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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.
Integerprogramming software systems
, 2004
"... Recent developments in integer–programming software systems have tremendously improved our ability to solve large–scale instances. We review the major algorithmic components of state–of–the–art solvers and discuss the options available to users to adjust the behavior of these solvers when default s ..."
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Cited by 37 (0 self)
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Recent developments in integer–programming software systems have tremendously improved our ability to solve large–scale instances. We review the major algorithmic components of state–of–the–art solvers and discuss the options available to users to adjust the behavior of these solvers when default settings do not achieve the desired performance level. Furthermore, we highlight advances towards integrated modeling and solution environments. We conclude with a discussion of model characteristics and substructures that pose challenges for integer–programming software systems and a perspective on features we may expect to see in these systems in the near future.
Noncommercial Software for MixedInteger Linear Programming
, 2004
"... We present an overview of noncommercial software tools for the solution of mixedinteger linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open s ..."
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Cited by 24 (1 self)
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We present an overview of noncommercial software tools for the solution of mixedinteger linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open source or other noncommercial licenses. Each package is categorized as a black box solver, a callable library, a solver framework, or some combination of these. The distinguishing features of all eight packages are described. The paper concludes with case studies that illustrate the use of two of the solver frameworks to develop custom solvers for specific problem classes and with benchmarking of the six black box solvers.
A Unified View on Hybrid Metaheuristics
, 2006
"... Abstract. Manifold possibilities of hybridizing individual metaheuristics with each other and/or with algorithms from other fields exist. A large number of publications documents the benefits and great success of such hybrids. This article overviews several popular hybridization approaches and class ..."
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Cited by 17 (3 self)
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Abstract. Manifold possibilities of hybridizing individual metaheuristics with each other and/or with algorithms from other fields exist. A large number of publications documents the benefits and great success of such hybrids. This article overviews several popular hybridization approaches and classifies them based on various characteristics. In particular with respect to lowlevel hybrids of different metaheuristics, a unified view based on a common pool template is described. It helps in making similarities and different key components of existing metaheuristics explicit. We then consider these key components as a toolbox for building new, effective hybrid metaheuristics. This approach of thinking seems to be superior to sticking too strongly to the philosophies and historical backgrounds behind the different metaheuristic paradigms. Finally, particularly promising possibilities of combining metaheuristics with constraint programming and integer programming techniques are highlighted. 1
Improving the Feasibility Pump
 DISCRETE OPTIMIZATION, SPECIAL ISSUE
, 2005
"... The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco [8, 7] has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modificati ..."
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Cited by 17 (3 self)
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The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco [8, 7] has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modification of the algorithm in order to find better solutions. Extensive computational results show the success of this variant: in 89 out of 121 MIP instances the modified version produces improved solutions in comparison to the original Feasibility Pump.
A Tutorial on Variable Neighborhood Search
 LES CAHIERS DU GERAD, HEC MONTREAL AND GERAD
, 2003
"... Variable Neighborhood Search (VNS) is a recent metaheuristic, or framework for building heuristics, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. In this tutorial we first present the ingre ..."
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Cited by 16 (3 self)
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Variable Neighborhood Search (VNS) is a recent metaheuristic, or framework for building heuristics, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. In this tutorial we first present the ingredients of VNS, i.e., Variable Neighborhood Descent (VND) and Reduced VNS (RVNS) followed by the basic and then the general scheme of VNS itself which contain both of them. Extensions are presented, in particular Skewed VNS (SVNS) which enhances exploration of far away valleys and Variable Neighborhood Decomposition Search (VNDS), a twolevel scheme for solution of large instances of various problems. In each case, we present the scheme, some illustrative examples and questions to be addressed in order to obtain an efficient implementation.
A good recipe for solving MINLPs.
 Hybridizing metaheuristics and mathematical programming, volume 10 of Annals of Information Systems,
, 2009
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Feasibility pump 2.0
, 2008
"... Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequ ..."
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Cited by 13 (1 self)
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Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found. In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics. In particular, we investigate the use of a divinglike procedure based on rounding and constraint propagation— a basic tool in Constraint Programming. Extensive computational results on binary and general integer MIPs from the literature show that the new approach produces a substantial improvement of the FP success rate, without slowingdown the method and with a significantly better quality of the feasible solutions found.
Branching on General Disjunctions
 MATHEMATICAL PROGRAMMING
, 2005
"... This paper considers a modification of the branchandcut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploit ..."
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Cited by 10 (2 self)
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This paper considers a modification of the branchandcut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploits the relation between branching disjunctions and intersection cuts. In this work, we focus on disjunctions defining the mixed integer Gomory cuts at an optimal basis of the linear programming relaxation. The procedure is tested on instances from the literature. Experiments show that, for a majority of the instances, the enumeration tree obtained by branching on these general disjunctions has a smaller size than the tree obtained by branching on variables, even when variable branching is performed using full strong branching.