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18
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 32 (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 31 (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
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 20 (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.
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 15 (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...
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 14 (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.
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 14 (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.
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 10 (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...
Integer Programming
 In Algorithms and Theory of Computation Handbook
, 1998
"... Integer programming is an expressive framework for modeling and solving discrete optimization problems that arise in a variety of contexts in the engineering sciences. Integer programming representations work with implicit algebraic constraints (linear equations and inequalities on integer valued ..."
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Cited by 7 (0 self)
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Integer programming is an expressive framework for modeling and solving discrete optimization problems that arise in a variety of contexts in the engineering sciences. Integer programming representations work with implicit algebraic constraints (linear equations and inequalities on integer valued variables) to capture the feasible set of alternatives, and linear objective functions (to minimize or maximize over the feasible set) that specify the criterion for defining optimality. This algebraic approach permits certain natural extensions of the powerful methodologies of linear programming to be brought to bear on combinatorial optimization and on fundamental algorithmic questions in the geometry of numbers. 1 Introduction In 1957 the Higgins lecturer of mathematics at Princeton, Ralph Gomory, announced that he would lecture on solving linear programs in integers. The immediate reaction he received was: "But that's impossible!". This was his first indication that others had th...
Algorithmic Aspects of Using Small Instance Relaxations in Parallel BranchandCut
 IEEE Trans. El. Dev
, 1998
"... Essential for the success of branchandcut algorithms for solving combinatorial optimization problems are the availability of reasonable tight relaxations and effective routines for solving the associated separation problems. In this paper we introduce the concept of small instance relaxations whic ..."
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Cited by 3 (0 self)
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Essential for the success of branchandcut algorithms for solving combinatorial optimization problems are the availability of reasonable tight relaxations and effective routines for solving the associated separation problems. In this paper we introduce the concept of small instance relaxations which can be particularly useful for problems with symmetric structure. Small instance relaxations base on the facets of polytopes associated with small instances of the combinatorial optimization problem to be solved and can be generated automatically by facet enumeration. For a certain class of symmetric problems, we describe a general approach to the separation problem. Algorithmic aspects of using small instance relaxations effectively (parallel separation, facet selection, cutting plane selection) are discussed in detail. Extensive computational results are presented for the linear ordering problem and a certain betweenness problem. 1 Introduction During the last years, branchandcut algo...