Skip to main content

Advertisement

SpringerLink
Log in

A novel solver for multi-objective optimization: dynamic non-dominated sorting genetic algorithm (DNSGA)

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

Abstract

Non-dominated sorting is a critical component of all multi-objective evolutionary algorithms (MOEAs). A large percentage of computational cost of MOEAs is spent on non-dominated sorting. So, the complexity of non-dominated sorting method in a large extent decides the efficiency of the MOEA. In this paper, we present a novel non-dominated sorting method called the dynamic non-dominated sorting (DNS). It is based on the sorting of real number sequence instead of dominance comparisons. The computational complexity of DNS is \(O(mN\log N)\) (m is the number of objectives, N is the population size), which equals to the best record so far. In the numerical experiments, we verify the outperformance of DNS comparing with other non-dominated sorting methods. Based on DNS, we introduce a novel multi-objective genetic algorithm called the dynamic non-dominated sorting genetic algorithm (DNSGA). Numerical experiments on DNSGA are also given. The results show that DNSGA outperforms some other MOEAs on both general-scale and large-scale multi-objective problems.

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

Similar content being viewed by others

References

  • Cheng R, Jin Y, Olhofer M et al (2016) Test problems for large-scale multiobjective and many-objective optimization. IEEE Trans Cybern 47(12):4108–4121

    Article  Google Scholar 

  • Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7(3):205–230

    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

    Article  Google Scholar 

  • Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Advanced Information and knowledge processing. Springer, London

    Google Scholar 

  • Deb K, Sindhya K, Okabe T (2007) Self-adaptive simulated binary crossover for real-parameter optimization. In: Proceedings of the 9th annual conference on genetic and evolutionary computation, pp 1187–1194

  • Deep K, Thakur M (2007) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230

    MathSciNet  MATH  Google Scholar 

  • Du Y, Xie L, Liu J, Wang Y, Xu Y, Wang S (2014) Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method. Desalination 333(1):66–81

    Article  Google Scholar 

  • Fan Z, Li W, Cai X, Li H, Wei C, Zhang Q, Deb K, Goodman E (2019) Push and pull search for solving constrained multi-objective optimization problems. Swarm Evol Comput 44:665–679

    Article  Google Scholar 

  • Goldberg, D (1989) Genetic algorithms in search, optimization, and machine learning. In: NN Schraudolph J, vol 3, No. 1

  • Guo Y, He J, Xu L, Liu W (2019) A novel multi-objective particle swarm optimization for comprehensible credit scoring. Soft Comput 23(18):9009–9023

    Article  Google Scholar 

  • Gutjahr WJ, Pichler A (2016) Stochastic multi-objective optimization: a survey on non-scalarizing methods. Ann Oper Res 236(2):475–499

    Article  MathSciNet  MATH  Google Scholar 

  • Harik GR, Lobo FG, Goldberg DE (1999) The compact genetic algorithm. IEEE Trans Evol Comput 3(4):287–297

    Article  Google Scholar 

  • Hei Y, Zhang C, Song W, Kou Y (2019) Energy and spectral efficiency tradeoff in massive mimo systems with multi-objective adaptive genetic algorithm. Soft Comput 23(16):7163–7179

    Article  Google Scholar 

  • Jiang S, Yang S (2016) Evolutionary dynamic multiobjective optimization: benchmarks and algorithm comparisons. IEEE Trans Cbern 47(1):198–211

    Article  Google Scholar 

  • Li H, Zhang Q, Deng J (2016) Biased multiobjective optimization and decomposition algorithm. IEEE Trans Cybern 47(1):52–66

    Article  Google Scholar 

  • Long Q (2014) A constraint handling technique for constrained multi-objective genetic algorithm. Swarm Evol Comput 15:66–79

    Article  Google Scholar 

  • Long Q, Wu C, Huang T, Wang X (2015) A genetic algorithm for unconstrained multi-objective optimization. Swarm Evol Comput 22:1–14

    Article  Google Scholar 

  • Long Q, Wu X, Wu C (2020) Non-dominated sorting methods for multi-objective optimization: review and numerical comparison. J Manag Optim 21(1):34–51

    Google Scholar 

  • Ma X, Liu F, Qi Y, Wang X, Li L, Jiao L, Yin M, Gong M (2016) A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables. IEEE Trans Evolut Comput 20(2):275–298

    Article  Google Scholar 

  • McClymont K, Keedwell E (2012) Deductive sort and climbing sort: new methods for non-dominated sorting. Evol Comput 20(1):1–26

    Article  Google Scholar 

  • Mirjalili S (2019) Evolutionary algorithms and neural networks. In: Studies in computational intelligence, vol 780, Springer

  • Mlakar M, Petelin D, Tušar T, Filipič B (2015) Gp-demo: differential evolution for multiobjective optimization based on gaussian process models. Eur J Oper Res 243(2):347–361

    Article  MathSciNet  MATH  Google Scholar 

  • Nikhil A, Anil K, Varun B (2017) A new design method for stable iir filters with nearly linear-phase response based on fractional derivative and swarm intelligence. IEEE Trans Emerg Top Comput Intell 1(6):464–477

    Article  Google Scholar 

  • Nikhil A, Anil K, Varun B (2018) Design of digital iir filter with low quantization error using hybrid optimization technique. Soft Comput 22:2953–2971

    Article  Google Scholar 

  • Nikhil A, Anil K, Varun B (2019) A new method for designing of stable digital iir filter using hybrid method. Circuits Syst Signal Process 38:2187–2226

    Article  MathSciNet  Google Scholar 

  • Nikhil A, Anil K, Varun B (2020) Design of infinite impulse response filter using fractional derivative constraints and hybrid particle swarm optimization. Circuits Syst Signal Process 39:6162–6190

    Article  Google Scholar 

  • Passos F, González-Echevarría R, Roca E, Castro-López R, Fernández F (2019) A two-step surrogate modeling strategy for single-objective and multi-objective optimization of radiofrequency circuits. Soft Comput 23(13):4911–4925

    Article  Google Scholar 

  • Qiu X, Xu JX, Tan KC, Abbass HA (2016) Adaptive cross-generation differential evolution operators for multiobjective optimization. IEEE Trans Evol Comput 20(2):232–244

    Article  Google Scholar 

  • Ruiz AB, Saborido R, Luque M (2015) A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm. J Global Optim 62(1):101–129

    Article  MathSciNet  MATH  Google Scholar 

  • Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tian Y, Zhang X, Wang C, Jin Y (2019a) An evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Evolut Comput 24(2):380–393

    Article  Google Scholar 

  • Tian Y, Zheng X, Zhang X, Jin Y (2019b) Efficient large-scale multiobjective optimization based on a competitive swarm optimizer. IEEE Transa Cybern 50(8):3696–3708

    Article  Google Scholar 

  • Wang H, Yao X (2013) Corner sort for pareto-based many-objective optimization. IEEE Trans Cybern 44(1):92-102

    Article  Google Scholar 

  • Wang R, Zhou Z, Ishibuchi H, Liao T, Zhang T (2016) Localized weighted sum method for many-objective optimization. IEEE Trans Evolut Comput 22(1):3–18

    Article  Google Scholar 

  • Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85

    Article  Google Scholar 

  • Yang MD, Lin MD, Lin YH, Tsai KT (2017) Multiobjective optimization design of green building envelope material using a non-dominated sorting genetic algorithm. Appl Therm Eng 111:1255–1264

    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

    Article  Google Scholar 

  • 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. University of Essex, Colchester, UK and Nanyang technological University, Singapore, special session on performance assessment of multi-objective optimization algorithms, technical report 264

  • Zhang X, Tian Y, Cheng R, Jin Y (2014) An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans Evol Comput 19(2):201–213

    Article  Google Scholar 

  • Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 19(6):761–776

    Article  Google Scholar 

  • Zhang Y, Yang GDGZS, Chen D (2019) A novel cacor-svr multi-objective optimization approach and its application in aerodynamic shape optimization of high-speed train. Soft Comput 23(13):5035–5051

    Article  Google Scholar 

  • 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(1):32–49

    Article  Google Scholar 

  • Zhou Y, Chen Z, Zhang J (2017) Ranking vectors by means of the dominance degree matrix. IEEE Trans Evol Comput 21(1):34–51

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grants No. 11871128) and the Open Project Funded by the Chongqing Key Lab on IFBDA, School of Mathematical Sciences,Chongqing Normal University, Chongqing China (Grants No. CSSXKFKTZ201804). The authors of this paper would like to thank editors and reviews for their constructive comments and suggestions.

Author information

Authors and Affiliations

  1. School of Science, Southwest University of Science and Technology, Mianyang, 621010, China

    Qiang Long

  2. School of Mathematical Science, Chongqing Normal University, Chongqing, 400047, China

    Guoquan Li

  3. School of Engineering, Computing and Mathematics, Curtin University, Bentley, 6102, Australia

    Lin Jiang

Authors
  1. Qiang Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoquan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiang Long.

Ethics declarations

Author contributions

All authors contributed to the study conception and design. Material preparation and data collection were performed by QL and GL. The analysis and code were done by QL. The first draft of the manuscript was written by LJ and then polished by QL and GL. All authors read and approved the final manuscript.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Long, Q., Li, G. & Jiang, L. A novel solver for multi-objective optimization: dynamic non-dominated sorting genetic algorithm (DNSGA). Soft Comput 26, 725–747 (2022). https://doi.org/10.1007/s00500-021-06223-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-06223-0

Keywords

Search

Navigation