Skip to main content
SpringerLink
Log in

An Enhanced Subregion Dominance Relation for Evolutionary Many-Objective Optimization

  • Conference paper
  • First Online:
International Conference on Neural Computing for Advanced Applications (NCAA 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1869))

Included in the following conference series:

  • 352 Accesses

Abstract

Pareto dominance-based approach is a classical method for solving multi-objective optimization problems (MOPs). However, as the number of objectives increases, the selection pressure drops sharply. Solutions with good convergence and diversity are hardly obtained. To tackle these issues, this paper proposes an enhanced subregion dominance (called ESD-dominance) relation for evolutionary many-objective optimization. In ESD-dominance, individuals in the population are associated with a set of uniform reference vectors according to the Euclidean distance. Individuals associated with the same reference vector constitute a subregion. To enhance the convergence, each subregion is re-layered based on a new convergence metric. To maintain the diversity, the density in different subregions is considered. In order to validate the performance of ESD-dominance, a modified NSGA-II (called ESD-NSGA-II) algorithm is constructed based on the proposed dominance relation. In the experiments, a set of WFG benchmark problems with 3, 5, 8, and 15 objectives are tested. Computational results show the competitiveness of ESD-NSGA-II when compared with eight other state-of-the-art algorithms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Deb, K.: Multi-objective optimisation using evolutionary algorithms: an introduction. In: Wang, L., Ng, A., Deb, K. (eds.) Multi-objective Evolutionary Optimisation for Product Design and Manufacturing, pp. 3–34. Springer, London (2011). https://doi.org/10.1007/978-0-85729-652-8_1

    Chapter  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. Coello, C.A.C., Pulido, G.T., Lechuga, M.S.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)

    Article  Google Scholar 

  4. 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 (2013)

    Article  Google Scholar 

  5. 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 

  6. Sato, H., Aguirre, H.E., Tanaka, K.: Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70928-2_5

    Chapter  Google Scholar 

  7. Zhu, C., Xu, L., Goodman, E.D.: Generalization of pareto-optimality for many-objective evolutionary optimization. IEEE Trans. Evol. Comput. 20(2), 299–315 (2015)

    Article  Google Scholar 

  8. Ikeda, K., Kita, H., Kobayashi, S.: Failure of pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No. 01TH8546), vol. 2, pp. 957–962. IEEE (2001)

    Google Scholar 

  9. Yang, S., Li, M., Liu, X., Zheng, J.: A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 17(5), 721–736 (2013)

    Article  Google Scholar 

  10. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263–282 (2002)

    Article  Google Scholar 

  11. Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello, C.A.C., Molina, J.: Pareto-adaptive \(\epsilon \)-dominance. Evol. Comput. 15(4), 493–517 (2007)

    Article  Google Scholar 

  12. Batista, L.S., Campelo, F., Guimarães, F.G., Ramírez, J.A.: Pareto cone \(\varepsilon \)-dominance: improving convergence and diversity in multiobjective evolutionary algorithms. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 76–90. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19893-9_6

    Chapter  Google Scholar 

  13. Farina, M., Amato, P.: A fuzzy definition of “optimality” for many-criteria optimization problems. IEEE Trans. Syst. Man Cybern.-Part A Syst. Hum. 34(3), 315–326 (2004)

    Google Scholar 

  14. Zou, X., Chen, Y., Liu, M., Kang, L.: A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 38(5), 1402–1412 (2008)

    Google Scholar 

  15. Elarbi, M., Bechikh, S., Gupta, A., Said, L.B., Ong, Y.S.: A new decomposition-based NSGA-II for many-objective optimization. IEEE Trans. Syst. Man Cybern. Syst. 48(7), 1191–1210 (2017)

    Article  Google Scholar 

  16. Gu, Q., Chen, H., Chen, L., Li, X., Xiong, N.N.: A many-objective evolutionary algorithm with reference points-based strengthened dominance relation. Inf. Sci. 554, 236–255 (2021)

    Article  MathSciNet  Google Scholar 

  17. 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  MATH  Google Scholar 

  18. 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  MATH  Google Scholar 

  19. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  20. 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 

  21. Yuan, Y., Xu, H., Wang, B., Yao, X.: A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(1), 16–37 (2015)

    Article  Google Scholar 

  22. Wang, H., Jiao, L., Yao, X.: Two_arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19(4), 524–541 (2014)

    Article  Google Scholar 

  23. Tian, Y., Cheng, R., Zhang, X., Su, Y., Jin, Y.: A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans. Evol. Comput. 23(2), 331–345 (2018)

    Article  Google Scholar 

  24. Zhang, X., Tian, Y., Jin, Y.: A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19(6), 761–776 (2014)

    Article  Google Scholar 

  25. Deb, K., Agrawal, R.B., et al.: Simulated binary crossover for continuous search space. Complex Syst. 9(2), 115–148 (1995)

    MathSciNet  MATH  Google Scholar 

  26. Tian, Y., Cheng, R., Zhang, X., Jin, Y.: Platemo: a matlab platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput. Intell. Mag. 12(4), 73–87 (2017)

    Article  Google Scholar 

  27. Ishibuchi, H., Masuda, H., Tanigaki, Y., Nojima, Y.: Difficulties in specifying reference points to calculate the inverted generational distance for many-objective optimization problems. In: 2014 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM), pp. 170–177. IEEE (2014)

    Google Scholar 

  28. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

  29. Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30217-9_84

    Chapter  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 62166027), and Jiangxi Provincial Natural Science Foundation (No. 20212ACB212004).

Author information

Authors and Affiliations

  1. School of Information Engineering, Nanchang Institute of Technology, Nanchang, 330099, China

    Shuai Wang, Hui Wang, Zichen Wei & Futao Liao

  2. School of Computer Science, Wuhan University, Wuhan, 430072, China

    Feng Wang

Authors
  1. Shuai Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zichen Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Futao Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Feng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hui Wang .

Editor information

Editors and Affiliations

  1. Harbin Institute of Technology, Shenzhen, China

    Haijun Zhang

  2. Chaohu University, Hefei, China

    Yinggen Ke

  3. Chongqing University, Chongqing, China

    Zhou Wu

  4. South China Normal University, Guangzhou, China

    Tianyong Hao

  5. Hefei University of Technology, Hefei, China

    Zhao Zhang

  6. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  7. Chaohu University, Hefei, China

    Yuanyuan Mu

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, S., Wang, H., Wei, Z., Liao, F., Wang, F. (2023). An Enhanced Subregion Dominance Relation for Evolutionary Many-Objective Optimization. In: Zhang, H., et al. International Conference on Neural Computing for Advanced Applications. NCAA 2023. Communications in Computer and Information Science, vol 1869. Springer, Singapore. https://doi.org/10.1007/978-981-99-5844-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-5844-3_16

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5843-6

  • Online ISBN: 978-981-99-5844-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation