Abstract
In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability to combine complementary strengths of the two solution technologies. This research has reached a stage at which further development would benefit from a general-purpose modeling and solution system. We introduce here a system for integrated modeling and solution called SIMPL. Our approach is to view CP and OR techniques as special cases of a single method rather than as separate methods to be combined. This overarching method consists of an infer-relax-restrict cycle in which CP and OR techniques may interact at any stage. We describe the main features of SIMPL and illustrate its usage with examples.
This work has been supported by the National Science Foundation under grant ACI-0121497 and by the William Larimer Mellon Fellowship.
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
Balas, E.: Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89, 3–44 (1998)
Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling. Kluwer, Dordrecht (2001)
Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962)
Beringer, H., de Backer, B.: Combinatorial problem solving in constraint logic programming with cooperating solvers. In: Beierle, C., Plümer, L. (eds.) Logic Programming: Formal Methods and Practical Applications, Elsevier Science, Amsterdam (1995)
Berkelaar, M.: LP_SOLVE, Available from ftp://ftp.ics.ele.tue.nl/pub/lp_solve/
Bockmayr, A., Eisenbrand, F.: Combining logic and optimization in cutting plane theory. In: Kirchner, H., Ringeissen, C. (eds.) FroCos 2000. LNCS (LNAI), vol. 1794, pp. 1–17. Springer, Heidelberg (2000)
Bockmayr, A., Kasper, T.: Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing 10(3), 287–300 (1998)
Colombani, Y., Heipcke, S.: Mosel: An Overview. Dash Optimization (2002)
Dash Optimization. XPRESS-MP, http://www.dashoptimization.com
Eremin, A., Wallace, M.: Hybrid Benders decomposition algorithms in constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 1–15. Springer, Heidelberg (2001)
Focacci, F., Lodi, A., Milano, M.: Cost-based domain filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)
Focacci, F., Lodi, A., Milano, M.: Cutting planes in constraint programming: A hybrid approach. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 187–201. Springer, Heidelberg (2000)
Gutin, G., Punnen, A.P. (eds.): Traveling Salesman Problem and Its Variations. Kluwer, Dordrecht (2002)
Hooker, J.N.: Logic-Based Methods for Optimization. In: Wiley-Interscience Series in Discrete Mathematics and Optimization (2000)
Hooker, J.N.: Logic, optimization and constraint programming. INFORMS Journal on Computing 14(4), 295–321 (2002)
Hooker, J.N.: A framework for integrating solution methods. In: Bhargava, H.K., Ye, M. (eds.) Computational Modeling and Problem Solving in the Networked World, pp. 3–30. Kluwer, Dordrecht (2003); Plenary talk at the Eighth INFORMS Computing Society Conference (ICS)
Hooker, J.N.: Logic-based benders decomposition for planning and scheduling. GSIA, Carnegie Mellon University (2003) (manuscript)
Hooker, J.N., Osorio, M.A.: Mixed logical/linear programming. Discrete Applied Mathematics 96-97(1-3), 395–442 (1999)
Hooker, J.N., Ottosson, G.: Logic-based benders decomposition. Mathematical Programming 96, 33–60 (2003)
Hooker, J.N., Ottosson, G., Thorsteinsson, E., Kim, H.-J.: On integrating constraint propagation and linear programming for combinatorial optimization. In: Proceedings of the 16th National Conference on Artificial Intelligence, pp. 136–141. MIT Press, Cambridge (1999)
Hooker, J.N., Yan, H.: Logic circuit verification by Benders decomposition. In: Saraswat, V., Van Hentenryck, P. (eds.) Principles and Practice of Constraint Programming: The Newport Papers, pp. 267–288. MIT Press, Cambridge (1995)
Hooker, J.N., Yan, H.: A relaxation for the cumulative constraint. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 686–690. Springer, Heidelberg (2002)
ILOG S.A. The CPLEX mixed integer linear programming and barrier optimizer, http://www.ilog.com/products/cplex/
Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing 13(4), 258–276 (2001)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chichester (1985)
Leipert, S.: The tree interface version 1.0: A tool for drawing trees, Available at http://www.informatik.uni-koeln.de/old-ls_juenger/projects/vbctool.html
Milano, M., Ottosson, G., Refalo, P., Thorsteinsson, E.S.: The role of integer programming techniques in constraint programming’s global constraints. INFORMS Journal on Computing 14(4), 387–402 (2002)
Ottosson, G., Thorsteinsson, E.S., Hooker, J.N.: Mixed global constraints and inference in hybrid CLP-IP solvers. In: CP 1999 Post Conference Workshop on Large Scale Combinatorial Optimization and Constraints, pp. 57–78 (1999)
Refalo, P.: Tight cooperation and its application in piecewise linear optimization. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 375–389. Springer, Heidelberg (1999)
Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 369–383. Springer, Heidelberg (2000)
Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the National Conference on Artificial Intelligence, pp. 362–367 (1994)
Rodošek, R., Wallace, M., Hajian, M.T.: A new approach to integrating mixed integer programming and constraint logic programming. Annals of Operations Research 86, 63–87 (1999)
Thorsteinsson, E.S.: Branch-and-Check: A hybrid framework integrating mixed integer programming and constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 16–30. Springer, Heidelberg (2001)
Van Hentenryck, P.: The OPL Optimization Programming Language. MIT Press, Cambridge (1999)
Wallace, M., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12, 159–200 (1997)
Williams, H.P., Yan, H.: Representations of the all different predicate of constraint satisfaction in integer programming. INFORMS Journal on Computing 13(2), 96–103 (2001)
Yan, H., Hooker, J.N.: Tight representations of logical constraints as cardinality rules. Mathematical Programming 85, 363–377 (1999)
Yunes, T.H.: On the sum constraint: Relaxation and applications. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 80–92. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aron, I., Hooker, J.N., Yunes, T.H. (2004). SIMPL: A System for Integrating Optimization Techniques. In: Régin, JC., Rueher, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2004. Lecture Notes in Computer Science, vol 3011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24664-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-24664-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21836-4
Online ISBN: 978-3-540-24664-0
eBook Packages: Springer Book Archive