Abstract
We propose a new approach for understanding the algorithm-specific empirical hardness of 
-Hard problems. In this work we focus on the empirical hardness of the winner determination problem—an optimization problem arising in combinatorial auctions—when solved by ILOG’s CPLEX software. We consider nine widely-used problem distributions and sample randomly from a continuum of parameter settings for each distribution. We identify a large number of distribution-nonspecific features of data instances and use statistical regression techniques to learn, evaluate and interpret a function from these features to the predicted hardness of an instance.
We would like to acknowledge contributions by Rámon Béjar, Carla Gomes, Henry Kautz, Bart Selman, Lyle Ungar and Ioannis Vetsikas.
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References
D. Achlioptas, C. Gomes, H. Kautz, and B. Selman. Generating satisfiable instances. In AAAI-00, 2000.
A. Anderson, M. Tenhunen, and F. Ygge. Integer programming for combinatorial auction winner determination. In ICMAS, 2000.
P. Cheeseman, B. Kanefsky, and W. M. Taylor. Where the Really Hard Problems Are. In IJCAI-91, 1991.
S. de Vries and R. Vohra. Combinatorial auctions: A brief survey. Unpublished, 2000.
J. Friedman. Multivariate adaptive regression splines. Annals of Statistics, 19, 1991.
Y. Fujishima, K. Leyton-Brown, and Y. Shoham. Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches. In IJCAI-99, 1999.
Carla P. Gomes and Bart Selman. Problem structure in the presence of perturbations. In AAAI/IAAI, 1997.
R. Gonen and D. Lehmann. Optimal solutions for multi-unit combinatorial auctions: Branch and bound heuristics. In ACM Conference on Electronic Commerce, 2000.
T. Hastie, R. Tibshirani, and J. Friedman. Elements of Statistical Learning. Springer, 2001.
R. C. Holte. Combinatorial auctions, knapsack problems, and hill-climbing search. In Canadian Conference on AI, 2001.
H. H. Hoos and C. Boutilier. Solving combinatorial auctions using stochastic local search. In AAAI-00, 2000.
E. Horvitz, Y. Ruan, C. Gomes, H. Kautz, B. Selman, and M. Chickering. A bayesian approach to tackling hard computational problems, 2001.
R. Kastner, C. Hsieh, M. Potkonjak, and M. Sarrafzadeh. On the sensitivity of incremental algorithms for combinatorial auctions, 2002. UCLA CS Tech. Report 020000.
R. Korf and M. Reid. Complexity analysis of admissible heuristic search. AAAI-98, 1998.
K. Leyton-Brown, M. Pearson, and Y. Shoham. Towards a universal test suite for combinatorial auction algorithms. In ACM Conference on Electronic Commerce, 2000.
K. Leyton-Brown, Yoav Shoham, and Moshe Tennenholtz. An algorithm for multi-unit combinatorial auctions. In Proceedings of AAAI-00, 2000.
R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Determining computational complexity for characteristic ‘phase transitions‘. Nature, 400, 1998.
N. Nisan. Bidding and allocation in combinatorial auctions. In ACM Conference on Electronic Commerce, 2000.
D. C. Parkes. iBundle: An efficient ascending price bundle auction. In ACM Conference on Electronic Commerce, 1999.
M. H. Rothkopf, A. Pekec, and R. M. Harstad. Computationally manageable combinatorial auctions. Management Science, 44(8), 1998.
T. Sandholm. An algorithm for optimal winner determination in combinatorial auctions. In IJCAI-99, 1999.
T. Sandholm, S. Suri, A. Gilpin, and D. Levine. Cabob: A fast optimal algorithm for combinatorial auctions. In IJCAI-01, 2001.
Dale Schuurmans, Finnegan Southey, and Robert C. Holte. The exponentiated subgradient algorithm for heuristic boolean programming. In IJCAI-01, 2001.
J. Slaney and T. Walsh. Backbones in optimization and approximation. In IJCAI-01, 2001.
W. Zhang. State-Space Search: Algorithms, Complexity, Extensions, and Applications. Springer, 1999.
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Leyton-Brown, K., Nudelman, E., Shoham, Y. (2002). Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_37
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DOI: https://doi.org/10.1007/3-540-46135-3_37
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