Abstract
We propose a new top down search-based algorithm for compiling AND/OR Multi-Valued Decision Diagrams (AOMDDs), as representations of the optimal set of solutions for constraint optimization problems. The approach is based on AND/OR search spaces for graphical models, state-of-the-art AND/OR Branch-and-Bound search, and on decision diagrams reduction techniques. We extend earlier work on AOMDDs by considering general weighted graphs based on cost functions rather than constraints. An extensive experimental evaluation proves the efficiency of the weighted AOMDD data structure.
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.
References
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transaction on Computers 35, 677–691 (1986)
Fargier, H., Vilarem, M.: Compiling CSPs into tree-driven automata for interactive solving. Constraints 9(4), 263–287 (2004)
Hadzic, T., Andersen, H.R.: A BDD-based polytime algorithm for cost-bounded interactive configuration. In: National Conference on Artificial Intelligence (AAAI 2006) (2006)
Hadzic, T., Hooker, J.: Cost-bounded binary decision diagrams for 0-1 programming. In: International Conference on Integration of AI and OR Techniques (CPAIOR 2007) (2007)
Dechter, R., Mateescu, R.: AND/OR search spaces for graphical models. Artificial Intelligence 171, 73–106 (2007)
Marinescu, R., Dechter, R.: AND/OR branch-and-bound for graphical models. In: International Joint Conferences on Artificial Intelligence (IJCAI 2005), pp. 224–229 (2005)
Mateescu, R., Dechter, R.: Compiling constraint networks into AND/OR multi-valued decision diagrams (AOMDDs). In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 329–343. Springer, Heidelberg (2006)
Freuder, E.C., Quinn, M.J.: Taking advantage of stable sets of variables in constraint satisfaction problems. In: International Joint Conferences on Artificial Intelligence (IJCAI 1985), pp. 1076–1078 (1985)
Bayardo, R., Miranker, D.: A complexity analysis of space-bound learning algorithms for the constraint satisfaction problem. In: National Conference on Artificial Intelligence (AAAI 1996), pp. 298–304 (1996)
Marinescu, R., Dechter, R.: Memory intensive branch-and-bound search for graphical models. In: National Conference on Artificial Intelligence (AAAI 2006) (2006)
Marinescu, R., Dechter, R.: Best-first AND/OR search for graphical models. In: National Conference on Artificial Intelligence (AAAI 2007) (2007)
Bistarelli, S., Montanari, U., Rossi, F.: Semiring based constraint solving and optimization. Journal of ACM 44, 309–315 (1997)
Nemhauser, G., Wolsey, L.: Integer and combinatorial optimization. Wiley, Chichester (1988)
Bensana, E., Lemaitre, M., Verfaillie, G.: Earth observation satellite management. Constraints 4, 293–299 (1999)
Marinescu, R., Dechter, R.: AND/OR branch-and-bound search for pure 0/1 integer linear programming problems. In: International Conference on Integration of AI and OR Techniques (CPAIOR 2006), pp. 152–166 (2006)
Dantzig, G.: Maximization of a linear function of variables subject to linear inequalities. Activity Analysis of Production and Allocation (1951)
Leyton-Brown, K., Pearson, M., Shoham, Y.: Towards a universal test suite for combinatorial auction algorithms. ACM Electronic Commerce, 66–76 (2000)
Joy, S., Mitchell, J., Borchers, B.: A branch and cut algorithm for max-SAT and weighted max-SAT. Satisfiability Problem: Theory and Applications, 519–536 (1997)
de Givry, S., Larrosa, J., Schiex, T.: Solving max-SAT as weighted CSP. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mateescu, R., Marinescu, R., Dechter, R. (2007). AND/OR Multi-valued Decision Diagrams for Constraint Optimization. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)