[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

A model-based many-objective evolutionary algorithm with multiple reference vectors

  • Regular Paper
  • Published:
Progress in Artificial Intelligence Aims and scope Submit manuscript

Abstract

In order to estimate the Pareto front, most of the existing evolutionary algorithms apply the discovery of non-dominated solutions in search space, and most algorithms need appropriate diversity. Sometimes the Pareto front is so much thin and several dominated solutions exist beside the Pareto front. This paper proposes a new inverse model-based evolutionary algorithm with multiple reference vectors in order to exact place of possible Pareto front and then a collection of the exact places of vectors are produced and through this collection, the solutions which are beside the Pareto front mapping to the hyperplane and clustered in order to produce more effective reference vectors point to Pareto front which ultimately leads to the proper guide of diversity and convergence of population. The suggested method has been experimented on the benchmark test suite for CEC’2018 Competition (MaF1–15) and Walking Fish Group (WFG)) and expresses that the suggested strategy is encouraging.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Cheng, R.: Nature inspired optimization of large problems. Ph.D. thesis, University of Surrey (2016)

  2. Cheng, R., He, C., Jin, Y., Yao, X.: Model-based evolutionary algorithms: a short survey. Complex Intell. Syst. 4(4), 283–292 (2018)

    Article  Google Scholar 

  3. Hua, Y., Jin, Y., Hao, K., Cao, Y.: Generating multiple reference vectors for a class of many-objective optimization problems with degenerate pareto fronts. Complex Intell. Syst. 6, 272–285 (2020)

    Google Scholar 

  4. Krejca, M.: Theoretical analyses of evolutionary algorithms with a focus on estimation of distribution algorithms. In: Proceedings of the 10th Ph.D. Retreat of the HPI Research School on Service-oriented Systems Engineering, vol. 111, p. 129 (2018)

  5. Gao, S., de Silva, C.W.: Estimation distribution algorithms on constrained optimization problems. Appl. Math. Comput. 339, 323–345 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Cheng, R., Jin, Y., Narukawa, K., Sendhoff, B.: A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling. IEEE Trans. Evol. Comput. 19(6), 838–856 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Liu, B., Zhang, Q., Gielen, G.G.: A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Trans. Evol. Comput. 18(2), 180–192 (2013)

    Article  Google Scholar 

  9. Lin, Q., Liu, S., Wong, K.-C., Gong, M., Coello, C.A.C., Chen, J., Zhang, J.: A clustering-based evolutionary algorithm for many-objective optimization problems. IEEE Trans. Evol. Comput. 23(3), 391–405 (2018)

    Article  Google Scholar 

  10. Pan, L., He, C., Tian, Y., Su, Y., Zhang, X.: A region division based diversity maintaining approach for many-objective optimization. Integr. Comput.-Aid. Eng. 24(3), 279–296 (2017)

    Article  Google Scholar 

  11. Hua, Y., Jin, Y., Hao, K.: A clustering-based adaptive evolutionary algorithm for multiobjective optimization with irregular pareto fronts. IEEE Trans. Cybern. 49(7), 2758–2770 (2018)

    Article  Google Scholar 

  12. Cheng, R., Jin, Y., Olhofer, M., Sendhoff, B.: A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(5), 773–791 (2016)

    Article  Google Scholar 

  13. Liu, Q., Jin, Y., Heiderich, M., Rodemann, T., Adaptation of reference vectors for evolutionary many-objective optimization of problems with irregular pareto fronts. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1726–1733. IEEE (2019)

  14. Ge, H., Zhao, M., Sun, L., Wang, Z., Tan, G., Zhang, Q., Chen, C.P.: A many-objective evolutionary algorithm with two interacting processes: cascade clustering and reference point incremental learning. IEEE Trans. Evol. Comput. 23(4), 572–586 (2018)

    Article  Google Scholar 

  15. Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans. Evol. Comput. 12(1), 41–63 (2008)

  16. 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 (2018)

    Article  Google Scholar 

  17. Yang, Z., Qiu, H., Gao, L., Cai, X., Jiang, C., Chen, L.: Surrogate-assisted classification-collaboration differential evolution for expensive constrained optimization problems. Inf. Sci. 508, 50–63 (2020)

    Article  MathSciNet  Google Scholar 

  18. Tian, Y., Wang, H., Zhang, X., Jin, Y.: Effectiveness and efficiency of non-dominated sorting for evolutionary multi-and many-objective optimization. Complex Intell. Syst. 3(4), 247–263 (2017)

    Article  Google Scholar 

  19. Rasmussen, C.E.: Gaussian processes in machine learning. In: Summer School on Machine Learning, pp. 63–71. Springer (2003)

  20. Liu, H.-L., Gu, F., Zhang, Q.: Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans. Evol. Comput. 18(3), 450–455 (2013)

    Article  Google Scholar 

  21. Das, I., Dennis, J.E.: Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8(3), 631–657 (1998)

    Article  MathSciNet  Google Scholar 

  22. Cheng, R., Li, M., Tian, Y., Xiang, X., Zhang, X., Yang, S., Jin, Y., Yao, X.: Benchmark functions for the CEC’2018 competition on many-objective optimization. Technical report (2018)

  23. Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evol. Comput. 10(5), 477–506 (2006)

    Article  Google Scholar 

  24. Li, M., Yao, X.: Quality evaluation of solution sets in multiobjective optimisation: a survey. ACM Comput. Surv. (CSUR) 52(2), 26 (2019)

    Google Scholar 

  25. Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary computation and convergence to a pareto front. In: Late Breaking Papers at the Genetic Programming 1998 Conference, pp. 221–228 (1998)

  26. Wang, H., Jin, Y., Yao, X.: Diversity assessment in many-objective optimization. IEEE Trans. Cybern. 47(6), 1510–1522 (2016)

    Article  Google Scholar 

  27. Schott, J.R.: Fault tolerant design using single and multicriteria genetic algorithm optimization. Technical Report, Air Force Institute of Technology, Wright-Patterson AFB, OH (1995)

  28. Goli, A., Zare, H.K., Tavakkoli-Moghaddam, R., Sadegheih, A.: Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment. Comput. Intell. 36, 4–34 (2020)

    Article  MathSciNet  Google Scholar 

  29. Zhou, A., Zhang, Q., Jin, Y., Tsang, E., Okabe, T.: A model-based evolutionary algorithm for bi-objective optimization. In: IEEE Congress on Evolutionary Computation, pp. 2568–2575. IEEE (2005)

  30. Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Hoboken (2001)

    MATH  Google Scholar 

  31. Bosman, P.A., Thierens, D.: The Naive MIDEA: a baseline multi–objective EA. In: International Conference on Evolutionary Multi-Criterion Optimization, pp. 428–442. Springer (2005)

  32. Li, K., Omidvar, M.N., Deb, K., Yao, X.: Variable interaction in multi-objective optimization problems. In: International Conference on Parallel Problem Solving from Nature, pp. 399–409. Springer (2016)

Download references

Acknowledgements

Financial support from research office of Department of Computer, South Tehran Branch, Islamic Azad University, is acknowledged.

Author information

Authors and Affiliations

  1. Department of Computer, South Tehran Branch, Islamic Azad University, Tehran, Iran

    Pezhman Gholamnezhad, Ali Broumandnia & Vahid Seydi

Authors
  1. Pezhman Gholamnezhad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Broumandnia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vahid Seydi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Broumandnia.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Fully documented templates are available in the elsarticle package on CTAN.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gholamnezhad, P., Broumandnia, A. & Seydi, V. A model-based many-objective evolutionary algorithm with multiple reference vectors. Prog Artif Intell 11, 251–268 (2022). https://doi.org/10.1007/s13748-022-00283-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13748-022-00283-5

Keywords

Search

Navigation