Abstract
Large-scale sparse multiobjective optimization problems (SMOPs) widely exist in academic research and engineering applications. The curse of dimensionality and the fact that most decision variables take zero values make optimization very difficult. Sparse features are common to many practical complex problems currently, and using sparse features as a breakthrough point can enable many large-scale complex problems to be solved. We propose an efficient evolutionary algorithm based on deep reinforcement learning to solve large-scale SMOPs. Deep reinforcement learning networks are used for mining sparse variables to reduce the problem dimensionality, which is a challenge for large-scale multiobjective optimization. Then the three-way decision concept is used to optimize decision variables. The emphasis is on optimizing deterministic nonzero variables and continuously mining uncertain decision variables. Experimental results on sparse benchmark problems and real-world application problems show that the proposed algorithm performs well on SMOPs while being highly efficient.
Similar content being viewed by others
Data availability statement
The datasets generated during and analysed during the current study are available from the corresponding author on reasonable request.
References
Ye Tian, Chang L u, Zhang Xingyi, Cheng Fan, Jin Yaochu (2020) A pattern mining-based evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Cybern, pp 1–14
Sarker IH (2021) Machine learning: Algorithms, real-world applications and research directions. SN Comput Sci 2(3):1–21
Cope B, Kalantzis M (2022) The cybernetics of learning
Gong C, Ren T, Ye M, Liu Q (2021) Maxup: Lightweight adversarial training with data augmentation improves neural network training. In: Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition, pp 2474–2483
Zhang Q, Ma W, Li G, Ding J, Xie M (2022) Fault diagnosis of power grid based on variational mode decomposition and convolutional neural network. Electr Power Syst Res 208:107871
Tan Z, Wang H, Liu S (2021) Multi-stage dimension reduction for expensive sparse multi-objective optimization problems. Neurocomputing 440:159–174
Song X-F, Zhang Y, Gong D-W, Sun X-Y (2021) Feature selection using bare-bones particle swarm optimization with mutual information. Pattern Recogn 112:107804
Narkhede MV, Bartakke PP, Sutaone MS (2022) A review on weight initialization strategies for neural networks. Artif Intell Rev 55(1):291–322
Fan Z, Hu G, Sun X, Wang G, Dong J, Su C (2022) Self-attention neural architecture search for semantic image segmentation. Knowl-Based Syst 239:107968
Hashemi A, Dowlatshahi MB, Nezamabadi-pour H (2022) Ensemble of feature selection algorithms: a multi-criteria decision-making approach. Int J Mach Learn Cybern 13(1):49–69
Alhenawi E, Al-Sayyed R, Hudaib A, Mirjalili S (2022) Feature selection methods on gene expression microarray data for cancer classification: a systematic review. Comput Biol Med 140:105051
Shafiullah Md, Abido MA, Al-Mohammed AH (2022) Intelligent fault diagnosis for distribution grid considering renewable energy intermittency. Neural Comput Applic, pp 1–20
Zhang X, Tian Y, Cheng R, Jin Y (2018) A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans Evol Comput 22(1):97–112
Tian Y, Lu C, Zhang X, Tan KC, Jin Y (2020) Solving large-scale multi-objective optimization problems with sparse optimal solutions via unsupervised neural networks. IEEE Transactions on Cybernetics PP(99)
Tian Y, Zheng X, Zhang X, Jin Y (2019) Efficient large-scale multi-objective optimization based on a competitive swarm optimizer. IEEE Trans Cybern, pp 1–13
Tian Y, Si L, Zhang X, Cheng R, Jin Y (2021) Evolutionary large-scale multi-objective optimization: A survey. ACM Computing Surveys
Antonio LM, Coello CAC (2016) Indicator-based cooperative coevolution for multi-objective optimization. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp 991–998
Omidvar MN, Yang M, Yi Mei, Li X, Yao X (2017) Dg2: a faster and more accurate differential grouping for large-scale black-box optimization. IEEE Trans Evol Comput 21(6):929–942
Sun Y, Yue H (2022) An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping. Appl Intell 52(10):11569–11591
Ma X, Liu F, Qi Y, Wang X, Li L, Jiao L, Yin M, Gong M (2016) 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
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
Chen H, Ran C, Wen J, Li H, Jian W (2018) Solving large-scale many-objective optimization problems by covariance matrix adaptation evolution strategy with scalable small subpopulations. Inf Sci, p 509
Ding Z, Chen L, Sun D, Zhang X (2022) A multi-stage knowledge-guided evolutionary algorithm for large-scale sparse multi-objective optimization problems. Swarm Evol Comput 73:101119
Tian Y, Zhang X, Wang C, Jin Y (2020) An evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Evol Comput 24(2):380–393
Fournier-Viger P, Lin JC-W, Kiran RU, Koh YS, Thomas R (2017) A survey of sequential pattern mining. Data Sci Pattern Recognit 1(1):54–77
Alsahaf A, Petkov N, Shenoy V, Azzopardi George (2022) A framework for feature selection through boosting. Expert Syst Appl 187:115895
Shetty RD, Bhattacharjee S, Dutta A, Namtirtha A (2022) Gsi: An influential node detection approach in heterogeneous network using covid-19 as use case. IEEE Trans Comput Soc Syst
Zhang X, Duan F, Lei Z, Fan C, Jin Y, Ke T (2017) Pattern recommendation in task-oriented applications: a multi-objective perspective [application notes]. IEEE Comput Intell Mag 12(3):43–53
Zhang Y, Tian Y, Zhang X (2021) Improved sparseea for sparse large-scale multi-objective optimization problems. Complex Intell Syst, p 10
Liu CH, Chen Z, Tang J, Xu J, Piao C (2018) Energy-efficient uav control for effective and fair communication coverage: a deep reinforcement learning approach. IEEE J Sel Areas Commun 36 (9):2059–2070
Chen L, Jiang S, Liu J, Wang C, Zhang S, Xie C, Liang J, Xiao Y, Song R (2022) Rule mining over knowledge graphs via reinforcement learning. Knowl-Based Syst 242:108371
Fan T-H, Wang Y (2022) Soft actor-critic with integer actions. In: 2022 American Control Conference (ACC). IEEE, pp 2611–2616
Yuan Y, Lei L, Vu TX, Chatzinotas S, Sun S, Ottersten B (2021) Energy minimization in uav-aided networks: Actor-critic learning for constrained scheduling optimization. IEEE Trans Veh Technol 70 (5):5028–5042
Wei Y, Yu FR, Song M, Han Z (2019) Joint optimization of caching, computing, and radio resources for fog-enabled iot using natural actor-critic deep reinforcement learning. IEEE Int Things J 6(2):2061–2073
Liu C-L, Chang C-C, Tseng C-J (2020) Actor-critic deep reinforcement learning for solving job shop scheduling problems. IEEE Access 8:71752–71762
Vamvoudakis KG, Lewis FL (2010) Online actor–critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5):878–888
Kiumarsi B, Vamvoudakis KG, Modares H, Lewis FL (2017) Optimal and autonomous control using reinforcement learning: a survey. IEEE Trans Neural Netw Learn Syst 29(6):2042–2062
Gao M, Feng X, Yu H, Zheng Z (2022) Multi-granularity competition-cooperation optimization algorithm with adaptive parameter configuration. Appl Intell, pp 1–30
Schweighofer N, Doya K (2003) Meta-learning in reinforcement learning. Neural Netw 16 (1):5–9
Peng B, Li X, Gao J, Liu J, Chen Y-N, Wong K-F (2018) Adversarial advantage actor-critic model for task-completion dialogue policy learning. In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp 6149–6153
Zheng Y, Li X, Xu L (2020) Balance control for the first-order inverted pendulum based on the advantage actor-critic algorithm. Inter J Control Auto Syst 18(12):3093–3100
Mnih V, Badia AP, Mirza M, Graves A, Lillicrap T, Harley T, Silver D, Kavukcuoglu K (2016) Asynchronous methods for deep reinforcement learning. In: International conference on machine learning. PMLR, pp 1928–1937
Shang K, Ishibuchi H, He L, Pang LM (2021) A survey on the hypervolume indicator in evolutionary multiobjective optimization. IEEE Trans Evol Comput 25(1):1–20
Chen H, Dai X, Cai H, Zhang W, Yu Y (2019) Large-scale interactive recommendation with tree-structured policy gradient. In: Proceedings of the AAAI Conference on artificial intelligence, vol 33, pp 3312–3320
Zhao S, Liu R, Bo C, Zhao D (2022) Classification-labeled continuousization and multi-domain spatio-temporal fusion for fine-grained urban crime prediction. IEEE Trans Knowl Data Eng, pp 1–14
Yang S, Bo Y, Wong H-S, Kang Z (2019) Cooperative traffic signal control using multi-step return and off-policy asynchronous advantage actor-critic graph algorithm. Knowl-Based Syst 183:104855
Silver D, Schrittwieser J, Simonyan K, Antonoglou I, Huang A, Guez A, Hubert T, Baker L, Lai M, Bolton A et al (2017) Mastering the game of go without human knowledge. Nature 550 (7676):354–359
Zhang B, Hu W, Cao D, Li T, Zhang Z, Chen Z, Blaabjerg F (2021) Soft actor-critic–based multi-objective optimized energy conversion and management strategy for integrated energy systems with renewable energy. Energy Convers Manag 243:114381
Silver D, Huang A, Maddison CJ, Guez A, Sifre L, Van Den Driessche G, Schrittwieser J, Antonoglou I, Panneershelvam V, Lanctot M et al (2016) Mastering the game of go with deep neural networks and tree search. Nature 529(7587):484–489
Memarian F, Goo W, Lioutikov R, Niekum S, Topcu U (2021) Self-supervised online reward shaping in sparse-reward environments. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 2369–2375
Zhan J, Ye J, Ding W, Liu P (2021) A novel three-way decision model based on utility theory in incomplete fuzzy decision systems. IEEE Trans Fuzzy Syst
Yao Y (2021) The geometry of three-way decision. Appl Intell 51(9):6298–6325
Bo Y, Li J (2020) Complex network analysis of three-way decision researches. Int J Mach Learn Cybern 11(5):973–987
Yang X, Li T, Tan A (2020) Three-way decisions in fuzzy incomplete information systems. Int J Mach Learn Cybern 11(3):667–674
Li H, Zhang L, Huang B, Zhou X (2016) Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl-Based Syst 91:241–251
Zhang Q, Pang G, Wang G (2020) A novel sequential three-way decisions model based on penalty function. Knowl-Based Syst 192:105350
Ma Y, Bai Y (2020) A multi-population differential evolution with best-random mutation strategy for large-scale global optimization. Appl Intell 50(5):1510–1526
Wang H, Jiao L, Yao X (2015) Twoarch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19(4):524–541
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
Ishibuchi H, Imada R, Setoguchi Y, Nojima Y (2018) Reference point specification in inverted generational distance for triangular linear pareto front. IEEE Trans Evol Comput 22(6):961–975
Said R, Bechikh S, Louati A, Aldaej A, Said LB (2020) Solving combinatorial multi-objective bi-level optimization problems using multiple populations and migration schemes. IEEE Access 8:141674–141695
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No.62276097), Key Program of National Natural Science Foundation of China (No.62136003), National Key Research and Development Program of China (No. 2020YFB1711700), Special Fund for Information Development of Shanghai Economic and Information Commission (No.XX-XXFZ-02-20-2463) and Scientific Research Program of Shanghai Science and Technology Commission (No.21002411000).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethics approval
This paper does not contain any studies with human participants or animals performed by any of the authors.
Conflict of Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gao, M., Feng, X., Yu, H. et al. An efficient evolutionary algorithm based on deep reinforcement learning for large-scale sparse multiobjective optimization. Appl Intell 53, 21116–21139 (2023). https://doi.org/10.1007/s10489-023-04574-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-023-04574-9