An Algorithm for Combinatorial Double Auctions Based on Cooperative Coevolution of Particle Swarms

  • Fu-Shiung HsiehEmail author
  • Yi-Hong Guo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10868)


A combinatorial double auction is a type of double-side auction which makes buyers and sellers trade goods more conveniently than multiple combinatorial auctions. However, the winner determination problem (WDP) in combinatorial double auctions poses a challenge due to computation complexity. Particle swarm optimization (PSO) is one of the well-known meta-heuristic approaches to deal with complex optimization problems. Although there are many studies on combinatorial auctions, there is little study on application of PSO approach in combinatorial double auctions. In this paper, we consider combinatorial double auction problem in which there are transaction costs, supply constraints and non-negative surplus constraints. We formulate the WDP of combinatorial double auction problem as an integer programming problem formulation. As standard discrete PSO algorithm suffers from the premature convergence problem, we adopt a cooperative coevolution approach to develop a discrete cooperative coevolving particle swarm optimization (DCCPSO) algorithm that can scale with the problem better. The effectiveness of the proposed algorithm is illustrated by several numerical examples by comparing the results with standard DPSO algorithm.


Meta-heuristics Particle swarm Coevolution Combinatorial double auction Integer programming 



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


  1. 1.
    de Vries, S., Vohra, R.V.: Combinatorial auctions: a survey. INFORMS J. Comput. 15(3), 284–309 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Pekeč, A., Rothkopf, M.H.: Combinatorial auction design. Manag. Sci. 49(11), 1485–1503 (2003)CrossRefGoogle Scholar
  3. 3.
    Rothkopf, M., Pekeč, A., Harstad, R.: Computationally manageable combinational auctions. Manag. Sci. 44(8), 1131–1147 (1998)CrossRefGoogle Scholar
  4. 4.
    Xia, M., Stallaert, J., Whinston, A.B.: Solving the combinatorial double auction problem. Eur. J. Oper. Res. 164(1), 239–251 (2005)CrossRefGoogle Scholar
  5. 5.
    Vemuganti, R.R.: Applications of set covering, set packing and set partitioning models: a survey. In: Du, D.-Z. (ed.) Handbook of Combinatorial Optimization, vol. 1, pp. 573–746. Kluwer Academic Publishers, Netherlands (1998)CrossRefGoogle Scholar
  6. 6.
    Andersson, A., Tenhunen, M., Ygge, F.: Integer programming for combinatorial auction winner determination. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 39–46 (2000)Google Scholar
  7. 7.
    Fujishima, Y., Leyton-Brown, K., Shoham, Y.: Taming the computational complexity of combinatorial auctions: optimal and approximate approaches. In: Sixteenth International Joint Conference on Artificial Intelligence, pp. 548–553 (1999)Google Scholar
  8. 8.
    Hoos, H.H., Boutilier, C.: Solving combinatorial auctions using stochastic local search. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 22–29 (2000)Google Scholar
  9. 9.
    Sandholm, T.: An algorithm for optimal winner determination in combinatorial auctions. In: Proceedings of IJCAI 1999, Stockholm, pp. 542–547 (1999)Google Scholar
  10. 10.
    Sandholm, T.: Approaches to winner determination in combinatorial auctions. Decis. Support Syst. 28(1–2), 165–176 (2000)CrossRefGoogle Scholar
  11. 11.
    Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artif. Intell. 135(1–2), 1–54 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)Google Scholar
  13. 13.
    El-Galland, A.I., El-Hawary, M.E., Sallam, A.A.: Swarming of intelligent particles for solving the nonlinear constrained optimization problem. Eng. Intell. Syst. Electr. Eng. Commun. 9(3), 155–163 (2001)Google Scholar
  14. 14.
    Van den Bergh, F., Engelbrecht, A.P.: Cooperative learning in neural network using particle swarm optimizers. S. Afr. Comput. J. 26, 84–90 (2000)Google Scholar
  15. 15.
    Tasgetiren, M.F., Sevkli, M., Liang, Y.C., Gencyilmaz, G.: Particle swarm optimization algorithm for single machine total weighted tardiness problem. In: Proceedings of the IEEE congress on evolutionary computation, Oregon, Portland, vol. 2, pp. 1412–1419 (2004)Google Scholar
  16. 16.
    Kennedy, J., Eberhart, R.C., A discrete binary version of the particle swarm algorithm. In: 1997 IEEE International Conference on Systems, Man, and Cybernetics: Computational Cybernetics and Simulation, vol. 5, pp. 4104–4108 (1997)Google Scholar
  17. 17.
    Vesterstrom, J., Thomsen, R.: A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Proceedings of the 2004 Congress on Evolutionary Computation, vol. 2, pp. 1980–1987 (2004)Google Scholar
  18. 18.
    van den Bergh, F., Engelbrecht, A.P.: A cooperative approach to particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 225–239 (2004)CrossRefGoogle Scholar
  19. 19.
    Potter, M.A., De Jong, K.A.: A cooperative coevolutionary approach to function optimization. In: Davidor, Y., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 249–257. Springer, Heidelberg (1994). Scholar
  20. 20.
    Yang, Z., Tang, K., Yao, X.: Large scale evolutionary optimization using cooperative coevolution. Inf. Sci. 178(15), 2985–2999 (2008)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Li, X., Yao, X.: Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans. Evol. Comput. 16(2), 210–224 (2012)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Hsieh, F.-S.: A discrete particle swarm algorithm for combinatorial auctions. In: Tan, Y., Takagi, H. (eds.) ICSI 2017. LNCS, vol. 10385, pp. 201–208. Springer, Cham (2017). Scholar
  23. 23.
    Ravindran, A., Ragsdell, K.M., Reklaitis, G.V.: Engineering Optimization: Methods and Applications, 2nd edn. Wiley, Hoboken (2007)Google Scholar
  24. 24.
    Deb, K.: Optimization for Engineering Design: Algorithms and Examples. Prentice-Hall, New Delhi (2004)Google Scholar
  25. 25.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chaoyang University of TechnologyTaichungTaiwan

Personalised recommendations