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IEEE/CAA Journal of Automatica Sinica

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Q. Deng, Q. Kang, M. C. Zhou, X. Wang, S. Zhao, S. Wu, and M. Ghahramani, “Evolutionary algorithm based on surrogate and inverse surrogate models for expensive multiobjective optimization,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 5, pp. 1–13, May 2025.
Citation: Q. Deng, Q. Kang, M. C. Zhou, X. Wang, S. Zhao, S. Wu, and M. Ghahramani, “Evolutionary algorithm based on surrogate and inverse surrogate models for expensive multiobjective optimization,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 5, pp. 1–13, May 2025.

Evolutionary Algorithm Based on Surrogate and Inverse Surrogate Models for Expensive Multiobjective Optimization

Funds:  This work was supported in part by the National Natural Science Foundation of China (51775385), the Natural Science Foundation of Shanghai (23ZR1466000), the Shanghai Industrial Collaborative Science and Technology Innovation Project (2021-cyxt2-kj10), and the Innovation Program of Shanghai Municipal Education Commission (202101070007E00098)
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  • When dealing with expensive multiobjective optimization problems, majority of existing surrogate-assisted evolutionary algorithms (SAEAs) generate solutions in decision space and screen candidate solutions mostly by using designed surrogate models. The generated solutions exhibit excessive randomness, which tends to reduce the likelihood of generating good-quality solutions and cause a long evolution to the optima. To improve SAEAs greatly, this work proposes an evolutionary algorithm based on surrogate and inverse surrogate models by 1) employing a surrogate model in lieu of expensive (true) function evaluations; and 2) proposing and using an inverse surrogate model to generate new solutions. By using the same training data but with its inputs and outputs being reversed, the latter is simple to train. It is then used to generate new vectors in objective space, which are mapped into decision space to obtain their corresponding solutions. Using a particular example, this work shows its advantages over existing SAEAs. The results of comparing it with state-of-the-art algorithms on expensive optimization problems show that it is highly competitive in both solution performance and efficiency.

     

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  • [1]
    F. Li, L. Gao, W. Shen, X. Cai, and S. Huang, “A surrogate-assisted offspring generation method for expensive multi-objective optimization problems,” in Proc. IEEE Congr. Evolutionary Computation, Glasgow, UK, 2020, pp. 1–8.
    [2]
    B. Li, Y. Lu, H. Qian, W. Hong, P. Yang, and A. Zhou, “Regularity model based offspring generation in surrogate-assisted evolutionary algorithms for expensive multi-objective optimization,” Swarm Evol. Comput., vol. 86, p. 101506, Apr. 2024. doi: 10.1016/j.swevo.2024.101506
    [3]
    X. Wang, Q. Kang, M. Zhou, S. Yao, and A. Abusorrah, “Domain adaptation multitask optimization,” IEEE Trans. Cybern., vol. 53, no. 7, pp. 4567–4578, Jul. 2023. doi: 10.1109/TCYB.2022.3222101
    [4]
    X. Wang, Q. Kang, M. Zhou, Q. Deng, Z. Fan, and H. Liu, “Knowledge classification-assisted evolutionary multitasking for two-task multiobjective optimization problems,” IEEE/CAA J. Autom. Sinica, 2024, doi: 10.1109/JAS.2024.125070.
    [5]
    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
    [6]
    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
    [7]
    A. Kenny, T. Ray, and H. K. Singh, “An iterative two-stage multi-fidelity optimization algorithm for computationally expensive problems,” IEEE Trans. Evol. Comput., vol. 27, no. 3, pp. 520–534, Jun. 2023. doi: 10.1109/TEVC.2022.3170970
    [8]
    J. T. Wilson, F. Hutter, and M. P. Deisenroth, “Maximizing acquisition functions for Bayesian optimization,” Proc. 32nd Int. Conf. Neural Information Processing Systems, Montreal, Canada, 2018, pp. 9906–9917.
    [9]
    T. Chugh, Y. Jin, K. Miettinen, J. Hakanen, and K. Sindhya, “A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization,” IEEE Trans. Evol. Comput., vol. 22, no. 1, pp. 129–142, Feb. 2018. doi: 10.1109/TEVC.2016.2622301
    [10]
    Z. Song, H. Wang, C. He, and Y. Jin, “A kriging-assisted two-archive evolutionary algorithm for expensive many-objective optimization,” IEEE Trans. Evol. Comput., vol. 25, no. 6, pp. 1013–1027, Dec. 2021. doi: 10.1109/TEVC.2021.3073648
    [11]
    Y. Jin, H. Wang, T. Chugh, D. Guo, and K. Miettinen, “Data-driven evolutionary optimization: An overview and case studies,” IEEE Trans. Evol. Comput., vol. 23, no. 3, pp. 442–458, Jun. 2019. doi: 10.1109/TEVC.2018.2869001
    [12]
    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
    [13]
    D. Zhan, Y. Cheng, and J. Liu, “Expected improvement matrix-based infill criteria for expensive multiobjective optimization,” IEEE Trans. Evol. Comput., vol. 21, no. 6, pp. 956–975, Dec. 2017. doi: 10.1109/TEVC.2017.2697503
    [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]
    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
    [16]
    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
    [17]
    D. Guo, X. Wang, K. Gao, Y. Jin, J. Ding, and T. Chai, “Evolutionary optimization of high-dimensional multiobjective and many-objective expensive problems assisted by a dropout neural network,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 52, no. 4, pp. 2084–2097, Apr. 2022. doi: 10.1109/TSMC.2020.3044418
    [18]
    Z. Wang, Q. Zhang, Y. S. Ong, S. Yao, H. Liu, and J. Luo, “Choose appropriate subproblems for collaborative modeling in expensive multiobjective optimization,” IEEE Trans. Cybern., vol. 53, no. 1, pp. 483–496, Jan. 2023. doi: 10.1109/TCYB.2021.3126341
    [19]
    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
    [20]
    J. Knowles, “ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems,” IEEE Trans. Evol. Comput., vol. 10, no. 1, pp. 50–66, Feb. 2006. doi: 10.1109/TEVC.2005.851274
    [21]
    N. Namura, K. Shimoyama, and S. Obayashi, “Expected improvement of penalty-based boundary intersection for expensive multiobjective optimization,” IEEE Trans. Evol. Comput., vol. 21, no. 6, pp. 898–913, Dec. 2017. doi: 10.1109/TEVC.2017.2693320
    [22]
    Q. Zhang, W. Liu, E. Tsang, and B. Virginas, “Expensive multiobjective optimization by MOEA/D with Gaussian process model,” IEEE Trans. Evol. Comput., vol. 14, no. 3, pp. 456–474, Jun. 2010. doi: 10.1109/TEVC.2009.2033671
    [23]
    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
    [24]
    S. D. Handoko, C. K. Kwoh, and Y. S. Ong, “Feasibility structure modeling: An effective chaperone for constrained memetic algorithms,” IEEE Trans. Evol. Comput., vol. 14, no. 5, pp. 740–758, Oct. 2010. doi: 10.1109/TEVC.2009.2039141
    [25]
    L. Pan, C. He, Y. Tian, H. Wang, X. Zhang, and Y. Jin, “A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization,” IEEE Trans. Evol. Comput., vol. 23, no. 1, pp. 74–88, Feb. 2019. doi: 10.1109/TEVC.2018.2802784
    [26]
    C. He, S. Huang, R. Cheng, K. C. Tan, and Y. Jin, “Evolutionary multiobjective optimization driven by generative adversarial networks (GANs),” IEEE Trans. Cybern., vol. 51, no. 6, pp. 3129–3142, Jun. 2021. doi: 10.1109/TCYB.2020.2985081
    [27]
    T. Sonoda and M. Nakata, “Multiple classifiers-assisted evolutionary algorithm based on decomposition for high-dimensional multiobjective problems,” IEEE Trans. Evol. Comput., vol. 26, no. 6, pp. 1581–1595, Dec. 2022. doi: 10.1109/TEVC.2022.3159000
    [28]
    H. Wang, L. Jiao, and X. Yao, “Two_Arch2: An improved two-archive algorithm for many-objective optimization,” IEEE Trans. Evol. Comput., vol. 19, no. 4, pp. 524–541, Aug. 2015. doi: 10.1109/TEVC.2014.2350987
    [29]
    I. Giagkiozis and P. J. Fleming, “Pareto front estimation for decision making,” Evol. Comput., vol. 22, no. 4, pp. 651–678, Dec. 2014. doi: 10.1162/EVCO_a_00128
    [30]
    Q. Deng, Q. Kang, L. Zhang, M. Zhou, and J. An, “Objective space-based population generation to accelerate evolutionary algorithms for large-scale many-objective optimization,” IEEE Trans. Evol. Comput., vol. 27, no. 2, pp. 326–340, Apr. 2023. doi: 10.1109/TEVC.2022.3166815
    [31]
    Q. Deng, Q. Kang, M. Zhou, X. Wang, and A. Albeshri, “Activation function-assisted objective space mapping to enhance evolutionary algorithms for large-scale many-objective optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 55, no. 1, pp. 183–195, Jan. 2025. doi: 10.1109/TSMC.2024.3454051
    [32]
    R. Cheng, Y. Jin, K. Narukawa, and B. Sendhoff, “A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling,” IEEE Trans. Evol. Comput., vol. 19, no. 6, pp. 838–856, Dec. 2015. doi: 10.1109/TEVC.2015.2395073
    [33]
    H. Hao, A. Zhou, H. Qian, and H. Zhang, “Expensive multiobjective optimization by relation learning and prediction,” IEEE Trans. Evol. Comput., vol. 26, no. 5, pp. 1157–1170, Oct. 2022. doi: 10.1109/TEVC.2022.3152582
    [34]
    K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multiobjective optimization,” Evolutionary Multiobjective Optimization, A. Abraham, L. Jain, and R. Goldberg, Eds. London, U K: Springer, 2005, pp. 105–145.
    [35]
    D. R. Jones, “A taxonomy of global optimization methods based on response surfaces,” J. Global Optim., vol. 21, no. 4, pp. 345–383, Dec. 2001. doi: 10.1023/A:1012771025575
    [36]
    M. T. M. Emmerich, K. C. Giannakoglou, and B. Naujoks, “Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels,” IEEE Trans. Evol. Comput., vol. 10, no. 4, pp. 421–439, Aug. 2006. doi: 10.1109/TEVC.2005.859463
    [37]
    H. B. Nielsen, S. N. Lophaven, and J. Søndergaard, DACE——A MATLAB Kriging Toolbox, Technical University of Denmark, Copenhagen, Denmark, 2002.
    [38]
    E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. Da Fonseca, “Performance assessment of multiobjective optimizers: An analysis and review,” IEEE Trans. Evol. Comput., vol. 7, no. 2, pp. 117–132, Apr. 2003. doi: 10.1109/TEVC.2003.810758
    [39]
    L. While, P. Hingston, L. Barone, and S. Huband, “A faster algorithm for calculating hypervolume,” IEEE Trans. Evol. Comput., vol. 10, no. 1, pp. 29–38, Feb. 2006. doi: 10.1109/TEVC.2005.851275
    [40]
    Y. Tian, R. Cheng, X. Zhang, and Y. Jin, “PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [Educational Forum],” IEEE Comput. Intell. Mag., vol. 12, no. 4, pp. 73–87, Nov. 2017. doi: 10.1109/MCI.2017.2742868
    [41]
    J. Derrac, S. García, D. Molina, and F. Herrera, “A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms,” Swarm Evol. Comput., vol. 1, no. 1, pp. 3–18, Mar. 2011. doi: 10.1016/j.swevo.2011.02.002
    [42]
    R. Cheng, M. Li, Y. Tian, X. Zhang, S. Yang, Y. Jin, and X. Yao, “A benchmark test suite for evolutionary many-objective optimization,” Complex Intell. Syst., vol. 3, no. 1, pp. 67–81, Mar. 2017. doi: 10.1007/s40747-017-0039-7
    [43]
    H. Jain and K. Deb, “An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach,” IEEE Trans. Evol. Comput., vol. 18, no. 4, pp. 602–622, Aug. 2014. doi: 10.1109/TEVC.2013.2281534
    [44]
    Y. Zhao, C. Sun, J. Zeng, Y. Tan, and G. Zhang, “A surrogate-ensemble assisted expensive many-objective optimization,” Knowl.-Based Syst., vol. 211, p. 106520, Jan. 2021. doi: 10.1016/j.knosys.2020.106520
    [45]
    J. Li, M. Zhou, Q. Sun, X. Dai, and X. Yu, “Colored traveling salesman problem,” IEEE Trans. Cybern., vol. 45, p. 11, Nov. 2015.
    [46]
    Y. Feng, M. Zhou, G. Tian, Z. Li, Z. Zhang, Q. Zhang, and J. Tan, “Target disassembly sequencing and scheme evaluation for CNC machine tools using improved multiobjective ant colony algorithm and fuzzy integral,” IEEE Trans. Syst., Man, Cybern.: Syst., vol. 49, no. 12, pp. 2438–2451, Dec. 2019. doi: 10.1109/TSMC.2018.2847448
    [47]
    L. Huang, M. Zhou, H. Han, S. Wang, and A. Albeshri, “Learning-inspired immune algorithm for multiobjective-optimized multirobot maritime patrolling,” IEEE Internet Things J., vol. 11, no. 6, pp. 9870–9881, Mar. 2024. doi: 10.1109/JIOT.2023.3326567
    [48]
    H. Zhu, M. Zhou, Y. Xie, and A. Albeshri, “A self-adapting and efficient dandelion algorithm and its application to feature selection for credit card fraud detection,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 2, pp. 377–390, Feb. 2024. doi: 10.1109/JAS.2023.124008

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