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Soft Computing

, Volume 23, Issue 21, pp 11331–11341 | Cite as

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

  • Long Zhao
  • JingXuan WeiEmail author
Methodologies and Application
  • 95 Downloads

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.

Keywords

Bi-level optimization Particle swarm algorithm Sphere search Radial basis function (RBF) 

Notes

Acknowledgements

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

Compliance with ethical standards

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.

References

  1. Aiyoshi E, Shimizu K (1981) Hierarchical decentralized systems and its new solution by a barrier method. IEEE Trans Syst Man Cybern 6:444–449MathSciNetGoogle Scholar
  2. Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415MathSciNetCrossRefGoogle Scholar
  3. 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):3283–3302CrossRefGoogle Scholar
  4. 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):7191–7206CrossRefGoogle Scholar
  5. Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9(1):77–100MathSciNetCrossRefGoogle Scholar
  6. Bendsøe MP, Sigmund O (1995) Optimization of structural topology, shape, and material, vol 414. Springer, BerlinCrossRefGoogle Scholar
  7. Bianco L, Caramia M, Giordani S (2009) A bilevel flow model for hazmat transportation network design. Transp Res Part C Emerg Technol 17(2):175–196CrossRefGoogle Scholar
  8. Brotcorne L, Labbé M, Marcotte P, Savard G (2001) A bilevel model for toll optimization on a multicommodity transportation network. Transp Sci 35(4):345–358CrossRefGoogle Scholar
  9. Brown G, Carlyle M, Diehl D, Kline J, Wood K (2005) A two-sided optimization for theater ballistic missile defense. Oper Res 53(5):745–763MathSciNetCrossRefGoogle Scholar
  10. Brown GG, Carlyle WM, Harney RC, Skroch EM, Wood RK (2009) Interdicting a nuclear-weapons project. Oper Res 57(4):866–877CrossRefGoogle Scholar
  11. Christiansen S, Patriksson M, Wynter L (2001) Stochastic bilevel programming in structural optimization. Struct Multidiscip Optim 21(5):361–371CrossRefGoogle Scholar
  12. 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 39–43Google Scholar
  13. Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13(5):1194–1217MathSciNetCrossRefGoogle Scholar
  14. Herskovits J, Leontiev A, Dias G, Santos G (2000) Contact shape optimization: a bi-level programming approach. Struct Multidiscip Optim 20(3):214–221CrossRefGoogle Scholar
  15. Islam MM, Singh HK, Ray T (2017) A surrogate assisted approach for single-objective bilevel optimization. IEEE Trans Evolut Comput 21(5):681–696CrossRefGoogle Scholar
  16. Jackson I (1989) An order of convergence for some radial basis functions. IMA J Numer Anal 9(4):567–587MathSciNetCrossRefGoogle Scholar
  17. Leung YW, Wang Y (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evolut Comput 5(1):41–53CrossRefGoogle Scholar
  18. 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 1169–1178Google Scholar
  19. Mathieu R, Pittard L, Anandalingam G (1994) Genetic algorithm based approach to bi-level linear programming. RAIRO Oper Res 28(1):1–21MathSciNetCrossRefGoogle Scholar
  20. Missen RW, Smith WR (1982) Chemical reaction equilibrium analysis: theory and algorithms. Wiley, HobokenGoogle Scholar
  21. 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 322–327Google Scholar
  22. 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 1010–1016Google Scholar
  23. Sinha A, Malo P, Deb K (2013a) Efficient evolutionary algorithm for single-objective bilevel optimization. arXiv preprint arXiv:1303.3901
  24. 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 478–485Google Scholar
  25. Sinha A, Malo P, Deb K (2014) Test problem construction for single-objective bilevel optimization. Evolut Comput 22(3):439–477CrossRefGoogle Scholar
  26. 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 1877–1884Google Scholar
  27. Von Stackelberg H (1952) The theory of the market economy. Oxford University Press, OxfordGoogle Scholar
  28. 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 35–38Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyXidian UniversityXi’anChina

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