Skip to main content
SpringerLink
Log in

A nested particle swarm algorithm based on sphere mutation to solve bi-level optimization

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

Abstract

The problem of bi-level optimization has always been a hot topic due to its extensive application. Increasing size and complexity have prompted theoretical and practical interest in the design of effective algorithm. This paper adopts particle swarm algorithm (PSO) at both level. First, given the nested nature of bi-level problem, we introduce a hyper-sphere search into PSO as mutation operator to maintain the swarms diversity. Second, for complex constraints processing, the proposed algorithm adopts a dynamic constraint handling strategy, which makes the solution located on the constraint boundary easier to be obtained. Third, a quadratic approximation mutation is introduced into PSO, which guides particles to a better search area. Finally, the convergence is proved and the simulation results show that the proposed algorithm is effective.

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

Similar content being viewed by others

References

  • Aiyoshi E, Shimizu K (1981) Hierarchical decentralized systems and its new solution by a barrier method. IEEE Trans Syst Man Cybern 6:444–449

    MathSciNet  Google Scholar 

  • Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415

    Article  MathSciNet  Google Scholar 

  • Arqub OA, Mohammed AS, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302

    Article  Google Scholar 

  • Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191–7206

    Article  Google Scholar 

  • Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9(1):77–100

    Article  MathSciNet  Google Scholar 

  • Bendsøe MP, Sigmund O (1995) Optimization of structural topology, shape, and material, vol 414. Springer, Berlin

    Book  Google Scholar 

  • Bianco L, Caramia M, Giordani S (2009) A bilevel flow model for hazmat transportation network design. Transp Res Part C Emerg Technol 17(2):175–196

    Article  Google Scholar 

  • Brotcorne L, Labbé M, Marcotte P, Savard G (2001) A bilevel model for toll optimization on a multicommodity transportation network. Transp Sci 35(4):345–358

    Article  Google Scholar 

  • Brown G, Carlyle M, Diehl D, Kline J, Wood K (2005) A two-sided optimization for theater ballistic missile defense. Oper Res 53(5):745–763

    Article  MathSciNet  Google Scholar 

  • Brown GG, Carlyle WM, Harney RC, Skroch EM, Wood RK (2009) Interdicting a nuclear-weapons project. Oper Res 57(4):866–877

    Article  Google Scholar 

  • Christiansen S, Patriksson M, Wynter L (2001) Stochastic bilevel programming in structural optimization. Struct Multidiscip Optim 21(5):361–371

    Article  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995. MHS’95. IEEE, pp 39–43

  • Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13(5):1194–1217

    Article  MathSciNet  Google Scholar 

  • Herskovits J, Leontiev A, Dias G, Santos G (2000) Contact shape optimization: a bi-level programming approach. Struct Multidiscip Optim 20(3):214–221

    Article  Google Scholar 

  • Islam MM, Singh HK, Ray T (2017) A surrogate assisted approach for single-objective bilevel optimization. IEEE Trans Evolut Comput 21(5):681–696

    Article  Google Scholar 

  • Jackson I (1989) An order of convergence for some radial basis functions. IMA J Numer Anal 9(4):567–587

    Article  MathSciNet  Google Scholar 

  • Leung YW, Wang Y (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evolut Comput 5(1):41–53

    Article  Google Scholar 

  • Li X, Tian P, Min X (2006) A hierarchical particle swarm optimization for solving bi-level programming problems. In: International conference on artificial intelligence and soft computing. Springer, pp 1169–1178

  • Mathieu R, Pittard L, Anandalingam G (1994) Genetic algorithm based approach to bi-level linear programming. RAIRO Oper Res 28(1):1–21

    Article  MathSciNet  Google Scholar 

  • Missen RW, Smith WR (1982) Chemical reaction equilibrium analysis: theory and algorithms. Wiley, Hoboken

    Google Scholar 

  • Oduguwa V, Roy R (2002) Bi-level optimisation using genetic algorithm. In: 2002 IEEE international conference on artificial intelligence systems, 2002 (ICAIS 2002). IEEE, pp 322–327

  • Rudolph G, Agapie A (2000) Convergence properties of some multi-objective evolutionary algorithms. In: Proceedings of the 2000 congress on evolutionary computation, 2000. IEEE, vol 2, pp 1010–1016

  • Sinha A, Malo P, Deb K (2013a) Efficient evolutionary algorithm for single-objective bilevel optimization. arXiv preprint arXiv:1303.3901

  • Sinha A, Malo P, Frantsev A, Deb K (2013b) Multi-objective stackelberg game between a regulating authority and a mining company: a case study in environmental economics. In: 2013 IEEE congress on evolutionary computation (CEC). IEEE, pp 478–485

  • Sinha A, Malo P, Deb K (2014) Test problem construction for single-objective bilevel optimization. Evolut Comput 22(3):439–477

    Article  Google Scholar 

  • Sinha A, Malo P, Deb K (2016) Solving optimistic bilevel programs by iteratively approximating lower level optimal value function. In: IEEE Congress on evolutionary computation (CEC) 2016. IEEE, pp 1877–1884

  • Von Stackelberg H (1952) The theory of the market economy. Oxford University Press, Oxford

    Google Scholar 

  • Zhao L, Wei J, Li M (2017) Research on video server placement and flux plan based on GA. In: 2017 13th international conference on computational intelligence and security (CIS). IEEE, pp 35–38

Download references

Acknowledgements

This work is supported by the National Nature Science Foundation of China (No. 61203372).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Xidian University, Xi’an, China

    Long Zhao & JingXuan Wei

Authors
  1. Long Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JingXuan Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JingXuan Wei.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interests.

Ethical approval

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

Additional information

Communicated by V. Loia.

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

Zhao, L., Wei, J. A nested particle swarm algorithm based on sphere mutation to solve bi-level optimization. Soft Comput 23, 11331–11341 (2019). https://doi.org/10.1007/s00500-019-03888-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-03888-6

Keywords

Search

Navigation