scispace - formally typeset

Integer programming

About: Integer programming is a(n) research topic. Over the lifetime, 25381 publication(s) have been published within this topic receiving 618828 citation(s). more


Open accessBook
Alexander Schrijver1Institutions (1)
01 Dec 1986-
Abstract: Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear Diophantine Equations. Algorithms for Linear Diophantine Equations. Diophantine Approximation and Basis Reduction. POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming. The Structure of Polyhedra. Polarity, and Blocking and Anti--Blocking Polyhedra. Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming. The Simplex Method. Primal--Dual, Elimination, and Relaxation Methods. Khachiyana s Method for Linear Programming. The Ellipsoid Method for Polyhedra More Generally. Further Polynomiality Results in Linear Programming. INTEGER LINEAR PROGRAMMING. Introduction to Integer Linear Programming. Estimates in Integer Linear Programming. The Complexity of Integer Linear Programming. Totally Unimodular Matrices: Fundamental Properties and Examples. Recognizing Total Unimodularity. Further Theory Related to Total Unimodularity. Integral Polyhedra and Total Dual Integrality. Cutting Planes. Further Methods in Integer Linear Programming. References. Indexes. more

6,747 Citations

Open accessBook
01 Jan 1988-
Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes. more

Topics: Branch and price (68%), Integer points in convex polyhedra (66%), Branch and cut (65%) more

6,283 Citations

Open accessBook
01 Jan 1972-
Abstract: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected and much-cited text, a standard of graduate-level courses since 1972, presents a comprehensive treatment of the first two decades of research on integer programming. more

Topics: Branch and price (75%), Integer programming (70%), Inductive programming (69%) more

4,157 Citations

Open accessBook
01 Jan 1967-
Abstract: Overview of the operations research modelling approach introduction to linear programming solving linear programming problems - the Simplex Method the theory of the Simplex Method duality theory and sensitivity analysis other algorithms for linear programming the transportation and assignment problems network analysis, including Pert-CPM dynamic programming game theory integer programming non-linear programming Markov chains queueing theory the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation. more

Topics: Inductive programming (67%), Constraint programming (65%), Linear programming (64%) more

3,828 Citations

Open accessJournal ArticleDOI: 10.1016/0305-0548(86)90048-1
Fred Glover1Institutions (1)
Abstract: Integer programming has benefited from many innovations in models and methods. Some of the promising directions for elaborating these innovations in the future may be viewed from a framework that links the perspectives of artificial intelligence and operations research. To demonstrate this, four key areas are examined: 1. (1) controlled randomization, 2. (2) learning strategies, 3. (3) induced decomposition and 4. (4) tabu search. Each of these is shown to have characteristics that appear usefully relevant to developments on the horizon. more

Topics: Integer programming (56%), Tabu search (51%)

3,690 Citations

No. of papers in the topic in previous years

Top Attributes

Show by:

Topic's top 5 most impactful authors

Laurence A. Wolsey

73 papers, 15.3K citations

George L. Nemhauser

61 papers, 14.1K citations

Ignacio E. Grossmann

59 papers, 7.5K citations

Fred Glover

50 papers, 3.5K citations

Panos M. Pardalos

42 papers, 1.3K citations

Network Information
Related Topics (5)
Linear programming

32.1K papers, 920.3K citations

94% related
Scheduling (computing)

78.6K papers, 1.3M citations

94% related

23.1K papers, 565.2K citations

93% related
Job shop scheduling

35.2K papers, 658.3K citations

92% related
Stochastic programming

12.3K papers, 421K citations

92% related