Abstract
Option types are a powerful abstraction that allows the concise modelling of combinatorial problems where some decisions are relevant only if other decisions are made. They have a wide variety of uses: for example in modelling optional tasks in scheduling, or exceptions to a usual rule. Option types represent objects which may or may not exist in the constraint problem being modelled, and can take an ordinary value or a special value ⊤ indicating they are absent. The key property of variables of option types is that if they take the value ⊤ then the constraints they appear in should act as if the variable was not in the original definition. In this paper, we explore the different ways that basic constraints can be extended to handle option types, and we show that extensions of global constraints to option types cover existing and common variants of these global constraints. We demonstrate how we have added option types to the constraint modelling language MiniZinc. Constraints over variables of option types can either be handled by transformation into regular variables without extending the requirements on underlying solvers, or they can be passed directly to solvers that support them natively.
NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council. The first author was sponsored by the Australian Research Council grant DP110102258.
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
Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Global constraint catalogue: Past, present and future. Constraints 12(1), 21–62 (2007)
Bochvar, D., Bergmann, M.: On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus. History and Philosophy of Logic 2, 87–112 (1981)
Caballero, R., Stuckey, P.J., Tenoria-Fornes, A.: Finite type extensions in constraint programming. In: Schrijvers, T. (ed.) PPDP 2013, pp. 217–228. ACM Press (2013)
Castro, C., Manzano, S.: Variable and value ordering when solving balanced academic curriculum problems (2001), http://arxiv.org/abs/cs/0110007
Feydy, T., Stuckey, P.J.: Lazy clause generation reengineered. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 352–366. Springer, Heidelberg (2009)
Frisch, A.M., Stuckey, P.J.: The proper treatment of undefinedness in constraint languages. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 367–382. Springer, Heidelberg (2009)
Frisch, A.M., Harvey, W., Jefferson, C., Hernández, B.M., Miguel, I.: Essence: A constraint language for specifying combinatorial problems. Constraints 13(3), 268–306 (2008)
Geller, F., Veksler, M.: Assumption-based pruning in conditional CSP. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 241–255. Springer, Heidelberg (2005)
van Hoeve, W.J., Régin, J.C.: Open constraints in a closed world. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 244–257. Springer, Heidelberg (2006)
Kleene, S.C.: Introduction to Metamathematics. North Holland (1952)
Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: Wilson, D.C., Lane, H.C. (eds.) FLAIRS 2008, pp. 555–560. AAAI Press (2008)
Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: Reasoning with conditional time-intervals part II: An algebraical model for resources. In: Lane, H.C., Guesgen, H.W. (eds.) FLAIRS 2009, pp. 201–206. AAAI Press (2009)
Mittal, S., Falkenhainer, B.: Dynamic constraint satisfaction problems. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 25–32 (1990)
Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: Towards a standard CP modelling language. In: Bessiere, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)
Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)
Sabin, M., Freuder, E.C., Wallace, R.J.: Greater efficiency for conditional constraint satisfaction. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 649–663. Springer, Heidelberg (2003)
Schutt, A., Feydy, T., Stuckey, P.J.: Scheduling optional tasks with explanation. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 628–644. Springer, Heidelberg (2013)
Łukasiewicz, J.: On three-valued logic. In: Borkowski, L. (ed.) Selected works by Jan Łukasiewicz, pp. 87–88. North Holland (1970)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Mears, C., Schutt, A., Stuckey, P.J., Tack, G., Marriott, K., Wallace, M. (2014). Modelling with Option Types in MiniZinc. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-07046-9_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07045-2
Online ISBN: 978-3-319-07046-9
eBook Packages: Computer ScienceComputer Science (R0)