Skip to main content

Advertisement

SpringerLink
Log in

Chain-reaction solution update in MOEA/D and its effects on multi- and many-objective optimization

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

MOEA/D is one of the promising evolutionary algorithms for multi- and many-objective optimization. To improve the search performance of MOEA/D, this work focuses on the solution update method in the conventional MOEA/D and proposes its alternative, the chain-reaction solution update. The proposed method is designed to maintain and improve the variable (genetic) diversity in the population by avoiding duplication of solutions in the population. In addition, the proposed method determines the order of existing solutions to be updated depending on the location of each offspring in the objective space. Furthermore, when an existing solution in the population is replaced by a new offspring, the proposed method tries to reutilize the existing solution for other search directions by recursively performing the proposed chain-reaction update procedure. This work uses discrete knapsack and continuous WFG4 problems with 2–8 objectives. Experimental results using knapsack problems show the proposed chain-reaction update contributes to improving the search performance of MOEA/D by enhancing the diversity of solutions in the objective space. In addition, experimental results using WFG4 problems show that the search performance of MOEA/D can be further improved using the proposed method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Notes

  1. N is the population size, T is the neighborhood size, and \(T\le N\).

References

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

    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

    Article  MATH  Google Scholar 

  • Bowman VJ Jr (1976) On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. Lect Notes Econ Math Syst 130:76–86

    Article  Google Scholar 

  • Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, Part I: Solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Article  Google Scholar 

  • Gass S, Saaty T (1955) The computational algorithm for the parametric objective function. Nav Res Logist 2(1–2):39–45

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Hughes EJ (2005) Evolutionary many-objective optimisation: Many once or one many? Proc. of 2005 IEEE congress on evolutionary computation (CEC2005), pp 222–227

  • Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. Proc. of 2008 IEEE congress on evolutionary computation (CEC2008), pp 2424–2431

  • Jiang S, Cai Z, Zhang J, Ong YS (2011) Multiobjective optimization by decomposition with Pareto-adaptive weight vectors. In: Proc. of 2011 seventh international conference on natural computation (ICNC), pp 1260–1264

  • Ke L, Zhang Q, Battiti R (2013) MOEA/D-ACO: a multiobjective evolutionary algorithm using decomposition and antcolony. IEEE Trans Cybern 43(6):1845–1859

    Article  Google Scholar 

  • Li K, Zhang Q, Kwong S, Li M, Wang R (2014) Stable matching based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput 18(6):1–15

    Article  Google Scholar 

  • Li H, Landa-Silva D (2011) An adaptive evolutionary multi-objective approach based on simulated annealing. Evol Comput 19(4):561–595 (MIT press)

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Liu B, Fernández FV, Zhang Q, Pak M, Sipahi S, Gielen G (2010) An enhanced MOEA/D-DE and its application to multiobjective analog cell sizing. In: Proc. of 2010 IEEE congress on evolutionary computation (CEC’2010), pp 960–966

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

    Article  Google Scholar 

  • Martinez SZ, Coello CAC (2011) A multi-objective particle swarm optimizer based on decomposition. In: Proc. of 2011 genetic and evolutionary computation conference (GECCO’2011), pp 69–76

  • Martinez SZ, Derbel B, Liefooghe A, Brockhoff D, Aguirre H, Tanaka K (2015) Injecting CMA-ES into MOEA/D. In: Proc. of 2015 genetic and evolutionary computation conference (GECCO’2015), pp 783–790

  • Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, Norwell

    MATH  Google Scholar 

  • Moubayed NAl, Petrovski A, McCall J (2010) A novel smart multi-objective particle swarm optimisation using decomposition. In: Proc. of the 11th parallel problem solving from nature (PPSN XI), LNCS, Springer, pp 1–10

  • Murata T, Ishibuchi H, Gen M (2001) Specification of genetic search directions in cellular multi-objective genetic algorithm. In: Proc. of Int’l Conf. on evolutionary multi-criterion optimization 2001, LNCS, vol 1993, pp 82–95

  • Sato H (2014a) adaptive update range of solutions in MOEA/D for multi and many-objective optimization. In: Proc. of the tenth international conference on simulated evolution and learning (SEAL 2014), LNCS 8886, pp 274–286

  • Sato H (2014b) Inverted PBI in MOEA/D and its impact on the search performance on multi and many-objective optimization. In: Proc. of 2014 genetic and evolutionary computation conference (GECCO 2014), pp 645–652

  • Sato H, Aguirre H, Tanaka K (2004) Local dominance using polar coordinates to enhance multi-objective evolutionary algorithms. In: Proc. of 2004 IEEE congress on evolutionary computation (CEC2004), pp 188–195

  • Sato M, Aguirre H, Tanaka K (2006) Effects of \(\delta \)-similar elimination and controlled elitism in the NSGA-II multiobjective evolutionary algorithm. In: Proc. of 2006 IEEE congress on evolutionary computation (CEC2006), pp 1164–1171

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

    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: Proc. of 2009 IEEE congress on evolutionary computation (CEC’2009), pp 203–208

  • 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

    Article  Google Scholar 

  • Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, Zurich

  • Zitzler E, Kunzili S (2004) Indicator-based selection in multiobjective search. In: Proc. of the 8th Intl. Conf. on parallel problem solving from nature (PPSN-VIII), LNCS, vol 3242. Springer, pp 832–842

  • Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 26730129.

Author information

Authors and Affiliations

  1. Faculty of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan

    Hiroyuki Sato

Authors
  1. Hiroyuki Sato
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hiroyuki Sato.

Ethics declarations

Conflict of interest

The author declares no conflict of interest associated with this manuscript.

Additional information

Communicated by B. Xue and A. G. Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sato, H. Chain-reaction solution update in MOEA/D and its effects on multi- and many-objective optimization. Soft Comput 20, 3803–3820 (2016). https://doi.org/10.1007/s00500-016-2092-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2092-3

Keywords

Search

Navigation