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On the Reification of Global Constraints
 CONSTRAINTS
"... We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of total function constraints together with a constraint that can be easily reified. ..."
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We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of total function constraints together with a constraint that can be easily reified.
MiniZinc with Functions
"... Abstract. Functional relations are ubiquitous in combinatorial problems – the Global Constraint Catalog lists 120 functional constraints. This paper argues that the ability to express functional constraints with functional syntax leads to more elegant and readable models, and that it enables a bette ..."
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Abstract. Functional relations are ubiquitous in combinatorial problems – the Global Constraint Catalog lists 120 functional constraints. This paper argues that the ability to express functional constraints with functional syntax leads to more elegant and readable models, and that it enables a better translation of the models to different underlying solving technologies such as CP, MIP, or SAT. Yet, most modelling languages only support builtin functions, such as arithmetic, Boolean, or array access operations. Custom, userdefined functions are either not catered for at all, or they have an adhoc implementation without a useful semantics in Boolean contexts and not exploiting potential optimisations. This paper develops a translation from MiniZinc with userdefined functions to FlatZinc. The translation respects the relational semantics of MiniZinc, correctly dealing with partial functions in arbitrary Boolean contexts. At the same time, it takes advantage of the full potential of common subexpression elimination. 1
Explaining TimeTableEdgeFinding Propagation for the Cumulative Resource Constraint
"... Abstract. Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource co ..."
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Abstract. Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. Timetableedgefinding propagators are a recent development in cumulative propagators, that combine the current resource profile (timetable) during the edgefinding propagation. The current state of the art for solving scheduling and cutting problems involving cumulative constraints are lazy clause generation solvers, i.e., constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop a timetableedgefinding propagator for cumulative that explains its propagations. We give results using this propagator in a lazy clause generation system on resourceconstrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we are able to improve the lower bound of about 60 % of the remaining open instances, and close 6 open instances. 1
Reifying Global Constraints
, 2012
"... Global constraints were introduced two decades ago as a means to model some core aspects of combinatorial problems with one single constraint for which an efficient domain filtering algorithm can be provided, possibly using a complete change of representation. However, global constraints are just c ..."
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Global constraints were introduced two decades ago as a means to model some core aspects of combinatorial problems with one single constraint for which an efficient domain filtering algorithm can be provided, possibly using a complete change of representation. However, global constraints are just constraint schemas on which one would like to apply usual constraint operations such as reification, i.e. checking entailment, disentailment and negating the constraint. This is currently not the case in stateoftheart tools and was not considered in the global constraint catalog until recently. In this paper, we propose a general framework for reifying global constraints and apply it to some important constraints of the catalog, such as the cumulative constraint for instance. We show that several global constraints that were believed to be hard to negate can in fact be efficiently negated, and that entailment and disentailment can be efficiently tested. We also point out some new global constraints that are worth studying from this point of view and provide some performance figures obtained with an implementation in Choco.
Unsatisfiable Cores for Constraint Programming
"... Abstract. Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for softconstraint optimization problems in which the soft co ..."
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Abstract. Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for softconstraint optimization problems in which the soft constraints are mostly satisfied. Unsatisfiablecore approaches to solving soft constraint problems in Boolean Satisfiability (e.g. MAXSAT) force all soft constraints to hold initially. When solving fails they return an unsatisfiable core, as a set of soft constraints that cannot hold simultaneously. Using this information the problem is relaxed to allow certain soft constraint(s) to be violated and solving continues. Since Lazy Clause Generation (LCG) solvers can also return unsatisfiable cores we can adapt the MAXSAT unsatisfiable core approach to CP. We implement the original MAXSAT unsatisfiable core solving algorithms Wpm1, Msu3 in a stateoftheart LCG solver and show that there exist problems which benefit from this hybrid approach. 1