Abstract
Surrogate-assisted multi-objective evolutionary algorithms show excellent performance in solving expensive multi-objective optimization problems, but most of them do not work well for discontinuities Pareto fronts(PFs). To address this problem, a surrogate-assisted multi-objective evolutionary algorithm guided by hybrid reference points is proposed in this paper. The algorithm introduces a discontinuous region boundary point identification strategy to recognize the discontinuous information of PFs and set the reference points. Moreover, a two-stage multi-reference point-assisted management strategy is developed, which enables the algorithm to obtain better performance on different irregular discontinuous PFs. Experimental results show that the algorithm outperforms comparison algorithms on most of the problems with discontinuous PFs.
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References
Zhang, Q., Liu, W., Tsang, E., Virginas, B.: Expensive multiobjective optimization by MOEA/D with gaussian process model. IEEE Trans. Evol. Comput. 14, 456–474 (2010). https://doi.org/10.1109/TEVC.2009.2033671
He, C., Zhang, Y., Gong, D., Ji, X.: A review of surrogate-assisted evolutionary algorithms for expensive optimization problems. Expert Syst. Appl. 217 (2023). https://doi.org/10.1016/j.eswa.2022.119495
Jin, Y., Sendhoff, B.: A systems approach to evolutionary multiobjective structural optimization and beyond. IEEE Comput. Intell. Mag. 4, 62–76 (2009). https://doi.org/10.1109/MCI.2009.933094
Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol. Comput. 1, 32–49 (2011). https://doi.org/10.1016/j.swevo.2011.03.001
Chugh, T., Sindhya, K., Hakanen, J., Miettinen, K.: A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms. Soft. Comput. 23, 3137–3166 (2019). https://doi.org/10.1007/s00500-017-2965-0
He, Z., Yen, G.G., Zhang, J.: Fuzzy-based pareto optimality for many-objective evolutionary algorithms. IEEE Trans. Evol. Comput. 18, 269–285 (2014). https://doi.org/10.1109/TEVC.2013.2258025
Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19, 45–76 (2011). https://doi.org/10.1162/EVCO_a_00009
Qin, S., Sun, C., Zhang, G., He, X., Tan, Y.: A modified particle swarm optimization based on decomposition with different ideal points for many-objective optimization problems. Complex Intell. Syst. 6, 263–274 (2020). https://doi.org/10.1007/s40747-020-00134-7
Zhan, Z.-H., et al.: Matrix-based evolutionary computation. IEEE Trans. Emerg. Top. Comput. Intell. 6, 315–328 (2022). https://doi.org/10.1109/TETCI.2020.3047410
Song, Z., Wang, H., He, C., Jin, Y.: A kriging-assisted two-archive evolutionary algorithm for expensive many-objective optimization. IEEE Trans. Evol. Comput. 25, 1013–1027 (2021). https://doi.org/10.1109/TEVC.2021.3073648
Luo, J., Gupta, A., Ong, Y.-S., Wang, Z.: Evolutionary optimization of expensive multiobjective problems with co-sub-pareto front gaussian process surrogates. IEEE Trans. Cybern. 49, 1708–1721 (2019). https://doi.org/10.1109/TCYB.2018.2811761
Li, J., Wang, P., Dong, H., Shen, J., Chen, C.: A classification surrogate-assisted multi-objective evolutionary algorithm for expensive optimization. Knowl.-Based Syst. 242 (2022). https://doi.org/10.1016/j.knosys.2022.108416
Wei, F.-F., et al.: A classifier-assisted level-based learning swarm optimizer for expensive optimization. IEEE Trans. Evol. Comput. 25, 219–233 (2021). https://doi.org/10.1109/TEVC.2020.3017865
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: solving problems with box constraints. IEEE Trans. Evol. Comput. 18, 577–601 (2014). https://doi.org/10.1109/TEVC.2013.2281535
Lin, W., Lin, Q., Zhu, Z., Li, J., Chen, J., Ming, Z.: Evolutionary search with multiple utopian reference points in decomposition-based multiobjective optimization. Complexity (2019)https://doi.org/10.1155/2019/7436712
Xiong, J., Wang, R., Jiang, J.: Weapon selection and planning problems using moea/d with distance-based divided neighborhoods. Complexity (2019). https://doi.org/10.1155/2019/7589760
Zhou, J., Zhang, Y., Wang, J., Suganthan, P.N.: Localized constrained-domination principle for constrained multiobjective optimization. IEEE Trans. Syst. Man Cybern.-Syst. 54, 1376–1387 (2024). https://doi.org/10.1109/TSMC.2023.3324797
Pan, L., He, C., Tian, Y., Su, Y., Zhang, X.: A region division based diversity maintaining approach for many-objective optimization. Integr. Comput.-Aided Eng. 24, 279–296 (2017). https://doi.org/10.3233/ICA-170542
Li, X., Li, X., Wang, K.: A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts. J. Intell. Fuzzy Syst. 42, 5863–5883 (2022). https://doi.org/10.3233/JIFS-212426
Cheng, H., Li, L., You, L.: A weight vector adjustment method for decomposition-based multi-objective evolutionary algorithms. IEEE Access. 11, 42324–42330 (2023). https://doi.org/10.1109/ACCESS.2023.3270806
Liu, Q., Jin, Y., Heiderich, M., Rodemann, T.: Surrogate-assisted evolutionary optimization of expensive many-objective irregular problems. Knowl.-based Syst. 240, (2022). https://doi.org/10.1016/j.knosys.2022.108197
Namura, N.: Surrogate-assisted reference vector adaptation to various pareto front shapes for many-objective Bayesian optimization. In: 2021 IEEE Congress on Evolutionary Computation (CEC), pp. 901–908. IEEE (2021)
Islam, J., Nazir, A., Hossain, M.M., Alhitmi, H.K., Kabir, M.A., Jallad, A.-H.M.: A surrogate assisted quantum-behaved algorithm for well placement optimization. IEEE Access. 10, 17828–17844 (2022). https://doi.org/10.1109/ACCESS.2022.3145244
Pang, L.M., Ishibuchi, H., He, L., Shang, K., Chen, L.: Hypervolume-based cooperative coevolution with two reference points for multi-objective optimization. IEEE Trans. Evol. Comput. 1 (2023). https://doi.org/10.1109/TEVC.2023.3287399
Pan, L., He, C., Tian, Y., Wang, H., Zhang, X., Jin, Y.: A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Trans. Evol. Comput. 23, 74–88 (2019). https://doi.org/10.1109/TEVC.2018.2802784
Tian, J., Tan, Y., Zeng, J., Sun, C., Jin, Y.: Multiobjective infill criterion driven gaussian process-assisted particle swarm optimization of high-dimensional expensive problems. IEEE Trans. Evol. Comput. 23, 459–472 (2019). https://doi.org/10.1109/TEVC.2018.2869247
Knowles, J.: ParEGO: a hybrid algorithm with online landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evol. Comput. 10, 50–66 (2006). https://doi.org/10.1109/TEVC.2005.851274
Coello, C.A.C., Cortés, N.C.: Solving multiobjective optimization problems using an artificial immune system. Genet. Program Evolvable Mach. 6, 163–190 (2005)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3, 257–271 (1999). https://doi.org/10.1109/4235.797969
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This study was supported by the National Natural Science Foundation of China under Grant 62273348.
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Li, S., Zhang, Y., Wang, Q., He, L., Li, H., Ye, B. (2024). A Surrogate-Assisted Multi-objective Evolutionary Algorithm Guided by Hybrid Reference Points. In: Tan, Y., Shi, Y. (eds) Advances in Swarm Intelligence. ICSI 2024. Lecture Notes in Computer Science, vol 14788. Springer, Singapore. https://doi.org/10.1007/978-981-97-7181-3_35
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