Advertisement

Scaling Up the Sample Average Approximation Method for Stochastic Optimization with Applications to Trading Agents

  • Amy Greenwald
  • Bryan Guillemette
  • Victor Naroditskiy
  • Michael Tschantz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3937)

Abstract

The Sample Average Approximation (SAA) method is a technique for approximating solutions to stochastic programs. Here, we attempt to scale up the SAA method to harder problems than those previously studied. We argue that to apply the SAA method effectively, there are three parameters to optimize: the number of evaluations, the number of scenarios, and the number of candidate solutions. We propose an experimental methodology for finding the optimal settings of these parameters given fixed time and space constraints. We apply our methodology to two large-scale stochastic optimization problems that arise in the context of the annual Trading Agent Competition. Both problems are expressed as integer linear programs and solved using CPLEX. Runtime increases linearly with the number of scenarios in one of the problems, and exponentially in the other. We find that, in the former problem, maximizing the number of scenarios yields the best solution, while in the latter problem, it is necessary to evaluate multiple candidate solutions to find the best solution, since increasing the number of scenarios becomes expensive very quickly.

Keywords

Schedule Problem Supply Chain Management Combinatorial Auction Stochastic Optimization Problem Winner Determination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahmed, S., Shapiro, A.: The sample average approximation method for stochastic programs with integer recourse (submitted for publication, 2002)Google Scholar
  2. 2.
    Arunachalam, R., Sadeh, N.: The 2003 supply chain management trading agent competition. In: Third International Conference on Autonomous Agents and Multi-Agent Systems Workshop on Trading Agent Design and Analysis (July 2004)Google Scholar
  3. 3.
    Benisch, M., Greenwald, A., Grypari, I., Lederman, R., Naroditskiy, V., Tschantz, M.: Botticelli: A supply chain management agent. In: Third International Conference on Autonomous Agents and Multiagent Systems, vol. 3, pp. 1174–1181 (July 2004)Google Scholar
  4. 4.
    Benisch, M., Greenwald, A., Naroditskiy, V., Tschantz, M.: A stochastic programming approach to TAC SCM. In: Fifth ACM Conference on Electronic Commerce, pp. 152–160 (May 2004)Google Scholar
  5. 5.
    Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)MATHGoogle Scholar
  6. 6.
    Chang, H., Givan, R., Chong, E.: On-line Scheduling Via Sampling. In: Artificial Intelligence Planning and Scheduling (AIPS), Breckenridge, Colorado, pp. 62–71 (2000)Google Scholar
  7. 7.
    Cheng, S.F., Leung, E., Lochner, K.M., O’Malley, K., Reeves, D.M., Schvartzman, L.J., Wellman, M.P.: Walverine: A Walrasian trading agent. Decision Support Systems (to appear, 2004)Google Scholar
  8. 8.
    Greenwald, A., Boyan, J.: Bidding algorithms for simultaneous auctions: A case study. In: Proceedings of Third ACM Conference on Electronic Commerce, pp. 115–124 (2001)Google Scholar
  9. 9.
    Kleywegt, A.J., Shapiro, A., Homem de Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM Journal of Optimization 12, 479–502 (2001)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Rothkopf, M.H., Pekeč, A., Harstad, R.M.: Computationally manageable combinatorial auctions. Management Science 44(8) (1998)Google Scholar
  11. 11.
    Wellman, M.P., Wurman, P.R., O’Malley, K., Bangera, R., Lin, S., Reeves, D., Walsh, W.E.: A Trading Agent Competition. IEEE Internet Computing (April 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Amy Greenwald
    • 1
  • Bryan Guillemette
    • 1
  • Victor Naroditskiy
    • 1
  • Michael Tschantz
    • 1
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA

Personalised recommendations