 

  47. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    MathSciNet  Google Scholar 

  48. Kata Praditwong and Xin Yao. A new multi-objective evolutionary optimisation algorithm: The two-archive algorithm. In International Conference on Computational Intelligence and Security. Guangzhou, China., pages 95–104, 2006

  49. Mardé H, Engelbrecht Andries P (2013) Performance measures for dynamic multi-objective optimisation algorithms. Inf Sci 250(11):61–81

    Google Scholar 

  50. Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, and Eckart Zitzler. Scalable multi-objective optimization test problems. In Proceedings of the 2002 Congress on Evolutionary Computation. Honolulu, HI, USA, pages 1–6, 2002

  51. Cheng Ran, Li Miqing, Tian Ye, Zhang Xingyi, Yang Shengxiang, Jin Yaochu, Yao Xin (2017) A benchmark test suite for evolutionary many-objective optimization. Complex Intell Syst 3:67–81

    Google Scholar 

  52. D. A. Van Veldhuizen and G. B. Lamont. On measuring multiobjective evolutionary algorithm performance. In Proceedings of the 2000 Congress on Evolutionary Computation. La Jolla, CA, USA., pages 204–211, 2000

  53. Ciaccia Paolo, Patella Marco (2002) Searching in metric spaces with user-defined and approximate distances. Acm Trans Database Syst 27(4):398–437

    Google Scholar 

  54. Muruganantham A, Tan KC, Vadakkepat P (2015) Evolutionary dynamic multiobjective optimization via kalman filter prediction. IEEE Trans Cybern 46(12):1–12

    Google Scholar 

  55. Sun Hao, Ma Xuemin, Yang Jingming, Cui Huihui (2023) A two stages prediction strategy for evolutionary dynamic multi-objective optimization. Appl Intell 53:1115–1131

    Google Scholar 

  56. Qi Z, Bai Y, Yuhui S, Martin M (2022) Evolutionary dynamic multiobjective optimization via learning from historical search process. IEEE Trans Cybern 52:6119–6130

    Google Scholar 

  57. Ruochen Liu, Ping Yang, Jiangdi Liu (2021) A dynamic multi-objective optimization evolutionary algorithm for complex environmental changes. Knowl Based Syst 216:106612

    Google Scholar 

  58. Zhang Qingfu, Li Hui (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Google Scholar 

  59. Myles Hollander, Douglas A Wolfe, and Eric Chicken (1999) Nonparametric statistical methods. New York, NY,USA: Wiley

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Acknowledgements

This work was supported by the Project supported by the National key research and development program (No.2018Y FB1702300), the National Natural Science Foundation of China (Grant No.62003296, 61803327, 62073276), the Natural Science Foundation of Hebei (No.F2020203031), Science and Technology Research Projects of Hebei University (No.QN2020225), Provincial Key Laboratory Performance Subsidy Project (No.22567612H) and Hebei Province Graduate Innovation Funding Project (No.CXZZBS2022134). The authors would like to thank the editor and anonymous reviewers for their helpful comments and suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Engineering Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment, Yanshan University, Qinhuangdao, 066004, Hebei, People’s Republic of China

    Xuemin Ma, Hao Sun, Ziyu Hu, Lixin Wei & Jingming Yang

  2. Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, 066004, Hebei, China

    Xuemin Ma, Hao Sun, Ziyu Hu, Lixin Wei & Jingming Yang

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  1. Xuemin Ma
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Contributions

Research conception, design, material preparation, data collection and analysis were conducted by HS, ZH, LW and JY. The first draft of the manuscript was written by XM and HS, and all authors commented on the previous version of the manuscript. Final draft read and approved by all authors

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Correspondence to Hao Sun.

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Ma, X., Sun, H., Hu, Z. et al. Decision space information driven algorithm for dynamic multiobjective optimization with a changing number of objectives. Int. J. Mach. Learn. & Cyber. 15, 429–457 (2024). https://doi.org/10.1007/s13042-023-01918-2

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