Abstract
We study the automatic generation of primal and dual bounds from decision diagrams in constraint programming. In particular, we expand the functionality of the Haddock system to optimization problems by extending its specification language to include an objective function. We describe how restricted decision diagrams can be compiled in Haddock similar to the existing relaxed decision diagrams. Together, they provide primal and dual bounds on the objective function, which can be seamlessly integrated into the constraint programming search. The entire process is automatic and only requires a high-level user model specification. We evaluate our method on the sequential ordering problem and compare the performance of Haddock to a dedicated decision diagram approach. The results show that Haddock achieves comparable results in similar time, demonstrating the viability of our automated decision diagram procedures for constraint optimization problems.
Laurent Michel—Synchrony Chair in Cybersecurity.
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
Similar content being viewed by others
Notes
- 1.
For a maximization, \(U^\downarrow (s_\top )\) and \(U^\uparrow (s_\bot )\) give the upper bound.
- 2.
With a slight abuse of notation as we do not repeat the bounds on z and among since those properties are identical.
- 3.
Source code located at https://github.com/IsaacRudich/PnB_SOP.
References
Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. J. Math. Comput. Model. 20(12), 97–123 (1994)
Bergman, D., Cire, A.A., Van Hoeve, W.-J., Hooker, J.: Decision Diagrams for Optimization, vol. 1. Springer, Cham (2016)
Bergman, D., Cire, A.A., van Hoeve, W.-J., Hooker, J.N.: Discrete optimization with decision diagrams. INFORMS J. Comput. 28(1), 47–66 (2016)
Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: Proceedings of the 16th European Conference on Artificial Intelligence, ECAI 2004, pp. 146–150, NLD, August 2004. IOS Press (2004)
Fischetti, M., Glover, F. Lodi, A.: The feasibility pump. Math. Program. 104(1), 91–104 (2005). https://doi.org/10.1007/s10107-004-0570-3
Gentzel, R., Michel, L., van Hoeve, W.-J.: HADDOCK: a language and architecture for decision diagram compilation. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 531–547. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58475-7_31
Gentzel, R., Michel, L., van Hoeve, W.-J.: Heuristics for MDD propagation in HADDOCK. In: 28th International Conference on Principles and Practice of Constraint Programming (CP 2022), vol. 235 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 24:1–24:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
Gillard, X., Coppé, V., Schaus, P., Cire, A.A.: Improving the filtering of branch-and-bound MDD solver. In: Stuckey, P.J. (ed.) CPAIOR 2021. LNCS, vol. 12735, pp. 231–247. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78230-6_15
Pesant, G., Quimper, C., Zanarini, A.: Counting-based search: branching heuristics for constraint satisfaction problems. J. Artif. Intell. Res. 43, 173–210 (2012). https://doi.org/10.1613/jair.3463
Hoda, S., van Hoeve, W.-J., Hooker, J.N.: A systematic approach to MDD-based constraint programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 266–280. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15396-9_23
Keller, R.M.: Formal verification of parallel programs. Commun. ACM 19(7), 371–384 (1976)
Michel, L., Schaus, P., Van Hentenryck, P.: MiniCP: a lightweight solver for constraint programming. Math. Program. Comput. 13, 133–184 (2021)
Michel, L., Van Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29828-8_15
Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_41
Reinelt, G.: TSPLIB-a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)
Rudich, I., Cappart, Q., Rousseau, L.M.: Peel-and-bound: generating stronger relaxed bounds with multivalued decision diagrams. In: 28th International Conference on Principles and Practice of Constraint Programming (CP 2022), vol. 235 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 35:1–35:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
Van Hentenryck, P., Perron, L., Puget, J.F.: Search and Strategies in OPL. ACM Trans. Comput. Logic 1(2), 1–36 (2000)
Acknowledgements
Laurent Michel and Rebecca Gentzel were partially supported by Synchrony. Willem-Jan van Hoeve is partially supported by Office of Naval Research Grant No. N00014-21-1-2240 and National Science Foundation Award #1918102.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Gentzel, R., Michel, L., van Hoeve, WJ. (2023). Optimization Bounds from Decision Diagrams in Haddock. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-33271-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-33270-8
Online ISBN: 978-3-031-33271-5
eBook Packages: Computer ScienceComputer Science (R0)