Abstract
In a classical constrained optimization problem, the logical relationship among the constraints is normally the logical conjunction. However, in many real applications, the relationship among the constraints might be more complex. This paper investigates a generalized class of optimization problems whose constraints are connected by various kinds of logical operators in addition to conjunction. Such optimization problems have been rarely studied in literature in contrast to the classical ones. A framework which integrates classical optimization procedures into the DPLL(T) architecture for solving Satisfiability Modulo Theories (SMT) problems is proposed. Two novel techniques for improving the solving efficiency w.r.t. linear arithmetic theory are also presented. Experiments show that the proposed techniques are quite effective.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Barrett, C.W., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007), http://www.cs.nyu.edu/acsys/cvc3
Cheng, K.C., Yap, R.H.C.: Search space reduction and Russian doll search. In: Proceedings of the 22nd AAAI Conference on Artificial Intelligence (AAAI 2007) (2007)
Cimatti, A., Franzén, A., Griggio, A., Sebastiani, R., Stenico, C.: Satisfiability Modulo the Theory of Costs: Foundations and Applications. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 99–113. Springer, Heidelberg (2010)
Dutertre, B., de Moura, L.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006), http://yices.csl.sri.com/
Eén, N., Sorensson, N.: The MiniSat Page (2011), http://minisat.se/
Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast Decision Procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)
Hooker, J.N.: Logic, optimization, and constraint programming. INFORMS Journal on Computing 14, 295–321 (2002)
IBM. Cplex, http://www-01.ibm.com/software/integration/optimization/cplex-optimization-studio/
Hooker, J.N., Osorio, M.A.: Mixed logical-linear programming. Discrete Appl. Math. 96-97, 395–442 (October 1999)
Kroening, D., Strichman, O.: Decision Procedures. Springer (2008)
Ma, F., Liu, S., Zhang, J.: Volume Computation for Boolean Combination of Linear Arithmetic Constraints. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 453–468. Springer, Heidelberg (2009)
de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008), http://research.microsoft.com/projects/z3/index.html
Nieuwenhuis, R., Oliveras, A.: On SAT Modulo Theories and Optimization Problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, F., Yan, J., Zhang, J. (2012). Solving Generalized Optimization Problems Subject to SMT Constraints. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-29700-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29699-4
Online ISBN: 978-3-642-29700-7
eBook Packages: Computer ScienceComputer Science (R0)