Results 1 
6 of
6
Decomposition and dynamic cut generation in integer linear programming
, 2004
"... ..."
(Show Context)
A Decade of Combinatorial Optimization
, 1997
"... This paper offers a brief overview of the developments in combinatorial optimization during the past decade. We discuss improvements in polynomialtime algorithms for problems on graphs and networks, and review the methodological and computational progress in linear and integer optimization. Some of ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
This paper offers a brief overview of the developments in combinatorial optimization during the past decade. We discuss improvements in polynomialtime algorithms for problems on graphs and networks, and review the methodological and computational progress in linear and integer optimization. Some of the more prominent software packages in these areas are mentioned. With respect to obtaining approximate solutions to NPhard problems, we survey recent positive and negative results on polynomialtime approximability and summarize the advances in local search.
Decomposition in Integer Linear Programming
, 2009
"... Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associ ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit representation, with an implicitly defined polyhedron having a description of exponential size. In this paper, we first review these classical procedures and then introduce a new class of bounding methods called integrated decomposition methods, in which the bound yielded by traditional approaches is potentially improved by introducing a second implicitly defined polyhedron. We also discuss the concept of structured separation, which is related to the wellknown template paradigm for dynamically generating valid inequalities and is central to our algorithmic framework. Finally, we briefly introduce a software framework for implementing the methods discussed in the paper and illustrate the concepts through the presentation of applications. 1
Periodic Polyhedra
 Compiler Construction, 13th International Conference CC 2004, Part of ETAPS 2004
, 2004
"... This paper presents a new method for computing the integer hull of a parameterized rational polyhedron by introducing the concept of periodic polyhedron. Besides concerning generally parametric combinatorial optimization, the method has many applications for the analysis, optimization and paralleliz ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
This paper presents a new method for computing the integer hull of a parameterized rational polyhedron by introducing the concept of periodic polyhedron. Besides concerning generally parametric combinatorial optimization, the method has many applications for the analysis, optimization and parallelization of loop nests, especially in compilers.
International Book Series "Information Science and Computing " 115 MULTICRITERION PROBLEMS ON THE COMBINATORIAL SET OF POLYARRANGEMENTS
"... Abstract: The multicriterion problem of discrete optimization on the feasible combinatorial set of polyarrangements is examined. Structural properties of feasible region and different types of efficient decisions are explored. On the basis of development of ideas of Euclidean combinatorial optimizat ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: The multicriterion problem of discrete optimization on the feasible combinatorial set of polyarrangements is examined. Structural properties of feasible region and different types of efficient decisions are explored. On the basis of development of ideas of Euclidean combinatorial optimization and method of general criterion possible approaches for the solution of multicriterion combinatorial problem on the set of polyrrangements is developed and substantiated.