A decomposition-based evolutionary algorithm with adaptive weight adjustment for many-objective problems

Abstract

For many-objective optimization problems (MaOPs), how to get a set of solutions with good convergence and diversity is a difficult and challenging work. In this paper, a new decomposition-based evolutionary algorithm with adaptive weight adjustment is designed to obtain this goal. The proposed algorithm adopts the uniform design method to set the weight vectors which are uniformly distributed over the design space, and an adaptive weight adjustment is used to solve some MaOPs with complex Pareto optimal front (PF) (i.e., PF with a sharp peak of low tail or discontinuous PF). A selection strategy is used to help solutions to converge to the Pareto optimal solutions. Comparing with some efficient state-of-the-art algorithms, e.g., NSGAII-CE, MOEA/D and HypE, on some benchmark functions, the proposed algorithm is able to find more accurate Pareto front with better diversity.

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References

  1. Al Mpubayed N, Petrovski A, McCall J (2014) D2MOPSO: MOPSO based on decomposition and dominance with archiving using crowding distance in objective and solution spaces. Evol Comput 22(1):47–78

    Google Scholar 

  2. Asafuddoula M, Singh HK, Ray T (2017) An enhanced decomposition-based evolutionary algorithm with adaptive reference vectors. IEEE Trans Cybern 48(8):2321–2334

    Google Scholar 

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

    Google Scholar 

  4. Cai L, Qu S, Cheng G (2018a) Two-archive method for aggregation-based many-objective optimization. Inf Sci 422:305–317

    Google Scholar 

  5. Cai L, Qu S, Cheng G (2018b) Two-archive method for aggregation-based many-objective optimization. Inf Sci 422:305–317

    Google Scholar 

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

    Google Scholar 

  7. Dai C, Wang Y (2015) A new uniform evolutionary algorithm based on decomposition and CDAS for many-objective optimization. Knowl Based Syst 85:131–142

    Google Scholar 

  8. Deb K, Jain H (2014) 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

    Google Scholar 

  9. Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Congress on evolutionary computation (CEC 2002), pp 825–830

  10. Elarbi M, Bechikh S, Gupta A, Said LB, Ong Y-S (2018) A new decomposition-based NSGA-II for many-objective optimization. IEEE Trans Syst Man Cybern Syst 48(7):1191–1210

    Google Scholar 

  11. Fang KT, Wang Y (1994) Number-theoretic method in statistics. Chapman and Hall, London

    MATH  Google Scholar 

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

    Google Scholar 

  13. Friedrich T, Horoba C, Neumann F (2009) Multiplicative approximations and the hypervolume indicator. In: Proceedings of the 2009 genetic and evolutionary computation conference, pp 571–578

  14. 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

    MATH  Google Scholar 

  15. Hughes EJ (2005) Evolutionary many-objective optimisation: many once or one many. In: IEEE congress on evolutionary computation (CEC’05), Edinburgh, UK, vol 1, pp 222–227

  16. Jiang S, Yang S (2016) An improved multiobjective optimization evolutionary algorithm based on decomposition for complex Pareto fronts. IEEE Transa Cybern 46(2):421–437

    Google Scholar 

  17. Li H, Zhang QF (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13(2):284–302

    Google Scholar 

  18. Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694–716

    Google Scholar 

  19. Ma Qi Y, Liu X, Jiao F, Sun L, Wu J (2014) MOEA/D with adaptive weight adjustment. Evol Comput 22(2):231–264

    Google Scholar 

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

    Google Scholar 

  21. Robert S, Torrie J, Dickey D (1997) Principles and procedures of statistics: a biometrical approach. McGraw-Hill, New York

    Google Scholar 

  22. Sato H, Aguirre HE, Tanaka K (2007) Controlling dominance area of solutions and its impact on the performance of mOEAs. In: Obayashi S, Poloni C, Hiroyasu T, Murata T (eds) EMO 2007. LNCS, vol 4403. Springer, Heidelberg, pp 5–20

    Google Scholar 

  23. Saxena DK, Duro JA, Tiwari A, Deb K, Zhang Q (2013) Objective reduction in many-objective optimization: linear and nonlinear algorithms. IEEE Trans Evol Comput 17(1):77–99

    Google Scholar 

  24. Tan KC, Yang J, Goh CK (2006) A distributed cooperative coevolutionary algorithm for multiobjective optimization. IEEE Trans Evol Comput 10(5):527–549

    Google Scholar 

  25. Tian Y, Cheng R, Zhang X, Jin Y (2017) PlateEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput Intell Mag 12(4):73–87

    Google Scholar 

  26. Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Air Force Institute of Technology, Wright Patterson AFB

    Google Scholar 

  27. Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation-, and indicator-based methods in many-objective optimization. Lecture notes in computer science 4403: evolutionary multi-criterion optimization—EMO 2007. Springer, Berlin, pp 742–756

    Google Scholar 

  28. Wang L, Zhang Q, Zhou A (2016) Constrained subproblems in a decomposition-based multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20(3):475–480

    Google Scholar 

  29. Yuan Y, Hua X, Wang B, Zhang B, Yao X (2016) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20(2):180–198

    Google Scholar 

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

    Google Scholar 

  31. Zhang H, Zhang X, Gao X et al (2016) Self-organizing multiobjective optimization based on decomposition with neighborhood ensemble. Neurocomputing 173:1868–1884

    Google Scholar 

  32. Zhao SZ, Suganthan PN, Zhang QF (2012) Decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes. IEEE Trans Evol Comput 16(3):442–446

    Google Scholar 

  33. Zhou A, Zhang Q (2016) Are all the subproblems equally important? Resource allocation in decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evol Comput 20(1):52–64

    Google Scholar 

  34. Zhu H, He Z, Jia Y (2016) A novel approach to multiple sequence alignment using multiobjective evolutionary algorithm based on decomposition. IEEE J Biomed Health Inform 20(2):717–727

    Google Scholar 

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

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundations of China (Nos. 61502290, 61401263, 61672334 and 61673251), China Postdoctoral Science Foundation (No. 2015M582606), Fundamental Research Funds for the Central Universities (No. GK201603094 and No. GK201603002) and Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2016JQ6045 and 2015JQ6228).

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Dai, C., Lei, X. & He, X. A decomposition-based evolutionary algorithm with adaptive weight adjustment for many-objective problems. Soft Comput 24, 10597–10609 (2020). https://doi.org/10.1007/s00500-019-04565-4

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Keywords

  • Evolutionary algorithm
  • Many-objective optimization
  • Adaptive weight adjustment