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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 56 (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.
MALLBA: A library of skeletons for combinatorial optimisation
, 2002
"... The mallba project tackles the resolution of combinatorial optimization problems using algorithmic skeletons implemented in C++. MALLBA offers three families of generic resolution methods: exact,heuristic and hybrid. Moreover, for each resolution method, MALLBA provides three different implementatio ..."
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Cited by 18 (8 self)
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The mallba project tackles the resolution of combinatorial optimization problems using algorithmic skeletons implemented in C++. MALLBA offers three families of generic resolution methods: exact,heuristic and hybrid. Moreover, for each resolution method, MALLBA provides three different implementations: sequential, parallel for local area networks, and parallel for wide area networks (currently under development). This paper shows the architecture of the mallba library, presents some of its skeletons and offers several computational results to show the viability of the approach.
The ABACUS System for BranchandCutandPrice Algorithms in Integer Programming and Combinatorial Optimization
, 1998
"... The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms ..."
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Cited by 16 (0 self)
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The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an objectoriented software framework for branchandcutandprice algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses some difficulties in the implementation of branchandcutandprice algorithms for combinatorial optimization problems and shows how they are managed by ABACUS.
Design of Survivable Networks with Bounded Rings
, 2000
"... This dissertation is the result of a project funded by Belgacom, the Belgian telecommunication operator, dealing with the development of new models and optimization techniques for the longterm planning of the backbone network. The minimumcost twoconnected spanning network problem consists in find ..."
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Cited by 14 (4 self)
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This dissertation is the result of a project funded by Belgacom, the Belgian telecommunication operator, dealing with the development of new models and optimization techniques for the longterm planning of the backbone network. The minimumcost twoconnected spanning network problem consists in finding a network with minimal total cost for which there exist two nodedisjoint paths between every pair of nodes. This problem, arising from the need to obtain survivable communication and transportation networks, has been widely studied. In our model, the following constraint is added in order to increase the reliability of the network : each edge must belong to a cycle of length less than or equal to a given threshold value K. This condition ensures that when traffic between two nodes has to be redirected (e.g. in case of failure of an edge), we can limit the increase of the distance between these nodes. We investigate valid inequalities for this problem and provide numerical results obtai...
The Optimal Diversity Management Problem
 Operations Research
, 2004
"... In some industries, a certain part can be needed in a very large number of different configurations. This is the case, e.g., for the electrical wirings in european car factories. Fortunately, a given configuration can be replaced by a more complete, therefore also more expensive, one. The diversity ..."
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Cited by 13 (0 self)
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In some industries, a certain part can be needed in a very large number of different configurations. This is the case, e.g., for the electrical wirings in european car factories. Fortunately, a given configuration can be replaced by a more complete, therefore also more expensive, one. The diversity management problem consists in choosing an optimal set of some given number $k$ of configurations that will be produced, any non produced configuration being replaced by the cheapest produced one compatible with it. We model the problem as an integer linear program close to the one commonly used for the $k$median problem. Our aim is to solve those problems to optimality. The large scale instances we are interested in lead to difficult LP relaxations, which seem to be intractable by the best direct methods currently available. Most of this paper deals with the use of Lagrangean Relaxation to reduce the size of the problem in order to be able subsequently to solve it to optimality via classical integer optimization.
Parallel Branch and Cut for Capacitated Vehicle Routing
, 2002
"... Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy t ..."
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Cited by 12 (2 self)
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Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy to parallelize, achieving scalability can be a challenge. In more sophisticated variants, such as branch and cut, large amounts of data must be shared among the processors, resulting in increased parallel overhead. In this paper, we review the branch and cut algorithm for solving combinatorial optimization problems and describe the implementation of SYMPHONY, a library for implementing these algorithms in parallel. We then describe a solver for the vehicle routing problem that was implemented using SYMPHONY and analyze its parallel performance on a Beowulf cluster.
Exact and Memetic Algorithms for Two Network Design Problems
, 2004
"... This thesis focuses on two combinatorial optimization problems (COPs) that belong to the class of NPhard network design problems: The first one, vertex biconnectivity augmentation (V2AUG), appears in the design of survivable communication or electricity networks. In this problem we search for the s ..."
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Cited by 10 (4 self)
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This thesis focuses on two combinatorial optimization problems (COPs) that belong to the class of NPhard network design problems: The first one, vertex biconnectivity augmentation (V2AUG), appears in the design of survivable communication or electricity networks. In this problem we search for the set of connections of minimal total cost which, when added to an existing network, makes it survivable against failures of any single node. The second problem, the prizecollecting Steiner tree problem (PCST), describes a natural tradeoff between maximizing the sum of profits over all selected customers and minimizing the implementation costs, e.g. when designing a fiber optic or a district heating network. The available techniques for COPs can roughly be classified into two main categories: exact and heuristic algorithms. Exact algorithms are guaranteed to find an optimal solution and to prove its optimality for every instance of a COP. Due to sometimes exponential running times or memory requirements of exact algorithms we sometimes sacrifice the guarantee of finding optimal solutions for the sake of getting good solutions in a limited time and therefore use heuristic algorithms. This thesis provides tools that can solve given network design problems of respectable size to provable optimality. For fairly large instances, these tools obtain suboptimal,
The ring star problem: polyhedral analysis and exact algorithm
 NETWORKS
, 2004
"... In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cy ..."
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Cited by 9 (0 self)
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In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The problem has several applications in telecommunications network design and in rapid transit systems planning. It is an extension of the classical location–allocation problem introduced in the early 1960s, and closely related versions have been recently studied by several authors. This article formulates the problem as a mixedinteger linear program and strengthens it with the introduction of several families of valid inequalities. These inequalities are shown to be facetdefining and are used to develop a branchandcut algorithm. Computational results show that instances involving up to 300 vertices can be solved optimally using the proposed methodology.
Locating median cycles in networks
, 2005
"... In the median cycle problem the aim is to determine a simple cycle through a subset of vertices of a graph involving two types of costs: a routing cost associated with the cycle itself, and the cost of assigning vertices not on the cycle to visited vertices. The objective is to minimize the routing ..."
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Cited by 8 (0 self)
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In the median cycle problem the aim is to determine a simple cycle through a subset of vertices of a graph involving two types of costs: a routing cost associated with the cycle itself, and the cost of assigning vertices not on the cycle to visited vertices. The objective is to minimize the routing cost, subject to an upper bound on the total assignment cost. This problem arises in the location of a circularshaped transportation and telecommunication infrastructure. We present a mixed integer linear model, and strengthen it with the introduction of additional classes of nontrivial valid inequalities. Separation procedures are developed and an exact branchandcut algorithm is described. Computational results on instances from the classical TSP library and randomly generated ones confirm the efficiency of the proposed algorithm. An application related to the city of Milan (Italy) is also solved within reasonable computation time.
The design of the branchandcut system ABACUS
, 1997
"... The software system ABACUS is an objectoriented framework for the implementation of branchandcut and branchandprice algorithms. This paper describes the design of ABACUS including the design principles and the most important classes. ..."
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Cited by 6 (0 self)
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The software system ABACUS is an objectoriented framework for the implementation of branchandcut and branchandprice algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.