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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.
Constraint Integer Programming: a New Approach to integrate CP and MIP
, 2008
"... This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP ..."
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Cited by 34 (7 self)
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This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current stateoftheart commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.
SCIP  a framework to integrate Constraint and Mixed Integer Programming
, 2005
"... Constraint Programs and Mixed Integer Programs are closely related optimization problems originating from different scientific areas. Today’s stateoftheart algorithms of both fields have several strategies in common, in particular the branchandbound process to recursively divide the problem in ..."
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Cited by 33 (2 self)
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Constraint Programs and Mixed Integer Programs are closely related optimization problems originating from different scientific areas. Today’s stateoftheart algorithms of both fields have several strategies in common, in particular the branchandbound process to recursively divide the problem into smaller subproblems. On the other hand, the main techniques to process each subproblem are different, and it was observed that they have complementary strengths. We present the programming framework Scip that integrates techniques from both fields in order to exploit the strengths of both, Constraint Programming and Mixed Integer Programming. In contrast to other proposals of recent years to combine both fields, Scip does not focus on easy implementation and rapid prototyping, but is tailored towards expert users in need of full, indepth control and high performance.
A searchinferandrelax framework for integrating solution methods
 Computational Modeling and Problem Solving in the Networked World
, 2005
"... Abstract. We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL metho ..."
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Cited by 9 (4 self)
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Abstract. We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogoodbased methods, partialorder dynamic backtracking, various local search metaheuristics, and GRASPs (greedy randomized adaptive search procedures). The framework allows elements of different solution methods to be combined at will, resulting in a variety of integrated methods. These include continuous relaxations for global constraints, the linking of integer and constraint programming via Benders decomposition, constraint propagation in global optimization, relaxation bounds in local search and GRASPs, and many others. 1
Mixed Integer Programming vs. Logicbased Benders Decomposition for Planning and Scheduling ⋆
"... Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logicbased Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that describ ..."
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Cited by 2 (1 self)
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Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logicbased Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper. 1
Hybrid Modeling
"... The modeling practices of constraint programming (CP), artificial intelligence, and operations research must be reconciled and integrated if the computational benefits of combining their solution methods are to be realized in practice. This chapter focuses on CP and mixed integer/linear programming ..."
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The modeling practices of constraint programming (CP), artificial intelligence, and operations research must be reconciled and integrated if the computational benefits of combining their solution methods are to be realized in practice. This chapter focuses on CP and mixed integer/linear programming (MILP), in which modeling systems are most highly developed. It presents practical guidelines and supporting theory for the two types of modeling. It then suggests how an integrated modeling framework can be designed that retains, and even enhances, the modeling power of CP while allowing the full computational resources of both fields to be applied and combined. A series of examples are used to compare modeling practices in CP, MILP, and an integrated framework.
Automating Mathematical Program Transformations
 PADL 2010
, 2010
"... Mathematical programs (MPs) are a class of constrained optimization problems that include linear, mixedinteger, and disjunctive programs. Strategies for solving MPs rely heavily on various transformations between these subclasses, but most are not automated because MP theory does not presently tre ..."
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Cited by 2 (1 self)
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Mathematical programs (MPs) are a class of constrained optimization problems that include linear, mixedinteger, and disjunctive programs. Strategies for solving MPs rely heavily on various transformations between these subclasses, but most are not automated because MP theory does not presently treat programs as syntactic objects. In this work, we present the first syntactic definition of MP and of some widely used MP transformations, most notably the bigM and convex hull methods for converting disjunctive constraints. We use an embedded OCaml DSL on problems from chemical process engineering and operations research to compare our automated transformations to existing technology—finding that no one technique is always best—and also to manual reformulations—finding that our mechanizations are comparable to human experts. This work enables higherlevel solution strategies that can use these transformations as subroutines.
Operations Research Methods in Constraint Programming
"... A number of operations research (OR) methods have found their way into constraint programming (CP). This development is entirely natural, since OR and CP have similar goals. OR is essentially a variation on the scientific practice of mathematical modeling. It describes phenomena in a formal language ..."
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A number of operations research (OR) methods have found their way into constraint programming (CP). This development is entirely natural, since OR and CP have similar goals. OR is essentially a variation on the scientific practice of mathematical modeling. It describes phenomena in a formal language that allows one to deduce consequences in a rigorous way. Unlike a typical scientific model, however, an OR model has a prescriptive as well as a descriptive purpose. It represents a human activity with some freedom of choice, rather than a natural process. The laws of nature become constraints that the activity must observe, and the goal is to maximize some objective subject to the constraints. CP’s constraintoriented approach to problem solving poses a prescriptive modeling task very similar to that of OR. CP historically has been less concerned with finding optimal than feasible solutions, but this is a superficial difference. It is to be expected, therefore, that OR methods would find application in solving CP models. There remains a fundamental difference, however, in the way that CP and OR understand constraints. CP typically sees a constraint as a procedure, or at least as invoking a procedure, that operates on the solution space, normally by reducing variable domains.
Constraint Integer Programming: Techniques and Applications
, 2008
"... This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP ..."
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This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current stateoftheart commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.