Skip to main content
SpringerLink
Log in

An efficient local search algorithm for the winner determination problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

Combinatorial auction, which allows bidders to bid on combinations of items, is an important type of market mechanism. The winner determination problem (WDP) has extensive applications in combinatorial auctions, and attracts more and more attention due to its strong relevance to business. However, this problem is intractable in theory as it has been proven to be NP-hard, and is also a challenging combinatorial optimization problem in practice. This paper is devoted to designing an efficient heuristic algorithm for solving the WDP. This proposed heuristic algorithm dubbed abcWDP is based on an effective yet simple local search framework, and equipped with three novel strategies, i.e., configuration checking, free-bid exploiting, and pseudo-tie mechanism. Extensive computational experiments on a broad range of benchmarks demonstrate that abcWDP performs much better than state-of-the-art algorithms and CPLEX in terms of both revenue and running time. More encouragingly, our abcWDP algorithm as a sequential algorithm even achieves better computational results than the multi-thread implemented algorithm \(\hbox {CA}_\mathrm{RA}\), which confirms its efficiency.

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

Similar content being viewed by others

Notes

  1. http://wireless.fcc.gov/auctions.

  2. Our algorithm uses a random selection strategy to handle this situation.

  3. According to the Intel Ark, the differnence between E7-8830 and E7-4830 is only the max CPU configuration.

References

  • Andersson, A., Tenhunen, M., Ygge, F.: Integer programming for combinatorial auction winner determination. In: 4th International Conference on Multi-Agent Systems, ICMAS 2000, Boston, MA, USA, July 10–12, pp. 39–46 (2000)

  • Alidaee, B., Kochenberger, G.A., Lewis, K.R., Lewis, M.W., Wang, H.: A new approach for modeling and solving set packing problems. Eur. J. Oper. Res. 186(2), 504–512 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Ball, M., Donohue, G., Hoffman, K.: Auctions for the safe, efficient, and equitable allocation of airspace system resources. Comb. Auction 1, 507–538 (2006)

  • Boughaci, D.: Metaheuristic approaches for the winner determination problem in combinatorial auction. In: Artificial Intelligence, Evolutionary Computing and Metaheuristics—In the Footsteps of Alan Turing, pp. 775–791 (2013)

  • Boughaci, D., Benhamou, B., Drias, H.: Stochastic local search for the optimal winner determination problem in combinatorial auctions. In: Principles and Practice of Constraint Programming, 14th International Conference, CP 2008, Sydney, Australia, September 14–18. Proceedings, pp. 593–597 (2008)

  • Boughaci, D., Benhamou, B., Drias, H.: A memetic algorithm for the optimal winner determination problem. Soft. Comput. 13(8–9), 905–917 (2009)

    Article  Google Scholar 

  • Boughaci, D., Benhamou, B., Drias, H.: Local search methods for the optimal winner determination problem in combinatorial auctions. J. Math. Model. Algorithms 9(2), 165–180 (2010)

    Article  MathSciNet  Google Scholar 

  • Cai, S.: Balance between complexity and quality: Local search for minimum vertex cover in massive graphs. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25–31, pp. 747–753 (2015)

  • Cai, S., Su, K.: Configuration checking with aspiration in local search for SAT. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, July 22–26, Toronto, ON, Canada (2012)

  • Cai, S., Su, K.: Local search for boolean satisfiability with configuration checking and subscore. Artif. Intell. 204, 75–98 (2013)

    Article  MATH  Google Scholar 

  • Cai, S., Su, K., Sattar, A.: Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artif. Intell. 175(9–10), 1672–1696 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Cai, S., Su, K., Luo, C., Sattar, A.: NuMVC: an efficient local search algorithm for minimum vertex cover. J. Artif. Intell. Res. 46, 687–716 (2013)

    MathSciNet  MATH  Google Scholar 

  • Cai, S., Luo, C., Su, K.: Improving walksat by effective tie-breaking and efficient implementation. Comput. J. 58(11), 2864–2875 (2015)

    Article  Google Scholar 

  • de Andrade, C.E., Toso, R.F., Resende, M.G.C., Miyazawa, F.K.: Biased random-key genetic algorithms for the winner determination problem in combinatorial auctions. Evol. Comput. 23(2), 279–307 (2015)

    Article  Google Scholar 

  • Escudero, L.F., Landete, M., Marín, A.: A branch-and-cut algorithm for the winner determination problem. Decis. Support Syst. 46(3), 649–659 (2009)

    Article  Google Scholar 

  • Fujishima, Y., Leyton-Brown, K., Shoham, Y.: Taming the computational complexity of combinatorial auctions: optimal and approximate approaches. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 99, Stockholm, Sweden, July 31–August 6, vol. 2, pp 548–553 (1999)

  • Gao, C., Weise, T., Li, J.: A weighting-based local search heuristic algorithm for the set covering problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2014, Beijing, China, July 6–11, pp. 826–831 (2014)

  • Glover, F.: Tabu search–part I. ORSA J. Comput. 1(3), 190–206 (1989)

    Article  MATH  Google Scholar 

  • Glover, F.: Tabu search–part II. ORSA J. Comput. 2(1), 4–32 (1990)

    Article  MATH  Google Scholar 

  • Guo, Y., Lim, A., Rodrigues, B., Zhu, Y.: Heuristics for a bidding problem. Comput. Oper. Res. 33, 2179–2188 (2006)

    Article  MATH  Google Scholar 

  • Hoos, H.H., Boutilier, C.: Solving combinatorial auctions using stochastic local search. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on on Innovative Applications of Artificial Intelligence, July 30–August 3, Austin, TX, USA, pp. 22–29 (2000)

  • Lassouaoui, M., Boughaci, D.: A choice function hyper-heuristic for the winner determination problem. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2013)—Learning, Optimization and Interdisciplinary Applications, Canterbury, UK, September 2–4, pp. 303–314 (2013)

  • Lau, H.C., Goh, Y.G.: An intelligent brokering system to support multi-agent web-based 4 th-party logistics. In: Proceedings of 14th IEEE International Conference on Tools with Artificial Intelligence, 2002 (ICTAI 2002), pp. 154–161 (2002)

  • Leyton-Brown, K., Pearson, M., Shoham, Y.: Towards a universal test suite for combinatorial auction algorithms. In: EC, pp. 66–76 (2000a)

  • Leyton-Brown, K., Shoham, Y., Tennenholtz, M.: An algorithm for multi-unit combinatorial auctions. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on on Innovative Applications of Artificial Intelligence, July 30–August 3, Austin, TX, USA, pp. 56–61 (2000b)

  • Lin G, Zhu W, Ali M (2015) An effective discrete dynamic convexized method for solving the winner determination problem. J. Combin. Optim. 1–31

  • Luo, C., Cai, S., Wu, W., Su, K.: Focused random walk with configuration checking and break minimum for satisfiability. In: Principles and Practice of Constraint Programming—19th International Conference, CP 2013, Uppsala, Sweden, September 16–20, 2013. Proceedings, pp 481–496 (2013)

  • Luo, C., Cai, S., Wu, W., Su, K.: Double configuration checking in stochastic local search for satisfiability. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, July 27–31, 2014, Québec City, Québec, pp. 2703–2709 (2014)

  • Luo, C., Cai, S., Su, K., Wu, W.: Clause states based configuration checking in local search for satisfiability. IEEE Trans. Cybern. 45(5), 1014–1027 (2015a)

    Google Scholar 

  • Luo, C., Cai, S., Wu, W., Jie, Z., Su, K.: CCLS: an efficient local search algorithm for weighted maximum satisfiability. IEEE Trans. Comput. 64(7), 1830–1843 (2015b)

    Article  MathSciNet  MATH  Google Scholar 

  • Luo, C., Cai, S., Su, K., Huang, W.: CCEHC: an efficient local search algorithm for weighted partial maximum satisfiability. Artif. Intell. 243, 26–44 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Michiels, W., Aarts, E.H.L., Korst, J.H.M.: Theoretical Aspects of Local Search. Springer, New York (2007)

    MATH  Google Scholar 

  • Rothkopf, M.H., Pekeč, A., Harstad, R.M.: Computationally manageable combinational auctions. Manag. Sci. 44(8), 1131–1147 (1998)

    Article  MATH  Google Scholar 

  • Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artif. Intell. 135(1–2), 1–54 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Sandholm, T., Suri, S.: BOB: improved winner determination in combinatorial auctions and generalizations. Artif. Intell. 145(1–2), 33–58 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Sandholm, T., Suri, S., Gilpin, A., Levine, D.: CABOB: A fast optimal algorithm for combinatorial auctions. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Seattle, WA, USA, August 4–10, pp. 1102–1108 (2001)

  • Selman, B., Kautz, H.A., Cohen, B.: Noise strategies for improving local search. In: Proceedings of the 12th National Conference on Artificial Intelligence, Seattle, July 31–August 4, vol. 1, pp. 337–343 (1994)

  • Umetani, S.: Exploiting variable associations to configure efficient local search in large-scale set partitioning problems. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25–30, Austin, TX, USA, pp. 1226–1232 (2015)

  • Voudouris, C., Tsang, E.P.K.: Guided local search and its application to the traveling salesman problem. Eur. J. Oper. Res. 113(2), 469–499 (1999)

    Article  MATH  Google Scholar 

  • Xu, K., Zhang, Y., Shi, X., Wang, H., Wang, Y., Shen, M,: Online combinatorial double auction for mobile cloud computing markets. In: IEEE 33rd International Performance Computing and Communications Conference, IPCCC 2014, Austin, TX, USA, December 5–7, pp. 1–8 (2014)

  • Zhang, Z., He, H., Luo, Z., Qin, H., Guo, S.: An efficient forest-based tabu search algorithm for the split-delivery vehicle routing problem. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25–30, 2015, Austin, TX, USA, pp. 3432–3438 (2015)

Download references

Acknowledgements

The authors thank Carlos Eduardo de Andrade for kindly providing the code of \(\hbox {CA}_\mathrm{RA}\) and nice help on compiling as well as execution arguments. We also want to express our appreciation to anonymous reviewers for comments and advices.

Author information

Authors and Affiliations

  1. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130024, China

    Haochen Zhang & Minghao Yin

  2. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Shaowei Cai

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Chuan Luo

  4. State Key Laboratory of Mathematical Engineering and Advanced Computing, Wuxi, 214125, China

    Chuan Luo

Authors
  1. Haochen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shaowei Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chuan Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghao Yin.

Additional information

This work was supported in part by National Natural Science Foundation of China under Grant Nos. (61370156, 61503074, 61502464), Program for New Century Excellent Talents in University (NCET-13-0724) and the Open Project Program of the State Key Laboratory of Mathematical Engineering and Advanced Computing under Grant No. (2016A06).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Cai, S., Luo, C. et al. An efficient local search algorithm for the winner determination problem. J Heuristics 23, 367–396 (2017). https://doi.org/10.1007/s10732-017-9344-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-017-9344-y

Keywords

Search

Navigation