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An improved reference point based multi-objective optimization by decomposition

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Abstract

Reference point based multi-objective evolutionary algorithm by decomposition (RMEAD) considers reference points as users’ preferences. RMEAD not only focuses on searching the region of interest to find a set of preferred solutions, but also economizes a significant amount of computing resources. However, the base weight vectors in RMEAD may not be well estimated when confronting to hard multi-objective optimization problems. This paper modifies RMEAD to improve its performance on two aspects: firstly, a novel and simple approach to finding the base weight vectors is developed, the correctness of which is proved mathematically; secondly, a new updating weight vectors method is proposed. Abundant experiments show that the improved RMEAD (IRMEAD) could obtain significantly better results than RMEAD on all the test cases in terms of convergence and diversity. Besides, compared with recent proposed preference-based approach MOEA/D-PRE, IRMEAD outperforms it on most of the test instances.

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References

  1. Zhou B, Qu Y, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swar Evol Comput 1(1):32–49

    Article  Google Scholar 

  2. Coello CAC (2006) Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intel Mag 1(1):28–36

    Article  Google Scholar 

  3. Zhu H, He Z, Jia Y (2015) A novel approach to multiple sequence alignment using multi-objective evolutionary algorithm based on decomposition. IEEE J Biomed Health. doi:10.1109/JBHI.2015.2403397

    Google Scholar 

  4. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: nSGA-II. IEEE Trans Evolut Comput 6(2):182–197

    Article  Google Scholar 

  5. Zitzler E, Laumans M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. Technical report no 103. Swiss Federal Institute of Technology, Zurich

    Google Scholar 

  6. Xia H, Zhuang J, Yu D (2014) Combining crowding estimation in objective and decision space with multiple selection and search strategies for multi-objective evolutionary optimization. IEEE Trans Cyber 44(3):378–393

    Article  Google Scholar 

  7. Wang X, Dong L, Yan J (2012) Maximum ambiguity based sample selection in fuzzy decision tree induction. IEEE Trans Knowl Data Eng 24(8):1491–1505

    Article  Google Scholar 

  8. Fonseca CM, Fleming PJ (1994) Genetic algorithms for multiobjective optimization. Formulation, discussion and generalization. Aust Electron Eng 27(2):416–416

    Google Scholar 

  9. Coello CAC (2000) Handling preferences in evolutionary multiobjective optimization: a survey. In: Proceeding of the IEEE CEC, pp 30–37

  10. Rachmawati L, Srinivasan D (2006) Preference incorporation in multi-objective evolutionary algorithms: a survey. In: Proceeding of the IEEE CEC, pp 954–960

  11. Branke J, Kaussler T, Schmeck H (2001) Guidance in evolutionary multi-objective optimization. Adv Eng Softw 32(6):499–507

    Article  MATH  Google Scholar 

  12. Cvetkovic D, Parmee IC (2002) Preferences and their application in evolutionary multiobjective optimization. IEEE Trans Evolut Comput 6(1):42–57

    Article  Google Scholar 

  13. Deb K, Sundar J (2006) Reference point based multi-objective optimization using evolutionary algorithms. In: GECCO, pp 635–642

  14. Miettinen KM (1999) Nonlinear multiobjective optimization. Kluwer Academic, Boston, pp 155–159

    MATH  Google Scholar 

  15. Thiele L, Miettinen K, Korhonen PJ, Molina J (2009) A preference-based evolutionary algorithm for multi-objective optimization. Evol Comput 17(3):411–436

    Article  Google Scholar 

  16. Molina J, Santana LV, Hernandez-Diaz AG, Coello CAC, Caballero R (2009) g-dominance: reference point based dominance for multiobjective metaheuristics. Eur J Oper Res 197(2):685–692

    Article  MATH  Google Scholar 

  17. Said LB, Bechikh S, Ghedira K (2010) The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Trans Evolut Comput 14(5):801–818

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Tan YY, Jiao YC, Li H, Wang XK (2012) A modification to MOEA/D-DE for multiobjective optimization problems with complicated Pareto sets. Inf Sci 213:14–38

    Article  MathSciNet  MATH  Google Scholar 

  20. Gong MG, Liu F, Zhang W, Jiao L, Zhang Q (2011) Interactive MOEA/D for multi-objective decision making. In: GECCO, pp 721–728

  21. Deb K, Sinha A, Korhonen PJ, Wallenius J (2010) An interactive evolutionary multiobjective optimization method based on progressively approximated value functions. IEEE Trans Evolut Comput 14(5):723–739

    Article  Google Scholar 

  22. Mohammadi A, Omidvar MN, Li X (2012) Reference point based multi-objective optimization through decomposition. In: Proceeding of the IEEE WCCI, pp 1–8

  23. Wang R, Zhang T, Guo B (2013) An enhanced MOEA/D using uniform directions and a pre-organization procedure. In: Proceeding of the IEEE CEC, pp 2390–2397

  24. Gu F, Liu HL, Tan KC (2012) A multiobjective evolutionary algorithm using dynamic weight design method. Int J Innov Comput Inf Control 8(5):3677–3688

    Google Scholar 

  25. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195

    Article  Google Scholar 

  26. Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceeding of the IEEE CEC, pp 825–830

  27. Zhang Q, Zhou A, Zhao S, Suganthan P, Liu W, Tiwari S (2009) Multiobjective optimization test instances for the CEC 2009 special session and competition. Special session on performance assessment of multi-objective optimization algorithms. Technical report, University of Essex, Colchester

  28. Mohammadi A, Omidvar MN, Li X (2013) A new performance metric for user-preference based multi-objective evolutionary algorithms. In: Proceeding of the IEEE CEC, pp 2825–2832

  29. Yu G, Zheng J, Shen R, Li M (2015) Decomposing the user-preference in multiobjective optimization. Soft Comput. doi:10.1007/s00500-015-1736-z

    Google Scholar 

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Acknowledgments

This work was supported in part by the china science and technology project of ministry of transport under Grant 2011318740240 and by the Chongqing graduate education reformation research project under the no. yjg133005.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Software Theory and Technology, College of Computer Science, Chongqing University, Chongqing, China

    Huazheng Zhu, Zhongshi He & Yuanyuan Jia

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  1. Huazheng Zhu
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  2. Zhongshi He
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  3. Yuanyuan Jia
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Correspondence to Zhongshi He.

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Zhu, H., He, Z. & Jia, Y. An improved reference point based multi-objective optimization by decomposition. Int. J. Mach. Learn. & Cyber. 7, 581–595 (2016). https://doi.org/10.1007/s13042-015-0443-5

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