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A decomposition based multiobjective evolutionary algorithm with self-adaptive mating restriction strategy

  • Xin Li
  • Hu Zhang
  • Shenmin SongEmail author
Original Article

Abstract

MOEA/D decomposes the multiobjective optimization problem into a number of subproblems. However, one subproblem’s requirement for exploitation and exploration varies with the evolutionary process. Furthermore, different subproblems’ requirements for exploitation and exploration are also different as the subproblems have been solved in distinct degree. This paper proposes a decomposition based multiobjective evolutionary algorithm with self-adaptive mating restriction strategy (MOEA/D-MRS). Considering the distinct solved degree of the subproblems, each subproblem has a separate mating restriction probability to control the contributions of exploitation and exploration. Besides, the mating restriction probability is updated by the survival length at each generation to adapt to the changing requirements. The experimental results validate that MOEA/D-MRS performs well on two test suites.

Keywords

Multiobjective optimization Evolutionary algorithm MOEA/D Self-adaptive mating restriction 

Notes

Funding

This study was funded by China Aerospace Science and Technology Innovation Foundation (Grant number: CAST.No.JZ20160008), National Natural Science Foundation of China (Grant number: 61333003) and National Natural Science Foundation of China (Grant number: 61703382).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

References

  1. 1.
    Bader J, Zitzler E (2011) Hype: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19:45–76CrossRefGoogle Scholar
  2. 2.
    Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181:1653–1669CrossRefzbMATHGoogle Scholar
  3. 3.
    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 19:508–523Google Scholar
  4. 4.
    Cai X, Yang Z, Fan Z, Zhang Q (2017) Decomposition-based-sorting and angle-based-selection for evolutionary multiobjective and many-objective optimization. IEEE Trans Cybern 47:2824–2837CrossRefGoogle Scholar
  5. 5.
    Chiang TC, Lai YP (2011) MOEA/D-AMS: Improving MOEA/D by an adaptive mating selection mechanism. In: Evolutionary computation. IEEE, New Orleans, pp 1473–1480Google Scholar
  6. 6.
    Dai C, Wang Y (2015) A new decomposition based evolutionary algorithm with uniform designs for many-objective optimization. Appl Soft Comput 30:238–248CrossRefGoogle Scholar
  7. 7.
    Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New YorkzbMATHGoogle Scholar
  8. 8.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  9. 9.
    Gong M, Wang Z, Zhu Z, Jiao L (2017) A similarity-based multiobjective evolutionary algorithm for deployment optimization of near space communication system. IEEE Trans Evol Comput 21:878–897CrossRefGoogle Scholar
  10. 10.
    Gu F, Cheung YM (2018) Self-organizing map-based weight design for decomposition-based many-objective evolutionary algorithm. IEEE Trans Evol Comput 22:211–225CrossRefGoogle Scholar
  11. 11.
    Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. Lect Notes Comput Sci 3410:280–295CrossRefzbMATHGoogle Scholar
  12. 12.
    Ishibuchi H, Yu S, Masuda H, Nojima Y (2017) Performance of decomposition-based many-objective algorithms strongly depends on Pareto front shapes. IEEE Trans Evol Comput 21:169–190CrossRefGoogle Scholar
  13. 13.
    Jiang S, Yang S (2016) An improved multiobjective optimization evolutionary algorithm based on decomposition for complex Pareto fronts. IEEE Trans Cybern 46:421–437CrossRefGoogle Scholar
  14. 14.
    Jiang S, Yang S, Wang Y, Liu X (2018) Scalarizing functions in decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evol Comput 22:296–313CrossRefGoogle Scholar
  15. 15.
    Ke L, Zhang Q, Battiti R (2013) MOEA/D-ACO: A multiobjective evolutionary algorithm using decomposition and ant colony. IEEE Trans Cybern 43:1845–1859CrossRefGoogle Scholar
  16. 16.
    Ke L, Zhang Q, Battiti R (2014) Hybridization of decomposition and local search for multiobjective optimization. IEEE Trans Cybern 44:1808–1820CrossRefGoogle Scholar
  17. 17.
    Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13:284–302CrossRefGoogle Scholar
  18. 18.
    Li H, Zhang Q, Chen Q, Zhang L, Jiao YC (2016) Multiobjective differential evolution algorithm based on decomposition for a type of multiobjective bilevel programming problems. Knowl-Based Syst 107:271–288CrossRefGoogle Scholar
  19. 19.
    Li H, Zhang Q, Deng J (2016) Biased multiobjective optimization and decomposition algorithm. IEEE Trans Cybern 47:52–66CrossRefGoogle Scholar
  20. 20.
    Li K, Fialho A, Kwong S, Zhang Q (2014) Adaptive operator selection with bandits for a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 18:114–130CrossRefGoogle Scholar
  21. 21.
    Li K, Kwong S, Zhang Q, Deb K (2015) Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans Cybern 45:2076–2088CrossRefGoogle Scholar
  22. 22.
    Li K, Zhang Q, Kwong S, Li M, Wang R (2014) Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput 18:909–923CrossRefGoogle Scholar
  23. 23.
    Li X, Zhang H, Song S (2018) A self-adaptive mating restriction strategy based on survival length for evolutionary multiobjective optimization. Swarm Evol Comput.  https://doi.org/10.1016/j.swevo.2018.02.009 Google Scholar
  24. 24.
    Li Y, Zhou A, Zhang G (2014) An MOEA/D with multiple differential evolution mutation operators. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2014), Beijing, China, 2014c. IEEE, pp 397–404Google Scholar
  25. 25.
    Lin Q et al (2017) A diversity-enhanced resource allocation strategy for decomposition-based multiobjective evolutionary algorithm. IEEE Trans Cybern 48:2388–2401Google Scholar
  26. 26.
    Lin Q et al (2016) Adaptive composite operator selection and parameter control for multiobjective evolutionary algorithm. Inf Sci 339:332–352CrossRefGoogle Scholar
  27. 27.
    Lin Q, Tang C, Du Z, Li J, Chen J, Ming Z (2017) A novel adaptive control strategy for decomposition-based multiobjective algorithm. Comput Oper Res 78:94–107MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Lin S, Lin F, Chen H, Zeng W (2016) A MOEA/D-based multi-objective optimization algorithm for remote medical. Neurocomputing 220:5–16CrossRefGoogle Scholar
  29. 29.
    Liu HL, Chen L, Zhang Q, Deb K (2018) Adaptively allocating search effort in challenging many-objective optimization problems. IEEE Trans Evol Comput 22:433–448CrossRefGoogle Scholar
  30. 30.
    Ma X et al (2014) MOEA/D with opposition-based learning for multiobjective optimization problem. Neurocomputing 146:48–64CrossRefGoogle Scholar
  31. 31.
    Ma X, Liu F, Qi Y, Li L, Jiao L, Liu M, Wu J (2014) MOEA/D with Baldwinian learning inspired by the regularity property of continuous multiobjective problem. Neurocomputing 145:336–352CrossRefGoogle Scholar
  32. 32.
    Ma X, Zhang Q, Tian G, Yang J, Zhu Z (2018) On Tchebycheff decomposition approaches for multiobjective evolutionary optimization. IEEE Trans Evol Comput 22:226–244CrossRefGoogle Scholar
  33. 33.
    Mashwani WK, Salhi A (2014) Multiobjective memetic algorithm based on decomposition. Appl Soft Comput 21:221–243CrossRefGoogle Scholar
  34. 34.
    Ming M, Wang R, Zha Y, Zhang T (2017) Pareto adaptive penalty-based boundary intersection method for multi-objective optimization. Inf Sci 414:158–174MathSciNetCrossRefGoogle Scholar
  35. 35.
    Qi Y, Bao L, Ma X, Miao Q, Li X (2016) Self-adaptive multi-objective evolutionary algorithm based on decomposition for large-scale problems: a case study on reservoir flood control operation. Inf Sci 367–368:529–549CrossRefGoogle Scholar
  36. 36.
    Qi Y, Hou Z, Li H, Huang J, Li X (2015) A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows. Comput Oper Res 62:61–77MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Qi Y, Ma X, Liu F, Jiao L, Sun J, Wu J (2014) MOEA/D with adaptive weight adjustment. Evol Comput 22:231–264CrossRefGoogle Scholar
  38. 38.
    Sato H (2014) Inverted PBI in MOEA/D and its impact on the search performance on multi and many-objective optimization. In: Genetic and evolutionery computation conference (GECCO 2014), Vancouver, BC, Canada ACM, pp 645–652Google Scholar
  39. 39.
    Tan YY, Jiao YC, Li H, Wang XK (2013) MOEA/D+ uniform design: a new version of MOEA/D for optimization problems with many objectives. Comput Oper Res 40:1648–1660MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Trivedi A, Srinivasan D, Pal K, Saha C, Reindl T (2017) Enhanced multiobjective evolutionary algorithm based on decomposition for solving the unit commitment problem. IEEE Trans Ind Inf 11:1346–1357CrossRefGoogle Scholar
  41. 41.
    Trivedi A, Srinivasan D, Sanyal K, Ghosh A (2017) A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans Evol Comput 21:440–462Google Scholar
  42. 42.
    Venske SM, Gonçalves RA, Benelli EM, Delgado MR (2016) ADEMO/D: an adaptive differential evolution for protein structure prediction problem. Expert Syst Appl 56:209–226CrossRefGoogle Scholar
  43. 43.
    Wang L, Zhang Q, Zhou A, Gong M, Jiao L (2016) Constrained subproblems in a decomposition-based multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20:475–480CrossRefGoogle Scholar
  44. 44.
    Wang R, Zhou Z, Ishibuchi H, Liao T, Zhang T (2018) Localized weighted sum method for many-objective optimization. IEEE Trans Evol Comput 22:3–18CrossRefGoogle Scholar
  45. 45.
    Wang Z, Zhang Q, Li H, Ishibuchi H, Jiao L (2017) On the use of two reference points in decomposition based multiobjective evolutionary algorithms. Swarm Evol Comput 34:89–102CrossRefGoogle Scholar
  46. 46.
    Wang Z, Zhang Q, Zhou A, Gong M, Jiao L (2017) Adaptive replacement strategies for MOEA/D. IEEE Trans Cybern 46:474–486CrossRefGoogle Scholar
  47. 47.
    Wu M, Li K, Kwong S, Zhang Q, Zhang J (2018) Learning to decompose: a paradigm for decomposition-based multiobjective optimization. IEEE Trans Evol Comput.  https://doi.org/10.1109/TEVC.2018.2865931 Google Scholar
  48. 48.
    Wu M, Li K, Kwong S, Zhou Y, Zhang Q (2017) Matching-based selection with incomplete lists for decomposition multiobjective optimization. IEEE Trans Evol Comput 21:554–568CrossRefGoogle Scholar
  49. 49.
    Xing H, Wang Z, Li T, Li H, Qu R (2017) An improved MOEA/D algorithm for multi-objective multicast routing with network coding. Appl Soft Comput 59:88–103CrossRefGoogle Scholar
  50. 50.
    Yang S, Jiang S, Jiang Y (2016) Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes. Soft Comput 21:1–15Google Scholar
  51. 51.
    Yuan Y, Xu H, Wang B, Zhang B, Yao X (2016) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20:180–198CrossRefGoogle Scholar
  52. 52.
    Zhang H, Zhang X, Gao XZ, Song S (2016) Self-organizing multiobjective optimization based on decomposition with neighborhood ensemble. Neurocomputing 173:1868–1884CrossRefGoogle Scholar
  53. 53.
    Zhang J, Tang Q, Li P, Deng D, Chen Y (2016) A modified MOEA/D approach to the solution of multi-objective optimal power flow problem. Appl Soft Comput 47:494–514CrossRefGoogle Scholar
  54. 54.
    Zhang Q (2015) Multiobjective evolutionary algorithm based on decomposition for 3-objective optimization problems with objectives in different scales. Soft Comput 19:157–166CrossRefGoogle Scholar
  55. 55.
    Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731CrossRefGoogle Scholar
  56. 56.
    Zhang Q, Liu W, Li H (2009) The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the IEEE congress on evolutionary computation (CEC 09), Trondheim, Norway IEEE, pp 203–208Google Scholar
  57. 57.
    Zhang Q, Zhou A, Jin Y (2008) RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans Evol Comput 12:41–63CrossRefGoogle Scholar
  58. 58.
    Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the CEC 2009 special session and competition. Special session on performance assessment of multi-objective optimization algorithms, technique report. University of Essex, Colchester Technological University, SingaporeGoogle Scholar
  59. 59.
    Zhang YH, Gong YJ, Gu TL, Yuan HQ, Wei Z, Kwong S, Zhang J (2017) DECAL: decomposition-based coevolutionary algorithm for many-objective optimization. IEEE Trans Cybern.  https://doi.org/10.1109/TCYB.2017.2762701 Google Scholar
  60. 60.
    Zhao SZ, Suganthan PN, Zhang Q (2012) Decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes. IEEE Trans Evol Comput 16:442–446CrossRefGoogle Scholar
  61. 61.
    Zheng J, Yu G, Zhu Q, Li X, Zou J (2016) On decomposition methods in interactive user-preference based optimization. Appl Soft Comput 52:952–973CrossRefGoogle Scholar
  62. 62.
    Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1:32–49CrossRefGoogle Scholar
  63. 63.
    Zhou A, Zhang Q (2016) Are all the subproblems equally important? Resource allocation in decomposition-based multiobjective evolutionary algorithms. IEEE Trans Evol Comput 20:52–64CrossRefGoogle Scholar
  64. 64.
    Zitzler E, Künzli S (2004) Indicator-based selection in multiobjective search. Lect Notes Comput Sci 3242:832–842CrossRefGoogle Scholar
  65. 65.
    Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the Strength Pareto evolutionary algorithm. Swiss Federal Institute of Technology (ETH) Zurich, ZurichGoogle Scholar
  66. 66.
    Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3:257–271CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Control Theory and Guidance TechnologyHarbin Institute of TechnologyHarbinChina
  2. 2.Beijing Electro-Mechanical Engineering InstituteBeijingChina

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