Book ChapterDOI
Chapter VI Integer programming
George L. Nemhauser,Laurence A. Wolsey +1 more
- Vol. 1, pp 447-527
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TLDR
This chapter presents the mathematical foundations of integer optimization models and the algorithms that can be used to solve them, and discusses the formulations that are good with respect to the efficiency of solving them.Abstract:
Publisher Summary This chapter presents the mathematical foundations of integer optimization models and the algorithms that can be used to solve them. Integer programming deals with problems of maximizing or minimizing a function of many variables subject to inequality and equality constraints, and integrality restrictions on some or all of the variables. There are applications in mathematics to the subjects of combinatorics, graph theory, and logic. Statistical applications include problems of data analysis and reliability. Scientific applications involve problems in molecular biology, high energy physics, and X-ray crystallography. A political application concerns the division of a region into election districts. Some of these discrete optimization models are described in the chapter. The chapter focuses on problems using integer programming models, and discusses the formulations that are good with respect to the efficiency of solving them. Some important theoretical aspects of integer programming models, including fundamental relationships between integer and linear programs, and computational complexity are also discussed in this chapter.read more
Citations
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Improving Effectiveness of Intrusion Detection by Correlation Feature Selection
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Efficient reformulation for 0-1 programs: methods and computational results
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GLOPT { A Program for Constrained Global Optimization
TL;DR: GLOPT is a Fortran77 program for global minimization of a block-separable objective function subject to bound constraints and block- separable constraints that finds a nearly globally optimal point that is near a true local minimizer.
Parallel Branch and Bound on an MIMD System ; CU-CS-354-87
TL;DR: The notions of perfect parallel time and achieved efficiency are introduced to empirically measure the effects of parallelism, because the traditional notions of speedup and efficiency are not capable of fully characterizing the actual execution of an asyn-chronous parallel algorithm.
Journal ArticleDOI
Convex reformulations for solving a nonlinear network design problem
Jesco Humpola,Armin Fügenschuh +1 more
TL;DR: This work considers a nonlinear nonconvex network design problem that arises in natural gas or water transmission networks with active and passive components, that is, valves, compressors, control valves and pipelines, and a desired amount of flow at certain specified entry and exit nodes in the network.
References
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Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.