Abstract
For the latest two years, relation classification-based surrogate-assisted algorithms show good potential for solving expensive multi-objective optimization problems (EMOPs). In this category of methods, the used dominance relation that is vital for building training dataset and selecting promising solutions to reduce expensive real function evaluations (FEs). However, the existing studies are still at the initial stage and lack specific research on the dominance relation. This paper proposes a novel dominance relation called Difference Vector Angle Dominance with an angle threshold for EMOPs (called as DVAD-\(\varphi \)). The proposed DVAD-\(\varphi \) has adaptive selection pressure and considers the convergence and diversity of solutions when picking out superior solutions, which makes it beneficial to pick out promising solutions for expensive real FEs and reduce expensive real FEs. To be specific, we firstly give the definition of DVAD-\(\varphi \) that measures the superiority from one solution to another solution, where the angle threshold \(\varphi \) controls the selection pressure. Then, we propose an adaptive determination strategy of angle threshold based on bisection to set proper pressure for picking out promising solutions for expensive real FEs. Experiments have been conducted on 7 test functions from one benchmark set. The experimental results have verified the effectiveness of DVAD-\(\varphi \).
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References
Bosman, P., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 174–188 (2003). https://doi.org/10.1109/TEVC.2003.810761
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002 (Cat. No.02TH8600), vol. 1, pp. 825–830 (2002). https://doi.org/10.1109/CEC.2002.1007032
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(4), 577–601 (2014). https://doi.org/10.1109/TEVC.2013.2281535
Farzaneh, M., Mahdian Toroghi, R.: Music generation using an interactive evolutionary algorithm. In: Djeddi, C., Jamil, A., Siddiqi, I. (eds.) MedPRAI 2019. CCIS, vol. 1144, pp. 207–217. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-37548-5_16
Guo, D., Wang, X., Gao, K., Jin, Y., Ding, J., Chai, T.: Evolutionary optimization of high-dimensional multiobjective and many-objective expensive problems assisted by a dropout neural network. IEEE Trans. Syst. Man Cybern. Syst. 52(4), 2084–2097 (2022). https://doi.org/10.1109/TSMC.2020.3044418
Hao, H., Zhou, A., Qian, H., Zhang, H.: Expensive multiobjective optimization by relation learning and prediction. IEEE Trans. Evol. Comput. 26(5), 1157–1170 (2022). https://doi.org/10.1109/TEVC.2022.3152582
Jiang, M., Wang, Z., Qiu, L., Guo, S., Gao, X., Tan, K.C.: A fast dynamic evolutionary multiobjective algorithm via manifold transfer learning. IEEE Trans. Cybern. 51(7), 3417–3428 (2021). https://doi.org/10.1109/TCYB.2020.2989465
Jin, Y., Wang, H., Chugh, T., Guo, D., Miettinen, K.: Data-driven evolutionary optimization: an overview and case studies. IEEE Trans. Evol. Comput. 23(3), 442–458 (2019). https://doi.org/10.1109/TEVC.2018.2869001
Knowles, J.: Parego: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evol. Comput. 10(1), 50–66 (2006). https://doi.org/10.1109/TEVC.2005.851274
Lin, X., Zhang, Q., Kwong, S.: A decomposition based multiobjective evolutionary algorithm with classification. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 3292–3299 (2016). https://doi.org/10.1109/CEC.2016.7744206
Liu, S., Li, J., Lin, Q., Tian, Y., Tan, K.C.: Learning to accelerate evolutionary search for large-scale multiobjective optimization. IEEE Trans. Evol. Comput. 27(1), 67–81 (2023). https://doi.org/10.1109/TEVC.2022.3155593
McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)
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(1), 74–88 (2019). https://doi.org/10.1109/TEVC.2018.2802784
Shiratori, R., Nakata, M., Hayashi, K., Baba, T.: Particle swarm optimization of silicon photonic crystal waveguide transition. Opt. Lett. 46(8), 1904–1907 (2021)
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(6), 1013–1027 (2021). https://doi.org/10.1109/TEVC.2021.3073648
Sonoda, T., Nakata, M.: Multiple classifiers-assisted evolutionary algorithm based on decomposition for high-dimensional multiobjective problems. IEEE Trans. Evol. Comput. 26(6), 1581–1595 (2022). https://doi.org/10.1109/TEVC.2022.3159000
Tian, Y., Cheng, R., Zhang, X., Jin, Y.: PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput. Intell. Mag. 12(4), 73–87 (2017)
Wilcoxon, F.: Individual Comparisons by Ranking Methods. Springer, Cham (1992)
Xiao, J., Liang, J., Zhao, K., Yang, Z., Yu, M.: Multi-parameters optimization for electromagnetic acoustic transducers using surrogate-assisted particle swarm optimizer. Mech. Syst. Signal Process. 152, 107337 (2021). https://doi.org/10.1016/j.ymssp.2020.107337
Yu, G., Ma, L., Jin, Y., Du, W., Liu, Q., Zhang, H.: A survey on knee-oriented multiobjective evolutionary optimization. IEEE Trans. Evol. Comput. 26(6), 1452–1472 (2022). https://doi.org/10.1109/TEVC.2022.3144880
Yu, M., Li, X., Liang, J.: A dynamic surrogate-assisted evolutionary algorithm framework for expensive structural optimization. Struct. Multidiscip. Optim. 61, 711–729 (2020)
Yuan, Y., Banzhaf, W.: Expensive multiobjective evolutionary optimization assisted by dominance prediction. IEEE Trans. Evol. Comput. 26(1), 159–173 (2022). https://doi.org/10.1109/TEVC.2021.3098257
Zhang, J., Zhou, A., Zhang, G.: A classification and pareto domination based multiobjective evolutionary algorithm. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 2883–2890 (2015). https://doi.org/10.1109/CEC.2015.7257247
Zhang, Q., Liu, W., Tsang, E., Virginas, B.: Expensive multiobjective optimization by MOEA/D with gaussian process model. IEEE Trans. Evol. Comput. 14(3), 456–474 (2010). https://doi.org/10.1109/TEVC.2009.2033671
Zhu, S., Xu, L., Goodman, E.D., Lu, Z.: A new many-objective evolutionary algorithm based on generalized pareto dominance. IEEE Trans. Cybern. 52(8), 7776–7790 (2022). https://doi.org/10.1109/TCYB.2021.3051078
Acknowledgement
This work is supported in part by the NSFC Research Program (61906010, 62276010) and R &D Program of Beijing Municipal Education Commission (KM202010005032, KZ202210005009).
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Yang, C., Chen, J. (2024). Difference Vector Angle Dominance with an Angle Threshold for Expensive Multi-objective Optimization. In: Pan, L., Wang, Y., Lin, J. (eds) Bio-Inspired Computing: Theories and Applications. BIC-TA 2023. Communications in Computer and Information Science, vol 2061. Springer, Singapore. https://doi.org/10.1007/978-981-97-2272-3_7
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