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A new dominance relation based on convergence indicators and niching for many-objective optimization

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Abstract

Maintaining a good balance between convergence and diversity is crucial in many-objective optimization, while most existing dominance relations can not achieve a good balance between them. In this paper, we propose a new dominance relation to better balance the convergence and diversity. In the proposed dominance relation, a convergence indicator and a niching technique based adaptive parameter are adopted to ensure the convergence and diversity of the nondominated solution set. Based on the proposed dominance relation, a new many-objective evolutionary algorithm is proposed. In the algorithm, a new distribution estimation method is proposed to obtain better solutions for mating selection. Experimental results indicate that the proposed dominance relation outperforms existing dominance relations in balancing the convergence and diversity and the proposed algorithms has a competitive performance against several state-of-art many-objective evolutionary algorithms.

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References

  1. Bader J, Zitzler E (2011) Hype: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76

    Article  Google Scholar 

  2. Beume N, Naujoks B, Emmerich M (2007) Sms-emoa: Multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653–1669

    Article  Google Scholar 

  3. Borhani M (2020) A multicriteria optimization for flight route networks in large-scale airlines using intelligent spatial information. International Journal of Interactive Multimedia & Artificial Intelligence 6(1):123–131

  4. Brockhoff D, Friedrich T, Hebbinghaus N, Klein C, Neumann F, Zitzler E (2009) On the effects of adding objectives to plateau functions. IEEE Trans Evol Comput 13(3):591–603

    Article  Google Scholar 

  5. Cai X, Li Y, Fan Z, Zhang Q (2014) An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans Evol Comput 19(4):508–523

    Google Scholar 

  6. Chand S, Wagner M (2015) Evolutionary many-objective optimization: a quick-start guide. Surveys in Operations Research and Management Science 20(2):35–42

    Article  MathSciNet  Google Scholar 

  7. Cheng R, Rodemann T, Fischer M, Olhofer M, Jin Y (2017) Evolutionary many-objective optimization of hybrid electric vehicle control: from general optimization to preference articulation. IEEE Transactions on Emerging Topics in Computational Intelligence 1(2):97–111

    Article  Google Scholar 

  8. Corne DW, Jerram NR, Knowles JD, Oates MJ (2001) Pesa-ii: Region-based selection in evolutionary multiobjective optimization. In: Proceedings of the 3rd annual conference on genetic and evolutionary computation, pp 283–290

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

    Article  MathSciNet  Google Scholar 

  10. Deb K (2001) Multi-objective optimization using evolutionary algorithms, vol 16. John Wiley & Sons

  11. Deb K, Goyal M (1996) A combined genetic adaptive search (geneas) for engineering design. Comput Sci Inform 26:30–45

    Google Scholar 

  12. Deb K, Jain H (2013) 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

    Article  Google Scholar 

  13. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  14. Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Evolutionary multiobjective optimization, Springer, pp 105–145

  15. Elkasem AH, Kamel S, Rashad A, Melguizo FJ (2019) Optimal performance of doubly fed induction generator wind farm using multi-objective genetic algorithm. IJIMAI 5(5):48–53

    Article  Google Scholar 

  16. Farina M, Amato P (2004) A fuzzy definition of “optimality” for many-criteria optimization problems. IEEE Transactions on Systems Man, and Cybernetics-Part A:, Systems and Humans 34(3):315–326

    Article  Google Scholar 

  17. Fleming PJ, Purshouse RC, Lygoe RJ (2005) Many-objective optimization: An engineering design perspective. In: International conference on evolutionary multi-criterion optimization, Springer, pp 14–32

  18. Hadka D, Reed P (2013) Borg: an auto-adaptive many-objective evolutionary computing framework. Evol Comput 21(2):231–259

    Article  Google Scholar 

  19. He Z, Yen GG, Zhang J (2013) Fuzzy-based pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18(2):269–285

    Article  Google Scholar 

  20. Hernández Gómez R, Coello Coello CA (2015) Improved metaheuristic based on the r2 indicator for many-objective optimization. In: Proceedings of the 2015 annual conference on genetic and evolutionary computation, pp 679–686

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

    Article  Google Scholar 

  22. Ikeda K, Kita H, Kobayashi S (2001) 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. IEEE, pp 957–962

  23. Ishibuchi H, Setoguchi Y, Masuda H, Nojima Y (2016) Performance of decomposition-based many-objective algorithms strongly depends on pareto front shapes. IEEE Trans Evol Comput 21(2):169–190

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Li B, Li J, Tang K, Yao X (2015) Many-objective evolutionary algorithms: a survey. ACM Computing Surveys (CSUR) 48(1):1–35

    Article  Google Scholar 

  26. Li K, Zhang Q, Kwong S, Li M, Wang R (2013) Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput 18(6):909–923

    Google Scholar 

  27. Li K, Deb K, Zhang Q, Kwong S (2014) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694–716

    Article  Google Scholar 

  28. Li K, Deb K, Zhang Q, Kwong S (2015) Combining dominance and decomposition in evolutionary many-objective optimization. IEEE Trans Evol Comput 19(5):694–716

    Article  Google Scholar 

  29. Li M, Yang S, Liu X (2013) Shift-based density estimation for pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348–365

    Article  Google Scholar 

  30. Li M, Yang S, Liu X (2015) Bi-goal evolution for many-objective optimization problems. Artif Intell 228:45–65

    Article  MathSciNet  Google Scholar 

  31. Miettinen K (2012) Nonlinear multiobjective optimization, vol 12. Springer Science & Business Media

  32. Purshouse RC, Fleming PJ (2003) Evolutionary many-objective optimisation: an exploratory analysis. In: The 2003 congress on evolutionary computation, 2003. CEC’03, vol 3. IEEE, pp 2066–2073

  33. Purshouse RC, Fleming PJ (2007) On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput 11(6):770–784

    Article  Google Scholar 

  34. Sato H, Aguirre HE, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of moeas. In: International conference on evolutionary multi-criterion optimization, Springer, pp 5–20

  35. Sato H, Aguirre HE, Tanaka K (2010) Self-controlling dominance area of solutions in evolutionary many-objective optimization. In: Asia-Pacific conference on simulated evolution and learning, Springer, pp 455–465

  36. Sun Y, Yen GG, Yi Z (2018) Igd indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput 23(2):173–187

    Article  Google Scholar 

  37. Tian Y, Cheng R, Zhang X, Cheng F, Jin Y (2017) An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput 22(4):609–622

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Wang J, Cen B, Gao S, Zhang Z, Zhou Y (2018) Cooperative evolutionary framework with focused search for many-objective optimization. IEEE Transactions on Emerging Topics in Computational Intelligence

  41. Xiang Y, Zhou Y, Li M, Chen Z (2016) A vector angle-based evolutionary algorithm for unconstrained many-objective optimization. IEEE Trans Evol Comput 21(1):131–152

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  44. Yuan Y, Xu H, Wang B, Zhang B, Yao X (2015) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20(2):180– 198

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  47. Zhou A, Jin Y, Zhang Q, Sendhoff B, Tsang E (2006) Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 IEEE international conference on evolutionary computation, IEEE, pp 892–899

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

    Article  Google Scholar 

  49. Zitzler E, Künzli S (2004) Indicator-based selection in multiobjective search. In: International conference on parallel problem solving from nature, Springer, pp 832–842

  50. Zitzler E, Laumanns M, Thiele L (2001) Spea2: Improving the strength pareto evolutionary algorithm. TIK-report 103

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

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Nature Science Foundation of China (No. 61763010), in part by the Key Technologies R & D Program of Hebei (No. 19970311D), in part by the Educational Commission of Hebei Province of China (No. ZD2018083, ZD2018043, ZD2019134) and by the Startup Foundation for PhD of Hebei GEO University (No. BQ201322).

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Authors and Affiliations

  1. School of Information Engineering, Hebei GEO University, Shijiazhuang, 050031, China

    Feng Yang, Liang Xu, Xiaokai Chu & Shenwen Wang

  2. Laboratory of Artificial Intelligence and Machine Learning, Hebei GEO University, Shijiazhuang, 050031, China

    Feng Yang, Liang Xu, Xiaokai Chu & Shenwen Wang

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  1. Feng Yang
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  2. Liang Xu
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Correspondence to Shenwen Wang.

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Yang, F., Xu, L., Chu, X. et al. A new dominance relation based on convergence indicators and niching for many-objective optimization. Appl Intell 51, 5525–5542 (2021). https://doi.org/10.1007/s10489-020-01976-x

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