Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
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It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8].Abstract:
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed.read more
Citations
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Journal ArticleDOI
Decomposition Branching for Mixed Integer Programming
TL;DR: Decomposition branching as mentioned in this paper is a branch-and-bound-based approach for solving mixed integer programs (MIPs) that explores far fewer nodes and can be orders of magnitude faster than a commercial solver and an automatic Dantzig-Wolfe approach.
Journal ArticleDOI
A nonlinear Lagrangian dual for integer programming
TL;DR: A new nonlinear dual formulation of an exponential form is proposed for bounded integer programming that possesses an asymptotic strong duality property and guarantees a success in identifying a primal optimum solution.
Journal ArticleDOI
A New Decomposition-Based Pricing Technique For Solving Large-Scale Mixed IP with a Computer Technique
TL;DR: A new Decomposition-Based Pricing procedure to filter the unnecessary decision ingredients from large scale mixed integer programming (MIP) problem, where the variables are in huge number will be abated and the complicacy of restrictions will be straightforward.
Dissertation
New methods for the multi-skills project scheduling problem
TL;DR: This Phd Thesis introduces several procedures to solve the Multi-Skill Project Scheduling Problem (MSPSP), and developed and implemented a heuristic approach with the purpose of solving big sized instances.
Journal ArticleDOI
A reduction approach to the repeated assignment problem
TL;DR: This work derives upper and lower bounds respectively by a heuristic together with local search, and an efficient method solving the continuous relaxation, such that the related pegging test, to fix variables at zero or one, decomposes into K independent pegging tests to LAPs.
References
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Journal ArticleDOI
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
Journal ArticleDOI
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
TL;DR: The use of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions but can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set as mentioned in this paper.
Book ChapterDOI
Multicommodity Distribution System Design by Benders Decomposition
Arthur M. Geoffrion,G. W. Graves +1 more
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
Journal ArticleDOI
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.