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SCIP: solving constraint integer programs
, 2009
"... Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), wh ..."
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Cited by 122 (0 self)
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Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and noncommercial use and can be downloaded in source code. This paper gives an overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs. To illustrate the performance and flexibility of SCIP, we apply it to two different problem classes. First, we consider mixed integer programming and show by computational experiments that SCIP is almost competitive to specialized commercial MIP solvers, even though SCIP supports the more general constraint integer programming paradigm. We develop new ingredients that improve current MIP solving technology. As a second application, we employ SCIP to solve chip design verification problems as they arise in the logic design of integrated circuits. This application goes far beyond traditional MIP solving, as it includes several highly nonlinear constraints, which can be handled nicely within the constraint integer programming framework. We show anecdotally how the different solving techniques from MIP, CP, and SAT work together inside SCIP to deal with such constraint classes. Finally, experimental results show that our approach outperforms current stateoftheart techniques for proving the validity of properties on circuits containing arithmetic.
An integrated solver for optimization problems
, 2009
"... One of the central trends in the optimization community over the past several years has been the steady improvement of generalpurpose solvers. A logical next step in this evolution is to combine mixed integer linear programming, constraint programming, and global optimization in a single system. Re ..."
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Cited by 9 (2 self)
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One of the central trends in the optimization community over the past several years has been the steady improvement of generalpurpose solvers. A logical next step in this evolution is to combine mixed integer linear programming, constraint programming, and global optimization in a single system. Recent research in the area of integrated problem solving suggests that the right combination of different technologies can simplify modeling and speed up computation substantially. Nevertheless, integration often requires special purpose coding, which is timeconsuming and errorprone. We present a general purpose solver, SIMPL, that allows its user to replicate (and sometimes improve on) the results of custom implementations with concise models written in a highlevel language. We apply SIMPL to production planning, product configuration, machine scheduling, and truss structure design problems on which customized integrated methods have shown significant computational advantage. We obtain results that either match or surpass the original codes at a fraction of the implementation effort. 1
B.: Constraint Programming and Combinatorial Optimisation in Numberjack
 Proceedings of CPAIOR 2010, LNCS
, 2010
"... Abstract. Python benefits from a large and active programming community. Numberjack is a modelling package written in Python for embedding constraint programming and combinatorial optimisation into larger applications. It has been designed to seamlessly and efficiently support a number of underlying ..."
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Abstract. Python benefits from a large and active programming community. Numberjack is a modelling package written in Python for embedding constraint programming and combinatorial optimisation into larger applications. It has been designed to seamlessly and efficiently support a number of underlying combinatorial solvers. Currently, Numberjack supports three constraint programming solvers, one MIP solver, and one satisfiability solver – all available as opensource software. This paper illustrates many of the features of Numberjack through the use of several combinatorial optimisation problems. We also demonstrate a cloudbased configurator built with Numberjack, using services provided by Google to support a userinterface and backend reasoning capabilities. 1
Integrating operations research in constraint programming
, 2010
"... This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear p ..."
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Cited by 7 (0 self)
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This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.
Extending a CIP framework to solve MIQCPs
, 2010
"... This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MILP and CP technologies, in particular for th ..."
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Cited by 6 (2 self)
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This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MILP and CP technologies, in particular for the linear relaxation and the discrete components of the problem. We use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints to relax the problem. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branchcutandprice framework SCIP. Computational experiments indicating the potential of the approach and evaluating the impact of the algorithmic components are provided.
P.J.: Half reification and flattening
 CP 2011, LNCS
, 2011
"... Abstract. Usually propagationbased constraint solvers construct a constraint network as a conjunction of constraints. They provide propagators for each form of constraint c. In order to increase expressiveness, systems also usually provide propagators for reified forms of constraints. A reified con ..."
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Abstract. Usually propagationbased constraint solvers construct a constraint network as a conjunction of constraints. They provide propagators for each form of constraint c. In order to increase expressiveness, systems also usually provide propagators for reified forms of constraints. A reified constraint b ↔ c associates a truth value b with a constraint c. With reified propagators, systems can express complex combinations of constraints using disjunction, implication and negation by flattening. In this paper we argue that reified constraints should be replaced by halfreified constraints of the form b → c. Halfreified constraints do not impose any extra burden on the implementers of propagators compared to unreified constraints, they can implement reified propagators without loss of propagation strength (assuming c is negatable), they extend automatically to global constraints, they simplify the handling of partial functions, and can allow flattening to give better propagation behavior. 1
MILP Software
"... This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose ..."
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Cited by 4 (0 self)
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This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose
Nonlinear pseudoboolean optimization: Relaxation or propagation?
 IN SAT 2009
, 2009
"... PseudoBoolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudoBoolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a lin ..."
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Cited by 4 (1 self)
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PseudoBoolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudoBoolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branchandcutandpropagate framework, resulting in an efficient nonlinear pseudoBoolean solver.
The polytope of contextfree grammar constraints
 INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS
, 2009
"... Contextfree grammar constraints enforce that a sequence of variables forms a word in a language defined by a contextfree grammar. The constraint has received a lot of attention in the last few years as it represents an effective and highly expressive modeling entity. Its application has been stud ..."
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Contextfree grammar constraints enforce that a sequence of variables forms a word in a language defined by a contextfree grammar. The constraint has received a lot of attention in the last few years as it represents an effective and highly expressive modeling entity. Its application has been studied in the field of Constraint Programming, Mixed Integer Programming, and SAT to solve complex decision problems such as shift scheduling. In this theoretical study we demonstrate how the constraint can be linearized efficiently. In particular, we propose a lifted polytope which has only integer extreme points. Based on this result, for shift scheduling problems we prove the equivalence of Dantzig’s original set covering model and a lately introduced grammarbased model.
Optimization Modulo Theories with Linear Rational Costs
 ACM Transactions on Computational Logics
, 2015
"... ar ..."