Skip to main content
SpringerLink
Log in

Enhancing SAEAs with unevaluated solutions: a case study of relation model for expensive optimization

  • Research Paper
  • Special Topic: Evolutionary Learning and Optimization
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) hold significant importance in resolving expensive optimization problems. Extensive efforts have been devoted to improving the efficiency of SAEAs through the development of proficient model-assisted solution selection methods, which, however, first requires generating high-quality solutions. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thereby affecting the quality of offspring solutions. This is a frequently encountered issue yet receives little attention. To address the issue, this paper presents a framework using unevaluated solutions to enhance the efficiency of SAEAs. The surrogate model is employed to identify high-quality solutions for the direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models to select the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the solution selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to enhance the efficiency of the algorithm significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bäck T, Fogel D B, Michalewicz Z. Handbook of Evolutionary Computation. Bristol: IOP Publishing Ltd., 1997

    Book  Google Scholar 

  2. Jin Y. Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evolary Comput, 2011, 1: 61–70

    Article  Google Scholar 

  3. Liu Y R, Hu Y Q, Qian H, et al. ZOOpt: a toolbox for derivative-free optimization. Sci China Inf Sci, 2022, 65: 207101

    Article  Google Scholar 

  4. Yang P, Zhang L, Liu H, et al. Reducing idleness in financial cloud via multi-objective evolutionary reinforcement learning based load balancer. 2023. ArXiv:2305.03463

  5. Li J Y, Zhan Z H, Zhang J. Evolutionary computation for expensive optimization: a survey. Mach Intell Res, 2022, 19: 3–23

    Article  Google Scholar 

  6. Zhan D, Xing H. Expected improvement for expensive optimization: a review. J Glob Optim, 2020, 78: 507–544

    Article  MathSciNet  Google Scholar 

  7. Zhang J, Zhou A, Zhang G. Preselection via classification: a case study on global optimisation. Int J Bio-Inspir Comput, 2018, 11: 267–281

    Article  Google Scholar 

  8. Hao H, Zhang J, Lu X, et al. Binary relation learning and classifying for preselection in evolutionary algorithms. IEEE Trans Evol Comput, 2020, 24: 1125–1139

    Article  Google Scholar 

  9. Liu B, Zhang Q, Gielen G G E. A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Trans Evol Comput, 2014, 18: 180–192

    Article  Google Scholar 

  10. Chen G, Zhang K, Xue X, et al. Surrogate-assisted evolutionary algorithm with dimensionality reduction method for water flooding production optimization. J Pet Sci Eng, 2020, 185: 106633

    Article  CAS  Google Scholar 

  11. Sun C, Jin Y, Cheng R, et al. Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Trans Evol Comput, 2017, 21: 644–660

    Article  Google Scholar 

  12. Willmes L, Back T, Jin Y, et al. Comparing neural networks and kriging for fitness approximation in evolutionary optimization. In: Proceedings of Congress on Evolutionary Computation, 2003. 663–670

  13. Li H, He F, Yan X. IBEA-SVM: an indicator-based evolutionary algorithm based on pre-selection with classification guided by SVM. Appl Math J Chin Univ, 2019, 34: 1–26

    Article  MathSciNet  CAS  Google Scholar 

  14. Pan L, He C, Tian Y, et al. A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput, 2019, 23: 74–88

    Article  Google Scholar 

  15. Loshchilov I, Schoenauer M, Sebag M. Comparison-based optimizers need comparison-based surrogates. In: Proceedings of International Conference on Parallel Problem Solving from Nature, 2010. 364–373

  16. Hao H, Zhou A, Qian H, et al. Expensive multiobjective optimization by relation learning and prediction. IEEE Trans Evol Comput, 2022, 26: 1157–1170

    Article  Google Scholar 

  17. Hao H, Zhou A, Zhang H. An approximated domination relationship based on binary classifiers for evolutionary multiobjective optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, 2021. 2427–2434

  18. Hao H, Zhou A. A relation surrogate model for expensive multiobjective continuous and combinatorial optimization. In: Proceedings of the 12th International Conference on Evolutionary Multi-Criterion Optimization, 2023. 205–217

  19. Yuan Y, Banzhaf W. Expensive multiobjective evolutionary optimization assisted by dominance prediction. IEEE Trans Evol Computat, 2022, 26: 159–173

    Article  Google Scholar 

  20. Tian Y, Hu J, He C, et al. A pairwise comparison based surrogate-assisted evolutionary algorithm for expensive multi-objective optimization. Swarm Evolary Comput, 2023, 80: 101323

    Article  Google Scholar 

  21. Zhang J, He L, Ishibuchi H. Dual-fuzzy-classifier-based evolutionary algorithm for expensive multiobjective optimization. IEEE Trans Evol Comput, 2023, 27: 1575–1589

    Article  Google Scholar 

  22. Zhou A, Zhang J, Sun J, et al. Fuzzy-classification assisted solution preselection in evolutionary optimization. In: Proceedings of the AAAI Conference on Artificial Intelligence, 2019. 2403–2410

  23. Li G, Wang Z, Gong M. Expensive optimization via surrogate-assisted and model-free evolutionary optimization. IEEE Trans Syst Man Cybern Syst, 2023, 53: 2758–2769

    Article  Google Scholar 

  24. Frazier P I. A tutorial on Bayesian optimization. 2018. arXiv:1807.02811

  25. Srinivas N, Krause A, Kakade S M, et al. Gaussian process optimization in the bandit setting: no regret and experimental design. 2009. ArXiv:0912.3995

  26. Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions. J Glob Opt, 1998, 13: 455–492

    Article  MathSciNet  Google Scholar 

  27. Mockus J. The application of Bayesian methods for seeking the extremum. In: Towards Global Optimization. Amsterdam: North-Holand, 1998

    Google Scholar 

  28. Hao H, Wang S, Li B, et al. A surrogate model assisted estimation of distribution algorithm with mutil-acquisition functions for expensive optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, 2022. 1–8

  29. Hoffman M, Brochu E, de Freitas N. Portfolio allocation for Bayesian optimization. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, Barcelona, 2011. 327–336

  30. Li F, Cai X, Gao L, et al. A surrogate-assisted multiswarm optimization algorithm for high-dimensional computationally expensive problems. IEEE Trans Cybern, 2021, 51: 1390–1402

    Article  PubMed  Google Scholar 

  31. Wei F F, Chen W N, Yang Q, et al. A classifier-assisted level-based learning swarm optimizer for expensive optimization. IEEE Trans Evol Comput, 2021, 25: 219–233

    Article  Google Scholar 

  32. Lian Y, Liou M S. Multiobjective optimization using coupled response surface model and evolutionary algorithm. AIAA J, 2005, 43: 1316–1325

    Article  ADS  Google Scholar 

  33. Zhou A, Zhang J, Sun J, et al. Fuzzy-classification assisted solution preselection in evolutionary optimization. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence, 2019. 2403–2410

  34. Zhang Q F, Li H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput, 2007, 11: 712–731

    Article  Google Scholar 

  35. Holland J H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Cambridge: MIT Press, 1992

    Book  Google Scholar 

  36. Storn R, Price K. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Glob Opt, 1997, 11: 341–359

    Article  MathSciNet  Google Scholar 

  37. Zhou A, Sun J, Zhang Q. An estimation of distribution algorithm with cheap and expensive local search methods. IEEE Trans Evol Comput, 2015, 19: 807–822

    Article  Google Scholar 

  38. Hollander M, Wolfe D A, Chicken E. Nonparametric Statistical Methods. Hoboken: John Wiley & Sons, 2013

    Google Scholar 

  39. 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, 2000, 42: 55–61

    Article  Google Scholar 

  40. Chen T, Guestrin C. XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016. 785–794

  41. Yao X, Liu Y, Lin G M. Evolutionary programming made faster. IEEE Trans Evol Comput, 1999, 3: 82–102

    Article  Google Scholar 

  42. Hansen N, Ostermeier A. Completely derandomized self-adaptation in evolution strategies. Evolary Comput, 2001, 9: 159–195

    Article  CAS  Google Scholar 

  43. Tian Y, Cheng R, Zhang X, et al. PlatEMO: a MATLAB platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag, 2017, 12: 73–87

    Article  Google Scholar 

  44. Friedman M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc, 1937, 32: 675–701

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 62306174), China Postdoctoral Science Foundation (Grant Nos. 2023M74225, 2023TQ0213), and National Supported Postdoctoral Research Program (Grant No. GZC20231588).

Author information

Authors and Affiliations

  1. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Hao Hao & Xiaoqun Zhang

  2. Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, Shanghai, 200062, China

    Aimin Zhou

  3. School of Computer Science and Technology, East China Normal University, Shanghai, 200062, China

    Aimin Zhou

Authors
  1. Hao Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoqun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aimin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aimin Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, H., Zhang, X. & Zhou, A. Enhancing SAEAs with unevaluated solutions: a case study of relation model for expensive optimization. Sci. China Inf. Sci. 67, 120103 (2024). https://doi.org/10.1007/s11432-023-3909-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-023-3909-x

Keywords

Search

Navigation