Abstract
Counting-based branching heuristics in CP have been very successful on a number of problems. Among the few remaining hurdles limiting their general applicability are the integration of counting information from auxiliary variables and the ability to handle combinatorial optimization problems. This paper proposes to answer these challenges by generalizing existing solution counting algorithms for constraints and by relaying counting information to the main branching variables through augmented element constraints. It offers more easily comparable solution counting information on variables and stronger back-propagation from the objective function in optimization problems. We provide supporting experimental results for the Capacitated Facility Location Problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Holmberg, K., Ronnqvist, M., Yuan, D.: An exact algorithm for the capacitated facility location problems with single sourcing. European Journal of Operational Research 113(3), 544–559 (1999)
Pesant, G., Quimper, C.-G.: Counting Solutions of Knapsack Constraints. In: Perron, L., Trick, M.A. (eds.) CPAIOR 2008. LNCS, vol. 5015, pp. 203–217. Springer, Heidelberg (2008)
Trick, M.A.: A dynamic programming approach for consistency and propagation for knapsack constraints. Annals of Operations Research 118, 73–84 (2003)
Walsh, T.: Search in a small world. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 1999, pp. 1172–1177. Morgan Kaufmann Publishers Inc., San Francisco (1999)
Zanarini, A., Pesant, G.: Solution Counting Algorithms for Constraint-Centered Search Heuristics. Constraints 14, 392–413 (2009)
Zanarini, A., Pesant, G.: More Robust Counting-Based Search Heuristics with Alldifferent Constraints. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 354–368. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pesant, G., Zanarini, A. (2011). Recovering Indirect Solution Densities for Counting-Based Branching Heuristics. In: Achterberg, T., Beck, J.C. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2011. Lecture Notes in Computer Science, vol 6697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21311-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-21311-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21310-6
Online ISBN: 978-3-642-21311-3
eBook Packages: Computer ScienceComputer Science (R0)