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Applied Intelligence

, Volume 49, Issue 11, pp 3845–3863 | Cite as

A discrete cooperatively coevolving particle swarm optimization algorithm for combinatorial double auctions

  • Fu-Shiung HsiehEmail author
  • Yi-Hong Guo
Article
  • 36 Downloads

Abstract

A combinatorial double auction is a type of double-side auction which makes buyers and sellers trade goods more conveniently than multiple combinatorial auctions. In this paper, we consider the combinatorial double auction problem in which there are transaction costs, supply constraints and surplus constraints. We formulate the WDP of combinatorial double auction problem as an integer programming problem formulation. The winner determination problem (WDP) in combinatorial double auctions poses a challenge due to computational complexity. Particle swarm optimization (PSO) is a well-known approach to deal with complex optimization problems. In the existing literature, different variants of PSO algorithms have been proposed. However, there still lacks a comparative study on effectiveness of applying different variants of PSO algorithms in combinatorial double auctions. As standard discrete PSO (DPSO) algorithm suffers from premature convergence problem, we adopt a coevolution approach to develop a discrete cooperatively coevolving particle swarm optimization (DCCPSO) algorithm that can scale with the problem. The effectiveness of the proposed algorithm is verified by comparing the results with several variants of PSO algorithms and Differential Evolution algorithms through simulation. Simulation results indicate that the proposed DCCPSO algorithm significantly outperforms these variants of PSO algorithms and Differential Evolution algorithms in most test cases of combinatorial double auctions.

Keywords

Particle swarm Coevolution Combinatorial double auction Integer programming 

Notes

Acknowledgements

This paper is currently supported in part by Ministry of Science and Technology, Taiwan under Grant MOST 106-2410-H-324-002-MY2.

References

  1. 1.
    MacMillan J (1994) Selling spectrum rights. J Econ Perspect 8:145–162CrossRefGoogle Scholar
  2. 2.
    Cramton P (2002) Spectrum auctions, chapter 14, 605–639. In: Cave M, Majumdar S, Vogelsang I (eds) Handbook of telecommunications economicsGoogle Scholar
  3. 3.
    Rassenti S, Smith V, Bulfin R (1982) A combinatorial auction mechanism for airport time slot allocation. Bell J Econ 13(2):402–417CrossRefGoogle Scholar
  4. 4.
    Xia M, Stallaert J, Whinston AB (2005) Solving the combinatorial double auction problem. Eur J Oper Res 164(1):239–251CrossRefGoogle Scholar
  5. 5.
    Zaidi BH, Hong SH (2018) Combinatorial double auctions for multiple microgrid trading. Electr Eng 100(2):1069–1083.  https://doi.org/10.1007/s00202-017-0570-y CrossRefGoogle Scholar
  6. 6.
    Tafsiri SA, Yousefi S (2018) Combinatorial double auction-based resource allocation mechanism in cloud computing market. J Syst Softw 137:322–334, ISSN 0164-1212.  https://doi.org/10.1016/j.jss.2017.11.044 CrossRefGoogle Scholar
  7. 7.
    de Vries S, Vohra RV (2003) Combinatorial auctions: a survey. INFORMS J Comput 15(3):284–309MathSciNetCrossRefGoogle Scholar
  8. 8.
    Pekeč A, Rothkopf MH (2003) Combinatorial auction design. Manag Sci 49(11):1485–1503CrossRefGoogle Scholar
  9. 9.
    Rothkopf M, Pekeč A, Harstad R (1998) Computationally manageable combinational auctions. Manag Sci 44(8):1131–1147CrossRefGoogle Scholar
  10. 10.
    Vemuganti RR (1998) Applications of set covering, set packing and set partitioning models: a survey. In: Du D-Z (ed) Handbook of combinatorial optimization, vol 1. Kluwer Academic Publishers, Netherlands, pp 573–746CrossRefGoogle Scholar
  11. 11.
    Andersson A, Tenhunen M, Ygge F (2000) Integer programming for combinatorial auction winner determination. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 39–46Google Scholar
  12. 12.
    Fujishima Y, Leyton-Brown K, Shoham Y (1999) Taming the computational complexity of combinatorial auctions: optimal and approximate approaches. In: Sixteenth international joint conference on artificial intelligence, pp.548–553Google Scholar
  13. 13.
    Hoos HH, Boutilier C (2000) Solving combinatorial auctions using stochastic local search. In: Proceedings of the seventeenth National Conference on artificial intelligence, pp. 22–29Google Scholar
  14. 14.
    Sandholm T (1999) An algorithm for optimal winner determination in combinatorial auctions. In: Proc. IJCAI’99, Stockholm, pp. 542–547Google Scholar
  15. 15.
    Sandholm T (2000) Approaches to winner determination in combinatorial auctions. Decis Support Syst 28(1–2):165–176CrossRefGoogle Scholar
  16. 16.
    Sandholm T (2002) Algorithm for optimal winner determination in combinatorial auctions. Artif Intell 135(1–2):1–54MathSciNetCrossRefGoogle Scholar
  17. 17.
    Hsieh FS, Liao CS (2015) Scalable multi-agent learning algorithms to determine winners in combinatorial double auctions. Appl Intell 43(2):308–324.  https://doi.org/10.1007/s10489-014-0643-9 CrossRefGoogle Scholar
  18. 18.
    Hsieh FS, Liao CS (2015) Schemes to reward winners in combinatorial double auctions based on optimization of surplus. Electron Commer Res Appl 14(6):405–417CrossRefGoogle Scholar
  19. 19.
    Gorbanzadeh F, Kazem AAP (2012) Hybrid genetic algorithms for solving winner determination problem in combinatorial double auction in grid. Int J Artif Intell 1(2):54–62.  https://doi.org/10.1016/j.elerap.2015.05.002 CrossRefGoogle Scholar
  20. 20.
    Hsieh FS (2017) A discrete particle swarm algorithm for combinatorial auctions, advances in swarm intelligence. ICSI 2017. Lect Notes Comput Sci 10385:201–208CrossRefGoogle Scholar
  21. 21.
    Eberhart RC, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: Porto VW, Saravanan N, Waagen D, Eiben AE (eds) Evolutionary programming VII. EP 1998, Lecture notes in computer science, vol 1447. Springer, Berlin, pp 611–616CrossRefGoogle Scholar
  22. 22.
    Hassan R, Cohanim B, Weck OD (2005) A comparison of particle swarm optimization and the genetic algorithm. 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, structures, structural dynamics, and materials and co-located conferences.  https://doi.org/10.2514/6.2005-1897
  23. 23.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proceedings of IEEE international conference on neural networks, Piscataway, NJ, pp. 1942–1948Google Scholar
  24. 24.
    El-Galland AI, El-Hawary ME, Sallam AA (2001) Swarming of intelligent particles for solving the nonlinear constrained optimization problem. International Journal of Engineering Intelligent Systems for Electrical Engineering and Communications (ENG INTELL SYST ELEC) 9(3):155–163Google Scholar
  25. 25.
    Van den Bergh F, Engelbrecht AP (2000) Cooperative learning in neural network using particle swarm optimizers. South African Computer Journal 26:84–90Google Scholar
  26. 26.
    Tasgetiren MF, Sevkli M, Liang YC, Gencyilmaz G (2004) Particle swarm optimization algorithm for single machine total weighted tardiness problem. Proceedings of the 2004 Congress on Evolutionary Computation 2:1412–1419CrossRefGoogle Scholar
  27. 27.
    Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. 1997 IEEE international conference on systems, man, and cybernetics: computational cybernetics and simulation 5:4104–4108Google Scholar
  28. 28.
    Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. Proceedings of the 2004 Congress on Evolutionary Computation 2:1980–1987CrossRefGoogle Scholar
  29. 29.
    van den Bergh F, Engelbrecht AP (2004) A cooperative approach to particle swarm optimization. IEEE Trans Evol Comput 8(3):225–239CrossRefGoogle Scholar
  30. 30.
    Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295CrossRefGoogle Scholar
  31. 31.
    Wang F, Zhang H, Li K, Lin Z, Yang J, Shen XL (2018) A hybrid particle swarm optimization algorithm using adaptive learning strategy. Inf Sci 436–437:162–177MathSciNetCrossRefGoogle Scholar
  32. 32.
    Potter MA, De Jong KA (1994) A cooperative coevolutionary approach to function optimization. Lect Notes Comput Sci 866:249–257CrossRefGoogle Scholar
  33. 33.
    Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999MathSciNetCrossRefGoogle Scholar
  34. 34.
    Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16(2):210–224CrossRefGoogle Scholar
  35. 35.
    Hsieh FS, Guo YH (2018) An algorithm for combinatorial double auctions based on cooperative coevolution of particle swarms. In: Mouhoub M, Sadaoui S, Ait Mohamed O, Ali M (eds) Recent Trends and Future Technology in Applied Intelligence. IEA/AIE 2018, Lecture Notes in Computer Science, vol 10868. Springer, pp 187–199Google Scholar
  36. 36.
    Hsieh FS, Guo YH (2018) Winner determination in combinatorial double auctions based on differential evolution algorithms. 2018 IEEE 42nd Annual Computer Software and Applications Conference (COMPSAC), Tokyo 2018, pp. 888–893Google Scholar
  37. 37.
    Ravindran K, Ragsdell M, Reklaitis GV (2007) Engineering optimization: methods and applications, Second edn. WileyGoogle Scholar
  38. 38.
    Deb K (2004) Optimization for engineering design: algorithms and examples. Prentice-HallGoogle Scholar
  39. 39.
    Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringChaoyang University of TechnologyTaichungTaiwan

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