Technical Note-An Improved Branch-and-Bound Method for Integer Programming
TLDR
Two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm are proposed, utilizing the integer requirements on nonbasic variables to calculate stronger "penalties" when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking.Abstract:
This note proposes two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm. The integer requirements on nonbasic variables are utilized to calculate stronger "penalties" when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking. This stronger criterion is obtained by making use of Gomory cutting-plane constraints. These modifications have produced considerable reductions of the searching effort required for pure integer and predominantly integer problems, and have the further advantage of being very easy to incorporate.read more
Citations
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Book ChapterDOI
Lagrangian Relaxation for Integer Programming
TL;DR: 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].
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Facility location models for distribution planning
TL;DR: This paper reviews some of the significant contributions which have been made to the relevant and current state of knowledge on where to best site warehouses in the warehouse industry.
Journal ArticleDOI
A Computational Study of Search Strategies for Mixed Integer Programming
TL;DR: The goal of this article is to survey many of the results regarding branch-and-bound search strategies and evaluate them again in light of the other advances that have taken place over the years.
Journal ArticleDOI
Integer Programming Algorithms: A Framework and State-of-the-Art Survey
TL;DR: A unifying framework is developed to facilitate the understanding of most known computational approaches to integer programming, and a number of currently operational algorithms are related to this framework.
Journal ArticleDOI
Lagrangean Relaxation Applied to Capacitated Facility Location Problems
Arthur M. Geoffrion,R. Me Bride +1 more
TL;DR: In this article, Lagrangean relaxation has been applied to capacitated facility location problems with arbitrary additional constraints, and a reasonably complete algebraic and geometric understanding of how and why it works has been obtained.
References
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Book ChapterDOI
An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
Book
An Algorithm for the Traveling Salesman Problem
TL;DR: A “branch and bound” algorithm is presented for solving the traveling salesman problem, where the set of all tours feasible solutions is broken up into increasingly small subsets by a procedure called branching.
Journal ArticleDOI
Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R&D Projects
TL;DR: Allocating funds to independent RD their effect on efficiency is shown through presentation of computational experience on problems with as many as 50 variables.