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Algorithms for hybrid MILP/CP models for a class of optimization problems
 INFORMS Journal on Computing
, 2001
"... The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered ..."
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Cited by 66 (11 self)
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The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have nonzero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CPbased branchandbound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the leastcost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILPCP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.
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 53 (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 Programming Based Column Generation with Knapsack Subproblems
 Journal of Heuristics
, 1999
"... . We present how to apply Constraint Based Column Generation to a large class of subproblems, namely Constrained Knapsack Problems (CKP). They evolve e.g. from Cutting Stock Problems (see [7]) with additional constraints on the cutting patterns. Focussing on Constrained Knapsack Problems, we deve ..."
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Cited by 42 (16 self)
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. We present how to apply Constraint Based Column Generation to a large class of subproblems, namely Constrained Knapsack Problems (CKP). They evolve e.g. from Cutting Stock Problems (see [7]) with additional constraints on the cutting patterns. Focussing on Constrained Knapsack Problems, we developed a new reduction algorithm for KP. It is being used as propagation routine for the CKP with O(n log n) preprocessing time and O(n) time per call. This sums up to an amortized time of O(n) for (log n) calls. Keywords: Constrained Based Column Generation, Constrained Knapsack Problems, Cutting Stock Problems, Reduction Algorithms. 1 Introduction Recently, a new framework for the integration of CP and OR within column generation approaches was developed, the so called Constraint Based Column Generation [11]. It describes a generic way of how to treat arbitrary constraints for the constrained subproblem in the column generation phase. The approach has been successfully used for the C...
On Integrating Constraint Propagation and Linear Programming for Combinatorial Optimization
, 2000
"... Integer programming and constraint (logic) programming are two traditional techniques for solving combinatorial optimization problems; the former based on linear programming relaxations and the latter on constraint propagation. Attempts to combine them have mainly focused on incorporating either ..."
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Cited by 36 (10 self)
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Integer programming and constraint (logic) programming are two traditional techniques for solving combinatorial optimization problems; the former based on linear programming relaxations and the latter on constraint propagation. Attempts to combine them have mainly focused on incorporating either technique into the framework of the other traditional models have been left intact. We argue that a rethinking of our modeling traditions is necessary to achieve the greatest benet of such an integration. We propose a declarative modeling framework in which the structure of the constraints indicates how LP and CP can interact to solve the problem. 1 Introduction Linear programming (LP) and constraint propagation (CP) are two complementary techniques with potential for integration to benet the solution of combinatorial optimization problems. Integer programming (IP) has been successfully applied to a range of problems, such as capital budgeting, bin packing and traveling salesman pr...
A Scheme for Unifying Optimization and Constraint Satisfaction Methods
, 2000
"... Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search a ..."
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Cited by 32 (5 self)
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Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities, the duality of search and inference and the duality of strengthening and relaxation. Optimization as well as constraint satisfaction methods can be seen as exploiting these dualities in their respective ways. Our proposal is that rather than employ either type of method exclusively, one can focus on how these dualities can be exploited in a given problem class. The resulting algorithm is likely to contain elements from both optimization and constraint satisfaction, and perhaps new methods that belong to neither.
BranchandCheck: A Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming
, 2001
"... We present BranchandCheck, a hybrid framework integrating Mixed Integer Programming and Constraint Logic Programming, which encapsulates the traditional Benders Decomposition and BranchandBound as special cases. In particular we describe its relation to Benders and the use of nogoods and linear ..."
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Cited by 27 (0 self)
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We present BranchandCheck, a hybrid framework integrating Mixed Integer Programming and Constraint Logic Programming, which encapsulates the traditional Benders Decomposition and BranchandBound as special cases. In particular we describe its relation to Benders and the use of nogoods and linear relaxations. We give two examples of how problems can be modelled and solved using BranchandCheck and present computational results demonstrating more than orderofmagnitude speedup compared to previous approaches. We also mention important future research issues such as hierarchical, dynamic and adjustable linear relaxations.
SCIP  a framework to integrate constraint and mixed integer programming
, 2004
"... 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 int ..."
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Cited by 24 (1 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.
Mixed Global Constraints and Inference in Hybrid CLPIP Solvers
, 2001
"... The complementing strengths of Constraint (Logic) Programming (CLP) and Mixed Integer Programming (IP) have recently received signicant attention. Although various optimization and constraint programming packages at a rst glance seem to support mixed models, the modeling and solution techniques ..."
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Cited by 16 (8 self)
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The complementing strengths of Constraint (Logic) Programming (CLP) and Mixed Integer Programming (IP) have recently received signicant attention. Although various optimization and constraint programming packages at a rst glance seem to support mixed models, the modeling and solution techniques encapsulated are still rudimentary. Apart from exchanging bounds for variables and objective, little is known of what constitutes a good hybrid model and how a hybrid solver can utilize the complementary strengths of inference and relaxations. This paper adds to the eld by identifying constraints as the essential link between CLP and IP and introduces an algorithm for bidirectional inference through these constraints. Together with new search strategies for hybrid solvers and cutgenerating mixed global constraints, solution speed is improved over both traditional IP codes and newer mixed solvers. Keywords: Mixed Integer Programming, Constraint Logic Programming, Integration, Mixed Global Contraints, Dynamic Linear Relaxations, Inference. AMS Subject classication: 68N99,68Q99,68T99,90C05,90C11,90C27. 1.
Augmenting Disjunctive Temporal Problems with FiniteDomain Constraints
 In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI2005
, 2005
"... We present a general framework for augmenting instances of the Disjunctive Temporal Problem (DTP) with finitedomain constraints. In this new formalism, the bounds of the temporal constraints become conditional on the finitedomain assignment. This hybridization makes it possible to reason simultane ..."
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Cited by 13 (5 self)
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We present a general framework for augmenting instances of the Disjunctive Temporal Problem (DTP) with finitedomain constraints. In this new formalism, the bounds of the temporal constraints become conditional on the finitedomain assignment. This hybridization makes it possible to reason simultaneously about temporal relationships between events as well as their nontemporal properties. We provide a special case of this hybridization that allows reasoning about a limited form of spatial constraints; namely, the travel time induced by the locations of a set of activities. We develop a leastcommitment algorithm for efficiently finding solutions to this combined constraint system and provide empirical results demonstrating the effectiveness of our approach.
Network Flow Problems in Constraint Programming
"... We introduce a new global constraint for modeling and solving network flow problems in constraint programming. We describe the declarative and operational semantics of the flow constraint and illustrate its use through a number of applications. ..."
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Cited by 11 (1 self)
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We introduce a new global constraint for modeling and solving network flow problems in constraint programming. We describe the declarative and operational semantics of the flow constraint and illustrate its use through a number of applications.