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22
A Unifying Framework for Integer and Finite Domain Constraint Programming
, 1997
"... We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capab ..."
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Cited by 35 (2 self)
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We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capabilities. We introduce symbolic constraint abstractions into integer programming. Finally, we discuss possible combinations of the two approaches.
Karmarkar's Algorithm and Combinatorial Optimization Problems
, 1988
"... Branchandcut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branchandcut method can be tailored to a specific integer programming problem, and how families of general cutting pla ..."
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Cited by 34 (6 self)
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Branchandcut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branchandcut method can be tailored to a specific integer programming problem, and how families of general cutting planes can be used to solve a wide variety of problems. Other important aspects of successful implementations are discussed in this chapter. The area of branchandcut algorithms is constantly evolving, and it promises to become even more important with the exploitation of faster computers and parallel computing. 1
Branch and infer: a unifying framework for integer and finite domain constraint programming
 INFORMS J. Comput
, 1998
"... We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer program ..."
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Cited by 27 (2 self)
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We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer programming, and to discuss possible combinations of the two approaches. C ombinatorial problems are ubiquitous in many real world applications like scheduling, planning, transportation, assignment, and many others. Besides special purpose algorithms to compute exact or approximate solutions, there exist also general approaches to solve this kind of problem. We are interested here in two such approaches: • Integer linear programming (ILP) • Finite domain constraint programming (CP(FD)) Integer linear programming has a long tradition in operations research and has produced a large number of impressive results during the last 40 years, see for example [37, 30]. Finite domain constraint programming is a promising new approach for solving complex combinatorial problems, which combines recent progress in programming language design, like constraint logic programming[29] or concurrent constraint programming,[42] with efficient constraint solving techniques from mathematics, artificial intelligence, and operations research, see for example [49, 50]. The aim of this paper is to develop a unifying framework for integer linear programming and finite domain constraint programming. On the one hand, we want to clarify the relationship between these two approaches and identify (some of) their strengths and weaknesses. On the other hand, we want to show how each of the two approaches may profit from the other and indicate possible ways towards their integration. This continues our previous work in
A polyhedral approach to sequence alignment problems
 DISCRETE APPL. MATH
, 2000
"... We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branchandcut algorithms. The Generalized Maximum Trace formulation captures several forms of multiple sequence alignment problems in a common framewo ..."
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Cited by 21 (1 self)
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We study two new problems in sequence alignment both from a practical and a theoretical view, using tools from combinatorial optimization to develop branchandcut algorithms. The Generalized Maximum Trace formulation captures several forms of multiple sequence alignment problems in a common framework, among them the original formulation of Maximum Trace. The RNA Sequence Alignment Problem captures the comparison of RNA molecules on the basis of their primary sequence and their secondary structure. Both problems have a characterization in terms of graphs which we reformulate in terms of integer linear programming. We then study the polytopes (or convex hulls of all feasible solutions) associated with the integer linear program for both problems. For each polytope we derive several classes of facetdefining inequalities and show that for some of these classes the corresponding separation problem can be solved in polynomial time. This leads to a polynomial time algorithm for pairwise sequence alignment that is not based on dynamic programming. Moreover, for multiple sequences the branchandcut algorithms for both sequence alignment problems are able to solve to optimality instances that are beyond the range of present dynamic programming approaches.
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 17 (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.
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
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Cited by 16 (9 self)
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Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.
A BranchandCut Approach to Physical Mapping of Chromosomes By Unique EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered ..."
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Cited by 14 (5 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 5276, 1995) first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness...
A BranchandCut Approach to Physical Mapping With EndProbes
, 1997
"... A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model o ..."
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Cited by 12 (0 self)
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A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig [AKWZ94] first considered a maximumlikelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics. We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the welldeveloped tools of integer linearprogramming and branchandcut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively...