Skip to main content
Log in

Decomposition-based multi-objective evolutionary algorithm with mating neighborhood sizes and reproduction operators adaptation

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Multi-objective evolutionary algorithms based on decomposition (MOEA/D) has demonstrated excellent performance in dealing with multi-objective optimization problems. As two essential issues in MOEA/D, mating neighborhood sizes and reproduction operators determine the exploitation and exploration abilities of the algorithm. This paper proposes a new decomposition-based multi-objective evolutionary algorithm with mating neighborhood sizes and reproduction operators adaptation (MOEA/D-ATO), which adaptively assigns the suitable combination of mating neighborhood size and reproduction operator to each subproblem at different searching stages. Numerical results indicate that the proposed adaptation is effective. Moreover, comparison with other adaptive steady-state MOEA/D variants and state-of-art generational MOEA/D variants shows that the proposed MOEA/D-ATO algorithm performs significantly better in terms of solution quality and CPU time.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Brest J, Greiner S, Boskovic B et al (2006) Self adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657. doi:10.1109/TEVC.2006.872133

    Article  Google Scholar 

  • Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653–1669. doi:10.1016/j.ejor.2006.08.008

    Article  MATH  Google Scholar 

  • Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume based many-objective optimization. Evol Comput 19(1):45–76. doi:10.1162/EVCO_a_00009

    Article  Google Scholar 

  • 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. doi:10.1109/4235.996017

    Article  Google Scholar 

  • Goncalves RA, Almeida CP, Pozo A (2015) Upper confidence bound (UCB) algorithms for adaptive operator selection in MOEA/D. In: 8th International conference on evolutionary multi-criterion optimization (EMO2015), Guimarães, Portugal, pp 411–425. doi:10.1007/978-3-319-15934-8_28

  • Iorio AW, Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of advances in artificial intelligence (AI2004), pp 861–872

  • Ishibuchi H, Narukawa K, Tsukamoto N, Nojima Y (2008) An empirical study on similarity-based mating for evolutionary multiobjective combinatorial optimization. Eur J Oper Res 188(1):57–75. doi:10.1016/j.ejor.2007.04.007

    Article  MATH  Google Scholar 

  • Ishibuchi H, Akedo N, Nojima Y (2013) Relation between neighborhood size and MOEA/D performance on many-objective problems. In: 7th International conference on evolutionary multi-criterion optimization (EMO2013), Sheffield, UK, pp 459–474. doi:10.1007/978-3-642-37140-0_35

  • Jiang S, Yang S (2015) An improved multiobjective optimization evolutionary algorithm based on decomposition for complex Pareto fronts. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2403131

  • Li H, Zhang Q (2009) Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 12(2):284–302. doi:10.1109/TEVC.2008.925798

    Article  Google Scholar 

  • Li K, Fialho A, Kwong S, Zhang Q (2014a) Adaptive operator selection with bandits for multiobjective evolutionary algorithm based decomposition. IEEE Trans Evol Comput 18(1):114–130. doi:10.1109/TEVC.2013.2239648

  • Li K, Zhang Q, Kwong S, Li M, Wang R (2014b) Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput 18(6):909–923. doi:10.1109/TEVC.2013.2293776

  • Li Y, Zhou A, Zhang G (2014c) An MOEA/D with multiple differential evolution mutation operators. In: Proceedings of the IEEE congress on evolutionary computation (CEC2014), China, pp 397–404. doi:10.1109/CEC.2014.6900339

  • Li K, Kwong S, Zhang Q, Deb K (2015a) Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans Cybern 45(10):2076–2088. doi:10.1109/TCYB.2014.2365354

  • Li YL, Zhou YR, Zhan ZH et al (2015b) A primary theoretical study on decomposition based multiobjective evolutionary algorithms. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2501315

  • Liu HL, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455. doi:10.1109/TEVC.2013.2281533

    Article  Google Scholar 

  • Ma XL, Liu F, Qi YT et al (2014a) MOEA/D with opposition-based learning for multiobjective optimization problem. Neurocomputing 146:48–64. doi:10.1016/j.neucom.2014.04.068

  • Ma XL, Liu F, Qi YT et al (2014b) MOEA/D with Baldwinian learning inspired by the regularity property of continuous multiobjective problem. Neurocomputing 145:336–352. doi:10.1016/j.neucom.2014.05.025

  • Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417. doi:10.1109/TEVC.2008.927706

    Article  Google Scholar 

  • Qi YT, Ma XL, Liu F et al (2014) MOEAD with adaptive weight adjustment. Evol Comput 22(2):231–264. doi:10.1162/EVCO_a_00109

    Article  Google Scholar 

  • Robic T, Filipic B (2005) DEMO: differential evolution for multi-objective optimization. In: Third international conference on evolutionary multi-criterion optimization (EMO2005), Guanajuato, Mexico, pp 520–533. doi:10.1007/978-3-540-31880-4_36

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359. doi:10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  • Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: Proceedings of the IEEE congress on evolutionary computation (CEC2013), México, pp 71–78. doi:10.1109/CEC.2013.6557555

  • Wang YN, Wu LH, Yuan XF (2010) Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Comput 14(3):193–209. doi:10.1007/s00500-008-0394-9

    Article  Google Scholar 

  • Wang Y, Cai Z, Zhang Q (2012) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66. doi:10.1109/TEVC.2010.2087271

    Article  Google Scholar 

  • Wang Z, Zhang Q, Zhou A et al (2015a) Adaptive replacement strategies for MOEA/D. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2403849

  • Wang L, Zhang Q, Zhou A et al (2015b) Constrained subproblems in decomposition based multiobjective evolutionary algorithm. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2457616

  • Zitzler E, Thiele L, Laumanns M et al (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132. doi:10.1109/TEVC.2003.810758

    Article  Google Scholar 

  • Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731. doi:10.1109/TEVC.2007.892759

    Article  Google Scholar 

  • Zhang Q, Zhou A, Zhao SZ et al (2008) Multiobjective optimization test instances for the CEC2009 special session and competition. Technical report, Nanyang Technological University, Singapore

  • Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958. doi:10.1109/TEVC.2009.2014613

    Article  Google Scholar 

  • 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 (CEC2009), Trondheim, pp 203–208. doi:10.1109/CEC.2009.4982949

  • Zhang Q, Li H, Maringer D et al (2010) MOEA/D with NBI-style Tchebycheff approach for portfolio management. In: Proceedings of the IEEE congress on evolutionary computation (CEC2010), Barcelona, pp 1–8. doi:10.1109/CEC.2010.5586185

  • Zhao SZ, Suganthan PN, Zhang Q (2012) Decomposition based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes. IEEE Trans Evol Comput 16(3):442–446. doi:10.1109/TEVC.2011.2166159

    Article  Google Scholar 

  • Zhou A, Zhang Q (2015) Are all the subproblems equally important? Resource allocation in decomposition based multiobjective evolutionary algorithms. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2424251

Download references

Acknowledgments

The work was supported in part by the National Natural Science Foundation of China (No. 61401523), in part by the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (No. 2014KQNCX002), in part by the International Science and Technology Cooperation Program of China (No. 2015DFR11050), and in part by the External Cooperation Program of Guangdong Province of China (No. 2013B051000060).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shao Yong Zheng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, S.X., Zheng, L.M., Liu, L. et al. Decomposition-based multi-objective evolutionary algorithm with mating neighborhood sizes and reproduction operators adaptation. Soft Comput 21, 6381–6392 (2017). https://doi.org/10.1007/s00500-016-2196-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2196-9

Keywords

Navigation