Classical cuts for mixed-integer programming and branch-and-cut

DOI10.1007/s10479-005-3453-yzbMath1135.90369OpenAlexW1964024778MaRDI QIDQ5896802

Manfred W. Padberg

Publication date: 7 March 2006

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10479-005-3453-y

zbMATH Keywords

cutting planesbranch-and-cutmixed-integer programmingGomory cuts

Mathematics Subject Classification ID

Mixed integer programming (90C11) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08)

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Uses Software

• bc-opt

Cites Work

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• Cutting planes in integer and mixed integer programming
• Optimization of a 532-city symmetric traveling salesman problem by branch and cut
• Valid inequalities and separation for capacitated economic lot sizing
• Lot-size models with backlogging: Strong reformulations and cutting planes
• Strong formulations for mixed integer programming: A survey
• The Boolean quadratic polytope: Some characteristics, facets and relatives
• On the solution of traveling salesman problems
• Geometric algorithms and combinatorial optimization
• Valid inequalities and facets of the capacitated plant location problem
• Cutting planes for integer programs with general integer variables
• Linear optimization and extensions.
• Location, scheduling, design and integer programming
• A cutting plane algorithm for minimum perfect 2-matchings
• Facets and algorithms for capacitated lot sizing
• \(bc\)-\(opt\): A branch-and-cut code for mixed integer programs
• Gomory cuts revisited
• On the symmetric travelling salesman problem I: Inequalities
• A Cutting Plane Algorithm for the Linear Ordering Problem
• On the Solution of Discrete Programming Problems
• Outline of an algorithm for integer solutions to linear programs
• Integer Programming and Pricing
• Minimizing Drum Latency Time
• An Automatic Method of Solving Discrete Programming Problems
• On the Uncapacitated Plant Location Problem. I: Valid Inequalities and Facets
• On the Uncapacitated Plant Location Problem. II: Facets and Lifting Theorems
• A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems
• A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs
• Aggregation and Mixed Integer Rounding to Solve MIPs
• Trees and Cuts
• Solving Large-Scale Zero-One Linear Programming Problems
• Valid Linear Inequalities for Fixed Charge Problems
• Strong Formulations for Multi-Item Capacitated Lot Sizing
• Computer Codes for Problems of Integer Programming
• (1,k)-configurations and facets for packing problems
• Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality
• Odd Minimum Cut-Sets and b-Matchings
• Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut
• On the existence of optimal solutions to integer and mixed-integer programming problems
• Technical Note—A Note on Zero-One Programming
• Facets of the knapsack polytope
• Technical Note—Facets and Strong Valid Inequalities for Integer Programs
• Using cutting planes to solve the symmetric Travelling Salesman problem
• Covering, Packing and Knapsack Problems
• Enumerative Methods in Integer Programming
• An Introduction to the Theory of Cutting-Planes
• Solving Airline Crew Scheduling Problems by Branch-and-Cut
• Solving Mixed Integer Programming Problems Using Automatic Reformulation
• On the facial structure of set packing polyhedra
• Préfermeture sur un ensemble ordonné
• A Simplified Primal (All-Integer) Integer Programming Algorithm
• A New Foundation for a Simplified Primal Integer Programming Algorithm
• Integer Linear Programming: A Study in Computational Efficiency
• An Improved Implicit Enumeration Approach for Integer Programming
• Letter to the Editor—Computational Results of an Integer Programming Algorithm
• Intersection Cuts—A New Type of Cutting Planes for Integer Programming
• Hypercylindrically Deduced Cuts in Zero-One Integer Programs
• Integer Programming Algorithms: A Framework and State-of-the-Art Survey