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Generating general-purpose cutting planes for mixed-integer programs / Franz Wesselmann. 2010
Inhalt
Introduction
Foundations
Integer Programming Preliminaries
Mixed-Integer Programs
Linear Programming Relaxation
Disjunctive Relaxation
Algorithms
Cutting Planes
Branch-and-Bound
State-of-the-Art
Single-Row Cutting Planes
Introduction
Literature Review
Chvátal-Gomory Cuts
Cutting Planes for MIPs
Multi-Row Cutting Planes
Introduction
Literature Review
Group Relaxations
Valid Inequalities
Required Work
Implementation and Numerical Results
Framework
MOPS - An MIP Solver
Implementation
Single-Row Cutting Plane Separators
Gomory Mixed-Integer Cuts
K-Cuts
Combined Gomory Mixed-Integer Cuts
Reduce-and-Split Cuts
Lift-and-Project Cuts
A new Pivoting Procedure for Strengthening Gomory Mixed-Integer Cuts
Strong Chvátal-Gomory Cuts
{0,12}-Chvátal-Gomory Cuts
Computational Results
Multi-Row Cutting Plane Separators
Maximal Lattice-Free Convex Sets
Selecting a Multi-Row Relaxation
Generating Intersection Cuts
Computational Results
Cutting Plane Selection and Management
Introduction
Cut Selection
Cut Pool and Cut Selection Algorithm
Computational Results
Summary and Concluding Remarks
Benchmarking Environment
Hard- and Software
Test Set
Evaluation Methods
Tables
Notation
List of Abbreviations
List of Figures
List of Tables
List of Algorithms
Bibliography
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