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Volume 11 Issue 5
May  2024

IEEE/CAA Journal of Automatica Sinica

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Article Contents
M. C. Zhou, M. Cui, D. Xu, S. Zhu, Z. Zhao, and  A. Abusorrah,  “Evolutionary optimization methods for high-dimensional expensive problems: A survey,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1092–1105, May 2024. doi: 10.1109/JAS.2024.124320
Citation: M. C. Zhou, M. Cui, D. Xu, S. Zhu, Z. Zhao, and  A. Abusorrah,  “Evolutionary optimization methods for high-dimensional expensive problems: A survey,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1092–1105, May 2024. doi: 10.1109/JAS.2024.124320

Evolutionary Optimization Methods for High-Dimensional Expensive Problems: A Survey

doi: 10.1109/JAS.2024.124320
Funds:  This work was supported in part by the Natural Science Foundation of Jiangsu Province (BK20230923, BK20221067), the National Natural Science Foundation of China (62206113, 62203093), Institutional Fund Projects Provided by the Ministry of Education and King Abdulaziz University (IFPIP-1532-135-1443), and FDCT (Fundo para o Desenvolvimento das Ciencias e da Tecnologia) (0047/2021/A1)
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  • Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems. The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems (HEPs). The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations. Moreover, it is hard to traverse the huge search space within reasonable resource as problem dimension increases. Traditional evolutionary algorithms (EAs) tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results. To reduce such evaluations, many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years. Yet there lacks a thorough review of the state of the art in this specific and important area. This paper provides a comprehensive survey of these evolutionary algorithms for HEPs. We start with a brief introduction to the research status and the basic concepts of HEPs. Then, we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects. We also give comparative results of some representative algorithms and application examples. Finally, we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.

     

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  • [1]
    H. Wang, Y. Jin, and J. O. Jansen, “Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system,” IEEE Trans. Evol. Comput., vol. 20, no. 6, pp. 939–952, Dec. 2016. doi: 10.1109/TEVC.2016.2555315
    [2]
    J. Zhang, F.-Y. Wang, K. Wang, W.-H. Lin, X. Xu, and C. Chen, “Data-driven intelligent transportation systems: A survey,” IEEE Trans. Intell. Transp. Syst., vol. 12, no. 4, pp. 1624–1639, Dec. 2011. doi: 10.1109/TITS.2011.2158001
    [3]
    J. Cheng, P. Jiang, Q. Zhou, J. Hu, and L. Shu, “A parallel constrained lower confidence bounding approach for computationally expensive constrained optimization problems,” Appl. Soft Comput., vol. 106, p. 107276, Jul. 2021. doi: 10.1016/j.asoc.2021.107276
    [4]
    W. K. Liu, S. Li, and H. S. Park, “Eighty years of the finite element method: Birth, evolution, and future,” Arch. Comput. Methods Eng., vol. 29, no. 6, pp. 4431–4453, Jun. 2022. doi: 10.1007/s11831-022-09740-9
    [5]
    T. Jansson, L. Nilsson, and M. Redhe, “Using surrogate models and response surfaces in structural optimization-with application to crashworthiness design and sheet metal forming,” Struct. Multidiscipl. Optim., vol. 25, no. 2, pp. 129–140, Jun. 2003. doi: 10.1007/s00158-002-0279-y
    [6]
    Y. Sun, M. Kirley, and S. K. Halgamuge, “Quantifying variable interactions in continuous optimization problems,” IEEE Trans. Evol. Comput., vol. 21, no. 2, pp. 249–264, Apr. 2017. doi: 10.1109/TEVC.2016.2599164
    [7]
    Y. Jin, “Surrogate-assisted evolutionary computation: Recent advances and future challenges,” Swarm Evol. Comput., vol. 1, no. 2, pp. 61–70, Jun. 2011. doi: 10.1016/j.swevo.2011.05.001
    [8]
    Z.-H. Zhan, L. Shi, K. C. Tan, and J. Zhang, “A survey on evolutionary computation for complex continuous optimization,” Artif. Intell. Rev., vol. 55, no. 1, pp. 59–110, Jan. 2022. doi: 10.1007/s10462-021-10042-y
    [9]
    J.-Y. Li, Z.-H. Zhan, and J. Zhang, “Evolutionary computation for expensive optimization: A survey,” Mach. Intell. Res., vol. 19, no. 1, pp. 3–23, Jan. 2022. doi: 10.1007/s11633-022-1317-4
    [10]
    Y. Wang, S. Gao, M. Zhou, and Y. Yu, “A multi-layered gravitational search algorithm for function optimization and real-world problems,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 94–109, Jan. 2021. doi: 10.1109/JAS.2020.1003462
    [11]
    Q. Fan and O. K. Ersoy, “Zoning search with adaptive resource allocating method for balanced and imbalanced multimodal multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1163–1176, Jun. 2021. doi: 10.1109/JAS.2021.1004027
    [12]
    C. He, Y. Zhang, D. Gong, and X. Ji, “A review of surrogate-assisted evolutionary algorithms for expensive optimization problems,” Expert Syst. Appl., vol. 217, p. 119495, May 2023. doi: 10.1016/j.eswa.2022.119495
    [13]
    F.-F. Wei, W.-N. Chen, Q. Yang, J. Deng, X.-N. Luo, H. Jin, and J. Zhang, “A classifier-assisted level-based learning swarm optimizer for expensive optimization,” IEEE Trans. Evol. Comput., vol. 25, no. 2, pp. 219–233, Apr. 2021. doi: 10.1109/TEVC.2020.3017865
    [14]
    R. G. Regis, “Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions,” IEEE Trans. Evol. Comput., vol. 18, no. 3, pp. 326–347, Jun. 2014. doi: 10.1109/TEVC.2013.2262111
    [15]
    C. A. C. Coello, “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art,” Comput. Methods Appl. Mech. Eng., vol. 191, pp. 11–12, Jan. 1245.
    [16]
    C. A. C. Coello, “Constraint-handling techniques used with evolutionary algorithms,” in Proc. Companion Conf. Genetic and Evolutionary Computation, Lisbon, Portugal, 2023, pp. 1248–1270.
    [17]
    Z. Lei, S. Gao, Z. Zhang, M. C. Zhou, and J. Cheng, “MO4: A many-objective evolutionary algorithm for protein structure prediction,” IEEE Trans. Evol. Comput., vol. 26, no. 3, pp. 417–430, Jun. 2022. doi: 10.1109/TEVC.2021.3095481
    [18]
    W. Li, L. He, and Y. Cao, “Many-objective evolutionary algorithm with reference point-based fuzzy correlation entropy for energy-efficient job shop scheduling with limited workers,” IEEE Trans. Cybern., vol. 52, no. 10, pp. 10721–10734, Oct. 2022. doi: 10.1109/TCYB.2021.3069184
    [19]
    X. Ruan, P. Jiang, Q. Zhou, J. Hu, and L. Shu, “Variable-fidelity probability of improvement method for efficient global optimization of expensive black-box problems,” Struct. Multidiscipl. Optim., vol. 62, no. 6, pp. 3021–3052, Aug. 2020. doi: 10.1007/s00158-020-02646-9
    [20]
    Y. Zhang, Z.-H. Han, and K.-S. Zhang, “Variable-fidelity expected improvement method for efficient global optimization of expensive functions,” Struct. Multidiscipl. Optim., vol. 58, no. 4, pp. 1431–1451, May 2018. doi: 10.1007/s00158-018-1971-x
    [21]
    M. Imani, M. Imani, and S. F. Ghoreishi, “Bayesian optimization for expensive smooth-varying functions,” IEEE Intell. Syst., vol. 37, no. 4, pp. 44–55, Jul.–Aug. 2022. doi: 10.1109/MIS.2022.3163227
    [22]
    N. Srinivas, A. Krause, S. M. Kakade, and M. W. Seeger, “Information-theoretic regret bounds for Gaussian process optimization in the bandit setting,” IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 3250–3265, May 2012. doi: 10.1109/TIT.2011.2182033
    [23]
    J. Li, P. Wang, H. Dong, J. Shen, and C. Chen, “A classification surrogate-assisted multi-objective evolutionary algorithm for expensive optimization,” Knowl.-Based Syst., vol. 242, p. 108416, Apr. 2022. doi: 10.1016/j.knosys.2022.108416
    [24]
    Y. Wang, J. Lin, J. Liu, G. Sun, and T. Pang, “Surrogate-assisted differential evolution with region division for expensive optimization problems with discontinuous responses,” IEEE Trans. Evol. Comput., vol. 26, no. 4, pp. 780–792, Aug. 2022. doi: 10.1109/TEVC.2021.3117990
    [25]
    M. Yu, J. Liang, Z. Wu, and Z. Yang, “A twofold infill criterion-driven heterogeneous ensemble surrogate-assisted evolutionary algorithm for computationally expensive problems,” Knowl.-Based Syst., vol. 236, p. 107747, Jan. 2022. doi: 10.1016/j.knosys.2021.107747
    [26]
    B. Liu, D. Zhao, P. Reynaert, and G. G. E. Gielen, “GASPAD: A general and efficient mm-wave integrated circuit synthesis method based on surrogate model assisted evolutionary algorithm,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 33, no. 2, pp. 169–182, Feb. 2014. doi: 10.1109/TCAD.2013.2284109
    [27]
    Y. Sun, H. Wang, B. Xue, Y. Jin, G. G. Yen, and M. Zhang, “Surrogate-assisted evolutionary deep learning using an end-to-end random forest-based performance predictor,” IEEE Trans. Evol. Comput., vol. 24, no. 2, pp. 350–364, Apr. 2020. doi: 10.1109/TEVC.2019.2924461
    [28]
    H. Wang and Y. Jin, “A random forest-assisted evolutionary algorithm for data-driven constrained multiobjective combinatorial optimization of trauma systems,” IEEE Trans. Cybern., vol. 50, no. 2, pp. 536–549, Feb. 2020. doi: 10.1109/TCYB.2018.2869674
    [29]
    B. Liu, Q. Zhang, and G. G. E. Gielen, “A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems,” IEEE Trans. Evol. Comput., vol. 18, no. 2, pp. 180–192, Apr. 2014. doi: 10.1109/TEVC.2013.2248012
    [30]
    C. Sun, Y. Jin, R. Cheng, J. Ding, and J. Zeng, “Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems,” IEEE Trans. Evol. Comput., vol. 21, no. 4, pp. 644–660, Aug. 2017. doi: 10.1109/TEVC.2017.2675628
    [31]
    C. Sun, J. Ding, J. Zeng, and Y. Jin, “A fitness approximation assisted competitive swarm optimizer for large scale expensive optimization problems,” Memetic. Comput., vol. 10, no. 2, pp. 123–134, Jun. 2018. doi: 10.1007/s12293-016-0199-9
    [32]
    H. Yu, Y. Tan, J. Zeng, C. Sun, and Y. Jin, “Surrogate-assisted hierarchical particle swarm optimization,” Inf. Sci., pp. 454–455, Jul. 2018.
    [33]
    J. Tian, Y. Tan, J. Zeng, C. Sun, and Y. Jin, “Multiobjective infill criterion driven Gaussian process-assisted particle swarm optimization of high-dimensional expensive problems,” IEEE Trans. Evol. Comput., vol. 23, no. 3, pp. 459–472, Jun. 2019. doi: 10.1109/TEVC.2018.2869247
    [34]
    X. Cai, H. Qiu, L. Gao, C. Jiang, and X. Shao, “An efficient surrogate-assisted particle swarm optimization algorithm for high-dimensional expensive problems,” Knowl.-Based Syst., vol. 184, p. 104901, Nov. 2019. doi: 10.1016/j.knosys.2019.104901
    [35]
    X. Cai, L. Gao, X. Li, and H. Qiu, “Surrogate-guided differential evolution algorithm for high dimensional expensive problems,” Swarm Evol. Comput., vol. 48, pp. 288–311, Aug. 2019. doi: 10.1016/j.swevo.2019.04.009
    [36]
    Z. Yang, H. Qiu, L. Gao, C. Jiang, and J. Zhang, “Two-layer adaptive surrogate-assisted evolutionary algorithm for high-dimensional computationally expensive problems,” J. Global Optim., vol. 74, no. 2, pp. 327–359, Mar. 2019. doi: 10.1007/s10898-019-00759-0
    [37]
    X. Wang, G. G. Wang, B. Song, P. Wang, and Y. Wang, “A novel evolutionary sampling assisted optimization method for high-dimensional expensive problems,” IEEE Trans. Evol. Comput., vol. 23, no. 5, pp. 815–827, Oct. 2019. doi: 10.1109/TEVC.2019.2890818
    [38]
    H. Yu, Y. Tan, C. Sun, and J. Zeng, “A generation-based optimal restart strategy for surrogate-assisted social learning particle swarm optimization,” Knowl.-Based Syst., vol. 163, pp. 14–25, Jan. 2019. doi: 10.1016/j.knosys.2018.08.010
    [39]
    X. Cai, L. Gao, and X. Li, “Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems,” IEEE Trans. Evol. Comput., vol. 24, no. 2, pp. 365–379, Apr. 2020. doi: 10.1109/TEVC.2019.2919762
    [40]
    J. Tian, C. Sun, Y. Tan, and J. Zeng, “Granularity-based surrogate-assisted particle swarm optimization for high-dimensional expensive optimization,” Knowl.-Based Syst., vol. 187, p. 104815, Jan. 2020. doi: 10.1016/j.knosys.2019.06.023
    [41]
    H. Dong and Z. Dong, “Surrogate-assisted grey wolf optimization for high-dimensional, computationally expensive black-box problems,” Swarm Evol. Comput., vol. 57, p. 100713, Sept. 2020. doi: 10.1016/j.swevo.2020.100713
    [42]
    P. Liao, C. Sun, G. Zhang, and Y. Jin, “Multi-surrogate multi-tasking optimization of expensive problems,” Knowl.-Based Syst., vol. 205, p. 106262, Oct. 2020. doi: 10.1016/j.knosys.2020.106262
    [43]
    G. Chen, Y. Li, K. Zhang, X. Xue, J. Wang, Q. Luo, C. Yao, and J. Yao, “Efficient hierarchical surrogate-assisted differential evolution for high-dimensional expensive optimization,” Inf. Sci., vol. 542, pp. 228–246, Jan. 2021. doi: 10.1016/j.ins.2020.06.045
    [44]
    F. Li, X. Cai, L. Gao, and W. Shen, “A surrogate-assisted multiswarm optimization algorithm for high-dimensional computationally expensive problems,” IEEE Trans. Cybern., vol. 51, no. 3, pp. 1390–1402, Mar. 2021. doi: 10.1109/TCYB.2020.2967553
    [45]
    S.-C. Chu, Z.-G. Du, Y.-J. Peng, and J.-S. Pan, “Fuzzy hierarchical surrogate assists probabilistic particle swarm optimization for expensive high dimensional problem,” Knowl.-Based Syst., vol. 220, p. 106939, May 2021. doi: 10.1016/j.knosys.2021.106939
    [46]
    H. Dong, P. Wang, X. Yu, and B. Song, “Surrogate-assisted teaching-learning-based optimization for high-dimensional and computationally expensive problems,” Appl. Soft Comput., vol. 99, p. 106934, Feb. 2021. doi: 10.1016/j.asoc.2020.106934
    [47]
    X. Ren, D. Guo, Z. Ren, Y. Liang, and A. Chen, “Enhancing hierarchical surrogate-assisted evolutionary algorithm for high-dimensional expensive optimization via random projection,” Complex Intell. Syst., vol. 7, no. 6, pp. 2961–2975, Jul. 2021. doi: 10.1007/s40747-021-00484-w
    [48]
    Y. Liu, J. Liu, and Y. Jin, “Surrogate-assisted multipopulation particle swarm optimizer for high-dimensional expensive optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 52, no. 7, pp. 4671–4684, Jul. 2022. doi: 10.1109/TSMC.2021.3102298
    [49]
    Q. Gu, Q. Wang, N. N. Xiong, S. Jiang, and L. Chen, “Surrogate-assisted evolutionary algorithm for expensive constrained multi-objective discrete optimization problems,” Complex Intell. Syst., vol. 8, no. 4, pp. 2699–2718, Feb.–Dec. 2022. doi: 10.1007/s40747-020-00249-x
    [50]
    X. Wang, L. Gao, and X. Li, “Multiple surrogates and offspring-assisted differential evolution for high-dimensional expensive problems,” Inf. Sci., vol. 592, pp. 174–191, May 2022. doi: 10.1016/j.ins.2022.01.052
    [51]
    F. Li, Y. Li, X. Cai, and L. Gao, “A surrogate-assisted hybrid swarm optimization algorithm for high-dimensional computationally expensive problems,” Swarm Evol. Comput., vol. 72, p. 101096, Jul. 2022. doi: 10.1016/j.swevo.2022.101096
    [52]
    G. Chen, K. Zhang, X. Xue, L. Zhang, C. Yao, J. Wang, and J. Yao, “A radial basis function surrogate model assisted evolutionary algorithm for high-dimensional expensive optimization problems,” Appl. Soft Comput., vol. 116, p. 108353, Feb. 2022. doi: 10.1016/j.asoc.2021.108353
    [53]
    J. Tian, M. Hou, H. Bian, and J. Li, “Variable surrogate model-based particle swarm optimization for high-dimensional expensive problems,” Complex Intell. Syst., vol. 9, no. 4, pp. 3887–3935, Feb.–Dec. 2023. doi: 10.1007/s40747-022-00910-7
    [54]
    J. Lin, C. He, and R. Cheng, “Adaptive dropout for high-dimensional expensive multiobjective optimization,” Complex Intell. Syst., vol. 8, no. 1, pp. 271–285, Feb.–Dec. 2022. doi: 10.1007/s40747-021-00362-5
    [55]
    M. Cui, L. Li, M. Zhou, and A. Abusorrah, “Surrogate-assisted autoencoder-embedded evolutionary optimization algorithm to solve high-dimensional expensive problems,” IEEE Trans. Evol. Comput., vol. 26, no. 4, pp. 676–689, Aug. 2022. doi: 10.1109/TEVC.2021.3113923
    [56]
    H. Zhen, W. Gong, L. Wang, F. Ming, and Z. Liao, “Two-stage data-driven evolutionary optimization for high-dimensional expensive problems,” IEEE Trans. Cybern., vol. 53, no. 4, pp. 2368–2379, Apr. 2023. doi: 10.1109/TCYB.2021.3118783
    [57]
    W. Wang, H.-L. Liu, and K. C. Tan, “A surrogate-assisted differential evolution algorithm for high-dimensional expensive optimization problems,” IEEE Trans. Cybern., vol. 53, no. 4, pp. 2685–2697, Apr. 2023. doi: 10.1109/TCYB.2022.3175533
    [58]
    L. Zheng, J. Shi, and Y. Yang, “A two-stage surrogate-assisted meta-heuristic algorithm for high-dimensional expensive problems,” Soft Comput., vol. 27, no. 10, pp. 6465–6486, Feb. 2023. doi: 10.1007/s00500-023-07855-0
    [59]
    J. Kůdela and R. Matoušek, “Combining lipschitz and RBF surrogate models for high-dimensional computationally expensive problems,” Inf. Sci., vol. 619, pp. 457–477, Jan. 2023. doi: 10.1016/j.ins.2022.11.045
    [60]
    J. Bi, Z. Wang, H. Yuan, J. Zhang, and M. C. Zhou, “Self-adaptive teaching-learning-based optimizer with improved RBF and sparse autoencoder for high-dimensional problems,” Inf. Sci., vol. 630, pp. 463–481, Jun. 2023. doi: 10.1016/j.ins.2023.02.044
    [61]
    J. W. Sammon, “A nonlinear mapping for data structure analysis,” IEEE Trans. Comput., vol. C-18, no. 5, pp. 401–409, May 1969. doi: 10.1109/T-C.1969.222678
    [62]
    R. L. Hardy, “Multiquadric equations of topography and other irregular surfaces,” J. Geophys. Res., vol. 76, no. 8, pp. 1905–1915, Mar. 1971. doi: 10.1029/JB076i008p01905
    [63]
    G. Li, Q. Zhang, Q. Lin, and W. Gao, “A three-level radial basis function method for expensive optimization,” IEEE Trans. Cybern., vol. 52, no. 7, pp. 5720–5731, Jul. 2022. doi: 10.1109/TCYB.2021.3061420
    [64]
    M. J. Er, S. Wu, J. Lu, and H. L. Toh, “Face recognition with radial basis function (RBF) neural networks,” IEEE Trans. Neural Netw., vol. 13, no. 3, pp. 697–710, May 2002. doi: 10.1109/TNN.2002.1000134
    [65]
    D. Guo, Z. Ren, Y. Liang, and A. Chen, “Scaling up radial basis function for high-dimensional expensive optimization using random projection,” in Proc. IEEE Congr. Evolutionary Computation, Glasgow, UK, 2020, pp. 1–8.
    [66]
    L. Breiman, “Random forests,” Mach. Learn., vol. 45, no. 1, pp. 5–32, Oct. 2001. doi: 10.1023/A:1010933404324
    [67]
    Y. Zhang, X.-F. Ji, X.-Z. Gao, D.-W. Gong, and X.-Y. Sun, “Objective-constraint mutual-guided surrogate-based particle swarm optimization for expensive constrained multimodal problems,” IEEE Trans. Evol. Comput., vol. 27, no. 4, pp. 908–922, Aug. 2023. doi: 10.1109/TEVC.2022.3182810
    [68]
    G. Li, Z. Wang, and M. Gong, “Expensive optimization via surrogate-assisted and model-free evolutionary optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 53, no. 5, pp. 2758–2769, May 2023. doi: 10.1109/TSMC.2022.3219080
    [69]
    D. Guo, Y. Jin, J. Ding, and T. Chai, “Heterogeneous ensemble-based infill criterion for evolutionary multiobjective optimization of expensive problems,” IEEE Trans. Cybern., vol. 49, no. 3, pp. 1012–1025, Mar. 2019. doi: 10.1109/TCYB.2018.2794503
    [70]
    J. E. Dennis and V. Torczon, “Managing approximation models in optimization,” in Multidisciplinary Design Optimization: State-of-the-Art, N. M. Alexandrov and M. Y. Hussaini, Eds. Philadelphia, USA: SIAM, 1997, pp. 330–374.
    [71]
    D. R. Jones, M. Schonlau, and W. J. Welch, “Efficient global optimization of expensive black-box functions,” J. Global Optim., vol. 13, no. 4, pp. 455–492, Dec. 1998. doi: 10.1023/A:1008306431147
    [72]
    A. Slowik and H. Kwasnicka, “Evolutionary algorithms and their applications to engineering problems,” Neural Computing and Applications, vol. 32, pp. 12363–12379, Aug. 2020.
    [73]
    B. Li, J. Li, K. Tang, and X. Yao, “Many-objective evolutionary algorithms: A survey,” ACM Comput. Surv., vol. 48, no. 1, p. 13, Sept. 2015.
    [74]
    A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P. N. Suganthan, and Q. Zhang, “Multiobjective evolutionary algorithms: A survey of the state of the art,” Swarm Evol. Comput., vol. 1, no. 1, pp. 32–49, Mar. 2011. doi: 10.1016/j.swevo.2011.03.001
    [75]
    J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. ICNN’95-Int. Conf. Neural Networks, Perth, Australia, 1995, pp. 1942–1948.
    [76]
    D. Wang, D. Tan, and L. Liu, “Particle swarm optimization algorithm: An overview,” Soft Comput., vol. 22, no. 2, pp. 387–408, Jan.–Dec. 2018. doi: 10.1007/s00500-016-2474-6
    [77]
    R. Cheng and Y. Jin, “A social learning particle swarm optimization algorithm for scalable optimization,” Inf. Sci., vol. 291, pp. 43–60, Jan. 2015. doi: 10.1016/j.ins.2014.08.039
    [78]
    R. Cheng and Y. Jin, “A competitive swarm optimizer for large scale optimization,” IEEE Trans. Cybern., vol. 45, no. 2, pp. 191–204, Feb. 2015. doi: 10.1109/TCYB.2014.2322602
    [79]
    Bilal, M. Pant, H. Zaheer, L. Garcia-Hernandez, and A. Abraham, “Differential evolution: A review of more than two decades of research,” Eng. Appl. Artif. Intell., vol. 90, p. 103479, Apr. 2020. doi: 10.1016/j.engappai.2020.103479
    [80]
    K. Price, R. M. Storn, and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization. Berlin, Germany: Springer, 2006.
    [81]
    R. V. Rao, V. J. Savsani, and D. P. Vakharia, “Teaching-learning-based optimization: An optimization method for continuous non-linear large scale problems,” Inf. Sci., vol. 183, no. 1, pp. 1–15, Jan. 2012. doi: 10.1016/j.ins.2011.08.006
    [82]
    H. Dong, P. Wang, C. Fu, and B. Song, “Kriging-assisted teaching-learning-based optimization (KTLBO) to solve computationally expensive constrained problems,” Inf. Sci., vol. 556, pp. 404–435, May 2021. doi: 10.1016/j.ins.2020.09.073
    [83]
    M. Cui, L. Li, and M. C. Zhou, “An autoencoder-embedded evolutionary optimization framework for high-dimensional problems,” in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, Toronto, Canada, 2020, pp. 1046–1051.
    [84]
    X. Wu, X. Peng, W. Chen, and W. Zhang, “A developed surrogate-based optimization framework combining HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems,” Struct. Multidiscipl. Optim., vol. 60, no. 2, pp. 663–680, Mar. 2019. doi: 10.1007/s00158-019-02228-4
    [85]
    F. Zou, D. Chen, and Q. Xu, “A survey of teaching-learning-based optimization,” Neurocomputing, vol. 335, pp. 366–383, Mar. 2019. doi: 10.1016/j.neucom.2018.06.076
    [86]
    M. Cui, L. Li, M. C. Zhou, J. Li, A. Abusorrah, and K. Sedraoui, “A bi-population cooperative optimization algorithm assisted by an autoencoder for medium-scale expensive problems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 1952–1966, Nov. 2022. doi: 10.1109/JAS.2022.105425
    [87]
    H. Yuan, Q. Hu, J. Bi, J. Lü, J. Zhang, and M. Zhou, “Profit-optimized computation offloading with autoencoder-assisted evolution in large-scale mobile-edge computing,” IEEE Internet Things J., vol. 10, no. 13, pp. 11896–11909, Jul. 2023. doi: 10.1109/JIOT.2023.3244665
    [88]
    X. Cheng, Y. Yu, and W. Hu, “Multi-surrogate-assisted stochastic fractal search algorithm for high-dimensional expensive problems,” Inf. Sci., vol. 640, pp. 119035, 2023.
    [89]
    M. Wu, J. Xu, L. Wang, C. Zhang, and H. Tang, “Adaptive multi-surrogate and module-based optimization algorithm for high-dimensional and computationally expensive problems,” Inf. Sci., vol. 645, p. 119308, 2023.
    [90]
    Z. Cao, C. Lin, M. Zhou, and J. Zhang, “Surrogate-assisted symbiotic organisms search algorithm for parallel batch processor scheduling,” IEEE/ASME Trans. Mechatronics, vol. 25, no. 5, pp. 2155–2166, Oct. 2020.
    [91]
    Z. Cao, C. Lin, M. Zhou, and R. Huang, “Scheduling semiconductor testing facility by using cuckoo search algorithm with reinforcement learning and surrogate modeling,” IEEE Trans. Autom. Science and Engineering, vol. 16, no.5, pp. 825–837, Apr. 2019.
    [92]
    P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y.-P. Chen, A. Auger, and S. Tiwari, “Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization,” Nanyang Technological University, Singapore, KanGAL Report 2005005, 2005.
    [93]
    C. Chen, X. Wang, H. Dong, and P. Wang, “Surrogate-assisted hierarchical learning water cycle algorithm for high-dimensional expensive optimization,” Swarm Evol. Comput., vol. 75, p. 101169, Dec. 2022. doi: 10.1016/j.swevo.2022.101169
    [94]
    X. Du, P. He, and J. R. R. A. Martins, “Rapid airfoil design optimization via neural networks-based parameterization and surrogate modeling,” Aerosp. Sci. Technol., vol. 113, p. 106701, Jun. 2021. doi: 10.1016/j.ast.2021.106701
    [95]
    B. M. Kulfan, “Universal parametric geometry representation method,” J. Aircr., vol. 45, no. 1, pp. 142–158, Jan. 2008. doi: 10.2514/1.29958
    [96]
    G. H. Cheng, A. Younis, K. H. Hajikolaei, and G. G. Wang, “Trust region based mode pursuing sampling method for global optimization of high dimensional design problems,” J. Mech. Des., vol. 137, no. 2, p. 021407, Feb. 2015. doi: 10.1115/1.4029219
    [97]
    C. Sun, B. Song, and P. Wang, “Parametric geometric model and shape optimization of an underwater glider with blended-wing-body,” Int. J. Nav. Archit. Ocean Eng., vol. 7, no. 6, pp. 995–1006, Nov. 2015. doi: 10.1515/ijnaoe-2015-0069
    [98]
    J. Li, Y. Han, K. Gao, X. Xiao, and P. Duan, “Bi-population balancing multi-objective algorithm for fuzzy flexible job shop with energy and transportation,” IEEE Trans. Autom. Sci. Eng., p. , 2023. doi: 10.1109/TASE.2023.3300922
    [99]
    Y. Du, J.-Q. Li, X.-L. Chen, P.-Y. Duan, and Q.-K. Pan, “Knowledge-based reinforcement learning and estimation of distribution algorithm for flexible job shop scheduling problem,” IEEE Trans. Emerg. Top. Comput. Intell., vol. 7, no. 4, pp. 1036–1050, Aug. 2023. doi: 10.1109/TETCI.2022.3145706
    [100]
    F. Zhang, Y. Mei, S. Nguyen, M. Zhang, and K. C. Tan, “Surrogate-assisted evolutionary multitask genetic programming for dynamic flexible job shop scheduling,” IEEE Trans. Evol. Comput., vol. 25, no. 4, pp. 651–665, Aug. 2021. doi: 10.1109/TEVC.2021.3065707
    [101]
    Y. Fu, M. C. Zhou, X. Guo, and L. Qi, “Scheduling dual-objective stochastic hybrid flow shop with deteriorating jobs via bi-population evolutionary algorithm,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 50, no. 12, pp. 5037–5048, Dec. 2020. doi: 10.1109/TSMC.2019.2907575
    [102]
    W. Du, W. Zhong, Y. Tang, W. Du, and Y. Jin, “High-dimensional robust multi-objective optimization for order scheduling: A decision variable classification approach,” IEEE Trans. Ind. Inf., vol. 15, no. 1, pp. 293–304, Jan. 2019. doi: 10.1109/TII.2018.2836189
    [103]
    Z. C. Cao, C. R. Lin, M. C. Zhou, and R. Huang, “Scheduling semiconductor testing facility by using cuckoo search algorithm with reinforcement learning and surrogate modeling,” IEEE Trans. Autom. Sci. Eng., vol. 16, no. 2, pp. 825–837, Apr. 2019. doi: 10.1109/TASE.2018.2862380
    [104]
    O. Sobeyko and L. Mönch, “Heuristic approaches for scheduling jobs in large-scale flexible job shops,” Comput. Oper. Res., vol. 68, pp. 97–109, Apr. 2016. doi: 10.1016/j.cor.2015.11.004
    [105]
    L. Sun, L. Lin, M. Gen, and H. Li, “A hybrid cooperative coevolution algorithm for fuzzy flexible job shop scheduling,” IEEE Trans. Fuzzy Syst., vol. 27, no. 5, pp. 1008–1022, May 2019. doi: 10.1109/TFUZZ.2019.2895562
    [106]
    L. Sun, L. Lin, H. Li, and M. Gen, “Large scale flexible scheduling optimization by a distributed evolutionary algorithm,” Comput. Ind. Eng., vol. 128, pp. 894–904, Feb. 2019. doi: 10.1016/j.cie.2018.09.025
    [107]
    J. Zhao, Z. Zhang, H. Yu, H. Ji, P. Li, W. Xi, J. Yan, and C. Wang, “Cloud-edge collaboration-based local voltage control for DGs with privacy preservation,” IEEE Trans. Ind. Inf., vol. 19, no. 1, pp. 98–108, Jan. 2023. doi: 10.1109/TII.2022.3172901
    [108]
    Q. Yuan, Y. Ye, Y. Tang, Y. Liu, and G. Strbac, “A novel deep-learning based surrogate modeling of stochastic electric vehicle traffic user equilibrium in low-carbon electricity-transportation nexus,” Appl. Energy, vol. 315, p. 118961, Jun. 2022. doi: 10.1016/j.apenergy.2022.118961
    [109]
    F.-F. Wei, W.-N. Chen, Q. Li, S.-W. Jeon, and J. Zhang, “Distributed and expensive evolutionary constrained optimization with on-demand evaluation,” IEEE Trans. Evol. Comput., vol. 27, no. 3, pp. 671–685, Jun. 2023. doi: 10.1109/TEVC.2022.3177936
    [110]
    S. Zhu, L. Xu, and E. D. Goodman, “Hierarchical topology-based cluster representation for scalable evolutionary multiobjective clustering,” IEEE Trans. Cybern., vol. 52, no. 9, pp. 9846–9860, Sept. 2022. doi: 10.1109/TCYB.2021.3081988
    [111]
    S. Zhu, L. Xu, E. D. Goodman, and Z. Lu, “A new many-objective evolutionary algorithm based on generalized Pareto dominance,” IEEE Trans. Cybern., vol. 52, no. 8, pp. 7776–7790, Aug. 2022. doi: 10.1109/TCYB.2021.3051078
    [112]
    R. Wang, W. Ma, M. Tan, G. Wu, L. Wang, D. Gong, and J. Xiong, “Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization,” Inf. Sci., vol. 546, pp. 1148–1165, Feb. 2021. doi: 10.1016/j.ins.2020.09.075
    [113]
    L. Cao, L. Xu, E. D. Goodman, C. Bao, and S. Zhu, “Evolutionary dynamic multiobjective optimization assisted by a support vector regression predictor,” IEEE Trans. Evol. Comput., vol. 24, no. 2, pp. 305–319, Apr. 2020. doi: 10.1109/TEVC.2019.2925722
    [114]
    D. Lim, Y.-S. Ong, and B.-S. Lee, “Inverse multi-objective robust evolutionary design optimization in the presence of uncertainty,” in Proc. 7th Annu. Workshop on Genetic and Evolutionary Computation, Washington, USA, 2005, pp. 55–62.
    [115]
    Z. Lu, G. Sreekumar, E. Goodman, W. Banzhaf, K. Deb, and V. N. Boddeti, “Neural architecture transfer,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 43, no. 9, pp. 2971–2989, Sept. 2021. doi: 10.1109/TPAMI.2021.3052758
    [116]
    R. T. Haftka, D. Villanueva, and A. Chaudhuri, “Parallel surrogate-assisted global optimization with expensive functions–A survey,” Struct. Multidiscipl. Optim., vol. 54, no. 1, pp. 3–13, Apr. 2016. doi: 10.1007/s00158-016-1432-3
    [117]
    M. Weber, F. Neri, and V. Tirronen, “Shuffle or update parallel differential evolution for large-scale optimization,” Soft Comput., vol. 15, no. 11, pp. 2089–2107, Nov. 2011. doi: 10.1007/s00500-010-0640-9
    [118]
    J. Tang, M. H. Lim, and Y. S. Ong, “Diversity-adaptive parallel memetic algorithm for solving large scale combinatorial optimization problems,” Soft Comput., vol. 11, no. 9, pp. 873–888, Jul. 2007. doi: 10.1007/s00500-006-0139-6
    [119]
    M. O. Akinsolu, B. Liu, V. Grout, P. I. Lazaridis, M. E. Mognaschi, and P. Di Barba, “A parallel surrogate model assisted evolutionary algorithm for electromagnetic design optimization,” IEEE Trans. Emerg. Top. Comput. Intell., vol. 3, no. 2, pp. 93–105, Apr. 2019. doi: 10.1109/TETCI.2018.2864747
    [120]
    Y.-J. Gong, W.-N. Chen, Z.-H. Zhan, J. Zhang, Y. Li, Q. Zhang, and J.-J. Li, “Distributed evolutionary algorithms and their models: A survey of the state-of-the-art,” Appl. Soft Comput., vol. 34, pp. 286–300, Sept. 2015. doi: 10.1016/j.asoc.2015.04.061
    [121]
    J. J. Liang, B. Y. Qu, and P. N. Suganthan, “Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization,” Nanyang Technological University, Singapore, 2013, pp. 490.
    [122]
    Z. Y. Zhao, M. C. Zhou, and S. X. Liu, “Iterated greedy algorithms for flow-shop scheduling problems: A tutorial,” IEEE Trans. Autom. Sci. Eng., vol. 19, no. 3, pp. 1941–1959, Jul. 2022. doi: 10.1109/TASE.2021.3062994
    [123]
    L. Zhou, Z. Liang, C.-A. Chou, and W. A. Chaovalitwongse, “Airline planning and scheduling: Models and solution methodologies,” Front. Eng. Manag., vol. 7, no. 1, pp. 1–26, Feb. 2020. doi: 10.1007/s42524-020-0093-5
    [124]
    L. Yue and H. Fan, “Dynamic scheduling and path planning of automated guided vehicles in automatic container terminal,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 2005–2019, Nov. 2022. doi: 10.1109/JAS.2022.105950
    [125]
    C. Liu, J. Wang, M. C. Zhou, and T. Zhou, “Intelligent optimization approach to cell formation and product scheduling for multifactory cellular manufacturing systems considering supply chain and operational error,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 53, no. 8, pp. 4649–4660, Aug. 2023. doi: 10.1109/TSMC.2023.3253471
    [126]
    L. Zhang, Q. Kang, Q. Deng, L. Xu, and Q. Wu, “A line complex-based evolutionary algorithm for many-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1150–1167, May 2023. doi: 10.1109/JAS.2023.123495

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    Highlights

    • Provide a comprehensive survey of the evolutionary algorithms for high-dimensional expensive problems (HEPs) encountered in real-world complex engineering system design and optimization
    • Introduce the research status and basic concepts of HEPs
    • Present representative evolutionary algorithms for HEPs
    • Present comparative results of some representative algorithms and application examples
    • Present open challenges and promising directions to advance the field of HEPs

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