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A dual decomposition strategy for large-scale multiobjective evolutionary optimization

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Abstract

Multiobjective evolutionary algorithms (MOEAs) have received much attention in multiobjective optimization in recent years due to their practicality. With limited computational resources, most existing MOEAs cannot efficiently solve large-scale multiobjective optimization problems (LSMOPs) that widely exist in the real world. This paper innovatively proposes a dual decomposition strategy (DDS) that can be embedded into many existing MOEAs to improve their performance in solving LSMOPs. Firstly, the outer decomposition uses a sliding window to divide large-scale decision variables into overlapped subsets of small-scale ones. A small-scale multiobjective optimization problem (MOP) is generated every time the sliding window slides. Then, once a small-scale MOP is generated, the inner decomposition immediately creates a set of global direction vectors to transform it into a set of single-objective optimization problems (SOPs). At last, all SOPs are optimized by adopting a block coordinate descent strategy, ensuring the solution’s integrity and improving the algorithm’s performance to some extent. Comparative experiments on benchmark test problems with seven state-of-the-art evolutionary algorithms and a deep learning-based algorithm framework have shown the remarkable efficiency and solution quality of the proposed DDS. Meanwhile, experiments on two real-world problems show that DDS can achieve the best performance beyond at least one order of magnitude with up to 3072 decision variables.

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References

  1. Ponsich A, Jaimes AL, Coello CAC (2012) A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications. IEEE Trans Evol Comput 17(3):321–344

    Article  Google Scholar 

  2. Gunantara N (2018) A review of multi-objective optimization: methods and its applications. Cogent Eng 5(1):1502242

    Article  Google Scholar 

  3. Ojha M, Singh KP, Chakraborty P, Verma S (2019) A review of multi-objective optimisation and decision making using evolutionary algorithms. Int J Bio Inspir Comput 14(2):69–84

    Article  Google Scholar 

  4. Falcón-Cardona JG, Coello CAC (2020) Indicator-based multi-objective evolutionary algorithms: a comprehensive survey. ACM Comput Surv (CSUR) 53(2):1–35

    Article  Google Scholar 

  5. Drechsler N, Drechsler R, Becker B (1999) Multi-objective optimization in evolutionary algorithms using satisfiability classes. In: International conference on computational intelligence, pp 108–117

  6. Ma X, Yu Y, Li X, Qi Y, Zhu Z (2020) A survey of weight vector adjustment methods for decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evol Comput 24(4):634–649

    Article  Google Scholar 

  7. Tian Y, Si L, Zhang X, Cheng R, He C, Tan KC, Jin Y (2021) Evolutionary large-scale multi-objective optimization: a survey. ACM Comput Surv (CSUR) 54(8):1–34

    Google Scholar 

  8. Ma X, Liu F, Qi Y, Wang X, Li L, Jiao L, Gong M (2015) A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables. IEEE Trans Evol Comput 20(2):275–298

    Article  Google Scholar 

  9. Zhang X, Tian Y, Cheng R, Jin Y (2016) A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans Evol Comput 22(1):97–112

    Article  Google Scholar 

  10. Omidvar M, Li X, Yao X (2021) A review of population-based metaheuristics for large-scale black-box global optimization: part B. IEEE Trans Evol Comput. https://doi.org/10.1109/TEVC.2021.3130835

    Article  Google Scholar 

  11. Oldewage ET, Engelbrecht AP, Cleghorn CW (2017) The merits of velocity clamping particle swarm optimisation in high dimensional spaces. In: 2017 IEEE symposium series on computational intelligence, pp 1–8

  12. Deb K, Myburgh C (2017) A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables. Eur J Oper Res 261(2):460–474

    Article  MATH  Google Scholar 

  13. Song A, Yang Q, Chen W-N, Zhang J (2016) A random-based dynamic grouping strategy for large scale multi-objective optimization. In: 2016 IEEE congress on evolutionary computation, pp 468–475

  14. Omidvar MN, Li X, Mei Y, Yao X (2013) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393

    Article  Google Scholar 

  15. Zille H, Ishibuchi H, Mostaghim S, Nojima Y (2017) A framework for large-scale multiobjective optimization based on problem transformation. IEEE Trans Evol Comput 22(2):260–275

    Article  Google Scholar 

  16. Mei Y, Li X, Yao X (2013) Cooperative coevolution with route distance grouping for large-scale capacitated arc routing problems. IEEE Trans Evol Comput 18(3):435–449

    Article  Google Scholar 

  17. Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999

    Article  MATH  Google Scholar 

  18. Van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239

    Article  Google Scholar 

  19. Chen W, Weise T, Yang Z, Tang K (2010) Large-scale global optimization using cooperative coevolution with variable interaction learning. In: International conference on parallel problem solving from nature, pp 300–309

  20. Omidvar MN, Li X, Mei Y, Yao X (2013) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393

    Article  Google Scholar 

  21. Li L, He C, Cheng R, Pan L (2021) Large-scale multiobjective optimization via problem decomposition and reformulation. In: 2021 IEEE congress on evolutionary computation, pp 2149–2155

  22. Tian Y, Zheng X, Zhang X, Jin Y (2019) Efficient large-scale multiobjective optimization based on a competitive swarm optimizer. IEEE Trans Cybern 50(8):3696–3708

    Article  Google Scholar 

  23. He C, Cheng R, Yazdani D (2020) Adaptive offspring generation for evolutionary large-scale multiobjective optimization. IEEE Trans Syst Man Cybern 52(2):786–798

    Article  Google Scholar 

  24. Qin S, Sun C, Jin Y, Tan Y, Fieldsend J (2021) Large-scale evolutionary multiobjective optimization assisted by directed sampling. IEEE Trans Evol Comput 25(4):724–738

    Article  Google Scholar 

  25. Wang Z, Hong H, Ye K, Zhang G-E, Jiang M, Tan KC (2021) Manifold interpolation for large-scale multiobjective optimization via generative adversarial networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3113158

    Article  Google Scholar 

  26. Wright SJ (2015) Coordinate descent algorithms. Math Program 151(1):3–34

    Article  MATH  Google Scholar 

  27. Huang P, Zou Z, Xia XG, Liu X, Liao G (2022) A novel dimension-reduced space-time adaptive processing algorithm for spaceborne multichannel surveillance radar systems based on spatial-temporal 2-D sliding window. IEEE Trans Geosci Remote Sens 60:1–21

    Google Scholar 

  28. Koshy P, Babu S, Manoj BS (2020) Sliding window blockchain architecture for internet of things. IEEE Internet Things J 7(4):3338–3348

    Article  Google Scholar 

  29. Jiang D, Liu J, Xu Z, Qin W (2011) Network traffic anomaly detection based on sliding window. In: 2011 International conference on electrical and control engineering, pp 4830–4833

  30. Coello Coello CA, Reyes Sierra M (2004) A study of the parallelization of a coevolutionary multi-objective evolutionary algorithm. In: Mexican international conference on artificial intelligence, pp 688–697

  31. Cheng R, Jin Y, Olhofer M (2016) Test problems for large-scale multiobjective and many-objective optimization. IEEE Trans Cybern 47(12):4108–4121

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer Science Business Media, Berlin

    MATH  Google Scholar 

  34. Li H, Zhang Q (2008) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13(2):284–302

    Article  Google Scholar 

  35. Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12(4):73–87

    Article  Google Scholar 

  36. Zhang H, Zhou A, Song S, Zhang Q, Gao X-Z, Zhang J (2016) A self-organizing multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20(5):792–806

    Article  Google Scholar 

  37. Liu Z-Z, Wang Y (2019) Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces. IEEE Trans Evol Comput 23(5):870–884

    Article  Google Scholar 

  38. Zhang J, Zhou A, Zhang G (2015) A classification and Pareto domination based multiobjective evolutionary algorithm. In: 2015 IEEE congress on evolutionary computation, pp 2883–2890

  39. Li H, Zhang Q, Deng JI (2016) Biased multiobjective optimization and decomposition algorithm. IEEE Trans Cybern 47(1):52–66

    Article  Google Scholar 

  40. Zhang X-Y, Jiang X-S, Zhang L (2016) A weight vector based multi-objective optimization algorithm with preference. Acta Geosci Sin 44(11):2639

    Google Scholar 

  41. He C, Li L, Tian Y, Zhang X, Cheng R, Jin Y, Yao X (2019) Accelerating large-scale multiobjective optimization via problem reformulation. IEEE Trans Evol Comput 23(6):949–961

    Article  Google Scholar 

  42. Yang X, Zou J, Yang S, Zheng J, Liu Y (2021) A fuzzy decision variables framework for large-scale multiobjective optimization. IEEE Trans Evol Comput. https://doi.org/10.1109/TEVC.2021.3118593

    Article  Google Scholar 

  43. Xu Y, Xu C, Zhang H, Huang L, Liu Y, Nojima Y, Zeng X (2022) A multi-population multi-objective evolutionary algorithm based on the contribution of decision variables to objectives for large-scale multi/many-objective optimization. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2022.3180214

    Article  Google Scholar 

  44. He C, Cheng R, Zhang C, Tian Y, Chen Q, Yao X (2020) Evolutionary large-scale multiobjective optimization for ratio error estimation of voltage transformers. IEEE Trans Evol Comput 24(5):868–881

    Article  Google Scholar 

  45. Eykholt K, Evtimov I, Fernandes E, Li B, Rahmati A, Xiao C, Prakash A, Kohno T, Song D (2018) Robust physical-world attacks on deep learning visual classification. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 1625–1634

  46. Krizhevsky A, Hinton G (2009) Learning multiple layers of features from tiny images

  47. Tian Y, Pan J, Yang S, Zhang X, He S, Jin Y (2022) Imperceptible and sparse adversarial attacks via a dual-population based constrained evolutionary algorithm. IEEE Trans Artif Intell. https://doi.org/10.1109/TAI.2022.316803

    Article  Google Scholar 

  48. Carlini N, Wagner D (2017) Towards evaluating the robustness of neural networks In: 2017 IEEE symposium on security and privacy, pp 39–57

  49. Kurakin A, Goodfellow IJ, Bengio S (2018) Adversarial examples in the physical world. In: Artificial intelligence safety and security, pp 99–112

  50. Su J, Vargas DV, Sakurai K (2019) One pixel attack for fooling deep neural networks. IEEE Trans Evol Comput 23(5):828–841

    Article  Google Scholar 

  51. Wiyatno R, Xu A (2018) Maximal jacobian-based saliency map attack. arXiv preprint arXiv:1808.07945

  52. Fan Y, Wu B, Li T, Zhang Y, Li M, Li Z, Yang Y (2020) Sparse adversarial attack via perturbation factorization. In: European conference on computer vision, pp 35–50

  53. Croce F, Hein M (2019) Sparse and imperceivable adversarial attacks. In: Proceedings of the IEEE/CVF international conference on computer vision, pp 4724–4732

  54. Ilyas A, Engstrom L, Athalye A, Lin JI (2018) Black-box adversarial attacks with limited queries and information. In: International conference on machine learning, pp 2137–2146

  55. Deng Y, Zhang C, Wang X (2019) A multi-objective examples generation approach to fool the deep neural networks in the black-box scenario. In: 2019 IEEE fourth international conference on data science in cyberspace, pp 92–99

  56. Li G, Wang W, Zhang W, Wang Z, Tu H, You W (2021) Grid search based multi-population particle swarm optimization algorithm for multimodal multi-objective optimization. Swarm Evol Comput 62:100843

    Article  Google Scholar 

  57. Wu J, Chen XY, Zhang H, Xiong LD, Lei H, Deng SH (2019) Hyperparameter optimization for machine learning models based on Bayesian optimization. J Electron Sci Technol 17(1):26–40

    Google Scholar 

  58. Dai P, Liu K, Feng L, Zhang H, Lee VCS, Son SH, Wu X (2018) Temporal information services in large-scale vehicular networks through evolutionary multi-objective optimization. IEEE Trans Intell Syst 20(1):218–231

    Article  Google Scholar 

  59. Millig GW, Cooper MC (1987) Methodology review: clustering methods. Appl Psychol Meas 11(4):329–354

    Article  Google Scholar 

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Acknowledgements

This work is partly supported by the NSFC Research Program (61906010, 62276010) and R&D Program of Beijing Municipal Education Commission (KZ202210005009, KM202010005032).

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  1. Beijing Municipal Key Laboratory of Multimedia and Intelligent Software Technology, College of Computer Science, Faculty of Information Technology, Beijing University of Technology, Beijing, China

    Cuicui Yang, Peike Wang & Junzhong Ji

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  1. Cuicui Yang
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Yang, C., Wang, P. & Ji, J. A dual decomposition strategy for large-scale multiobjective evolutionary optimization. Neural Comput & Applic 35, 3767–3788 (2023). https://doi.org/10.1007/s00521-022-08133-0

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